MULTIPLE SINK LOCATION PROBLEM AND ENERGY EFFICIENCY IN LARGE SCALE WIRELESS SENSOR NETWORKS

Transcription

1 MULTIPLE SINK LOCATION PROBLEM AND ENERGY EFFICIENCY IN LARGE SCALE WIRELESS SENSOR NETWORKS by Eylem İlker Oyman B.S. in Computer Engineering, Boğaziçi Univerity, 1993 B.S. in Mathematic, Boğaziçi Univerity, 1993 M.S. in Computer Engineering, Boğaziçi Univerity, 1996 Submitted to the Intitute for Graduate Studie in Science and Engineering in partial fulfillment of the requirement for the degree of Doctor of Philoophy Graduate Program in Computer Engineering Boğaziçi Univerity 2004

2 ii MULTIPLE SINK LOCATION PROBLEM AND ENERGY EFFICIENCY IN LARGE SCALE WIRELESS SENSOR NETWORKS APPROVED BY: Prof. Cem Eroy... (Thei Supervior) Prof. M. Ufuk Çağlayan... Prof. Bülent Örencik... Aoc. Prof. Can Özturan... Ait. Prof. Murat Zeren... DATE OF APPROVAL...

3 iii ACKNOWLEDGEMENTS It ha been a long tory ince thi work had tarted and until it could receive an end. Many valuable people have contributed to thi thei, not only academically but alo emotionally. Firt of all, I would like to thank to the profeor in my thei ury, Prof. M. Ufuk Çağlayan, Prof. Bülent Örencik, Aoc. Prof. Can Özturan, and Ait. Prof. Murat Zeren for their valuable comment and direction. Prof. Cem Eroy, my thei advior, helped me to focu on the work and howed me the way of being academically productive. The long running PhD tudy had many bureaucratic obtacle. However, our dear ecretary Sevgi Dikmen wa alway able to find a clean olution. Without her help, I could not urvive in the ungle. Many pecial thank The people in the Netlab were alway cloe, friendly and helpful. Their innovative idea have raied the value of thi work. Epecially, Kaan Bür, my friend, roommate, neighbor, and travel-mate I will never forget the tate of thoe repetitive lunche. In addition, Dr. Roy Küçükateş, being my partner ince the tone-age, wa really patient in the buine and alo helpful, epecially in the early tage of my Opnet work. Finally, I want to thank to my family. I felt their bleing, upport, encouragement and love alway with me. And, my Era, my dear wife She i my light in the darkne, my oai in the deert, my recue iland in the ocean. Having found her, the life ha become a meaning.

4 iv ABSTRACT MULTIPLE SINK LOCATION PROBLEM AND ENERGY EFFICIENCY IN LARGE SCALE WIRELESS SENSOR NETWORKS Energy i the mot critical reource in the life of a wirele enor node. Therefore, it uage mut be optimized to maximize the network life. Beide uing power adutable tranmitter circuitry, uage of multi-hop communication link hould be conidered to ave energy. Moreover, in large-cale network with a large number of enor node, multiple ink node hould be deployed, not only to increae the manageability of the network, but alo to reduce the energy diipation at each node. In thi thei, we introduce problem that are related with locating multiple ink node in the enor network area. We give a framework coniting of new formulation and definition for the multiple ink enor network. Then, we invetigate the ue of multi-hop communication link and compare the amount of energy gain upon alternative route uing analytical technique. We how that employing multi-hop link doe not alway reult in energy gain, and try to quantify ituation when it i advantageou. We alo how that neglecting the overhead energy and overemphaizing the importance of power adutable tranmitter circuitry could reult in coniderable energy lo. The analytical reult are validated uing imulation on different cenario. Then, we focu on the multiple ink location problem in large-cale wirele enor network. We propoe a mathematical formulation for enor network to calculate the energy diipation throughout the network. Then we tate different problem depending on the deign criteria. Finally, we conider locating ink node to the enor environment, where we are given a time contraint that tate the minimum required operation time. We ue imulation technique to tet our olution.

5 v ÖZET TELSİZ DUYARGA AĞLARINDA BİRDEN FAZLA MERKEZ YERLEŞTİRME PROBLEMİ VE ENERJİ VERİMLİLİĞİ Kablouz algılayıcı aygıtlarının ömürleri açıından, eneri en önemli kaynaktır. Bu yüzden, ağın ömrünü en üt düzeye çıkarabilmek için, enerinin kullanımı en iyi şekilde yönetilmelidir. Eneri taarrufu için, çıkış gücünün ayarlanabildiği verici devrelerini kullanmanın yanı ıra, çok zıplamalı konuşma hatları kullanılmalıdır. Bununla birlikte, çok fazla ayıda algılayıcıdan oluşan büyük ölçekli algılayıcı ağlarında, veri toplamak için birden fazla merkez kurulmalıdır. Bu ayede, hem ağ daha kolay yönetilebilecek, hem de her bir algılayıcının eneri harcamaı azaltılmış olacaktır. Bu tezde, birden fazla merkez düğümün algılayıcı ağı alanına yerleştirilmei ile ilgili problemleri ortaya çıkardık. Birden fazla merkezli algılayıcı ağları için yeni ifadeler ve tanımlar içeren bir çerçeve oluşturduk. Daha onra, çok hoplamalı konuşma hatlarının kullanılmaının eneri harcamaındaki etkiini inceleyerek, alternatif rotalardaki kazançları analitik tekniklerle karşılaştırdık. Bu ırada, çok hoplamalı konuşma hatlarının kullanılmaının her zaman eneri kazancını ağlamadığını göterdik. Bunun yanı ıra, her hoplamada harcanan fazla enerinin göz ardı edilmei ve çıkış gücünün ayarlanabildiği verici devrelerinin öneminin gereğinden fazla önemenmei durumunda büyük eneri kayıplarının oluştuğunu göterdik. Analitik onuçları, değişik enaryolar üzerinde çalıştırdığımız benzetim yöntemleriyle karşılaştırdık. Daha onra, büyük ölçekli algılayıcı ağlarındaki birden fazla merkez yerleştirme orunlarını inceledik. Ağ üzerindeki eneri harcamalarını heaplayabilmek için matematikel bir formülayon önerdik. Daha onra, taarım kriterlerine göre değişebilecek farklı orunları liteledik. Son olarak, algılayıcı ağı için verilecek en az çalışma ürei kııtını ağlayacak en az ayıda merkezin ağa yerleştirilmei orunu incelendi. Çözüm önerii benzetim yöntemleriyle ınandı.

6 vi TABLE OF CONTENTS ACKNOWLEDGEMENTS... iii ABSTRACT...iv ÖZET...v LIST OF FIGURES...x LIST OF TABLES...xiv LIST OF SYMBOLS/ABBREVIATIONS...xv 1. INTRODUCTION Contribution of the Thei Structure of the Thei WIRELESS SENSOR NETWORKS Current Senor Mote Sample Scenario Location Awarene MAC Layer Interface Routing Technique Packet Structure Energy Model Tranmitter Power Model Energy Conumption MULTIPLE SINK SENSOR NETWORK DEFINITIONS AND FORMULATIONS Motivation Formulation of the Multiple Sink Network Deign Problem Preliminarie Routing Path Length Branch Node Energy Diipation Counting the Packet Node Lifetime Invetment Cot...38

7 vii 3.3. Summary QUANTIFYING SAVED ENERGY BY MULTI-HOPPING Network Model Aumption Multi-Hop Link Energy Saving D Communication Link Iocele Triangular Communication Link Arbitrary Triangular Communication Link Generalization Simulation on the Energy Saving by Multi-hopping Simulation Setup Reult Concluion on the Energy Saving by Multi-hopping THE EFFECT OF OVERHEAD ENERGY TO THE NETWORK LIFETIME Motivation for Overhead Energy Conideration Simulation on the Effect of Overhead Energy Simulation Setup Reult Concluion on the Effect of Overhead Energy MULTIPLE SINK SENSOR NETWORK DESIGN PROBLEM Deign Criteria Number of Sink Network Lifetime Routing Cluter Member Location of Sink Data Generation Rate Energy Model Routing Deciion Minimum Energy Tree Minimize the Maximum Energy Diipation at Senor Node Minimize the Maximum Energy Path...77

8 viii Maximum Reidual Energy Path Redeployment Scenario Random Redeployment Neighborhood Redeployment Replacement Redundant Deployment Sink Location Problem Find the Bet Sink Location (BSL) Minimize the Number of Sink for a Predefined Minimum Operation Period (MSPOP) Find the Minimum Number of Sink while Maximizing the Network Life (MSMNL) Difference with Concentrator Location Problem A Solution Technique for the MSPOP Problem Deployment of the Senor Node Finding Location Information Collecting the Location Information from the Field Finding the Bet Location for K Sink Node Etimating the Network Lifetime Computational Experiment on Multiple Sink Senor Network Problem Simulation Setup Demontrative Example for the BSL Problem Application of the Solution Technique to the MSPOP Problem Concluion for the Computational Experiment CONCLUSION AND FUTURE WORK Concluion Future Work APPENDIX A: OPNET IMPLEMENTATION DETAILS A.1. Wirele Senor Network A.2. Node Model A.3. Network Layer Proce Model A.4. Data Link Layer Proce Model A.5. Packet Structure...107

9 REFERENCES ix

10 x LIST OF FIGURES Figure 2.1. Berkeley/Crobow Mica mote compared with a US quarter (25 mm)...5 Figure 2.2. Smart Dut Mote (5 mm)...6 Figure 2.3. General architecture of a enor node...6 Figure 2.4. Data delivery from ource to the ink uing intermediate node...12 Figure 2.5. Baic link layer packet tructure...12 Figure 3.1. A large-cale enor network with three cluter...19 Figure 3.2. A path from the enor i to the ink through intermediate node and k...21 Figure 3.3. (a) A enor network graph, (b) Correponding minimum energy tree...22 Figure 3.4. The et of relay node of the path Pi...26 Figure 3.5. The et of branch node of the relay node...29 Figure 3.6. The packet generation interarrival time ( n) Z for the initiator node i...35 i Figure 4.1. Radio tranmiion with different power level reult in different tranmiion range...43 Figure 4.2. Uing multi-hop link in routing deciion...44 Figure 4.3. Routing deciion alternative, (a) direct communication, (b) and (c) uing an intermediate node...45

11 xi Figure 4.4. Energy aving in 1-D communication cenario...46 Figure 4.5. Effect of α on energy aving in 1-D communication cenario...47 Figure 4.6. Energy aving in iocele triangular communication cenario...49 Figure 4.7. Effect of α on energy aving in iocele triangular communication cenario...50 Figure 4.8. Arbitrary triangular communication cenario...50 Figure 4.9. Energy aving in arbitrary triangular communication cenario...51 Figure Generalization into a multi-hop path...52 Figure Average hop count veru overhead energy τ (A = 200 m x 200 m, α = 3).54 Figure Average node energy veru overhead energy τ (A = 200 m x 200 m, α = 3)...55 Figure Average node energy veru average hop count (A = 200 m x 200 m, α = 3, only P cont node are ued)...56 Figure Average node energy veru overhead energy τ (A = 400 m x 400 m, α = 3)...56 Figure Average hop count veru overhead energy τ (A = 200 m x 200 m, only P cont node are ued)...57 Figure Average node energy veru overhead energy τ (A = 200 m x 200 m, only P cont node are ued)...58

12 xii Figure Average hop count veru path lo exponent α (A = 200 m x 200 m, τ = 20 mj, only P cont node are ued)...59 Figure 5.1. A ample network repreenting different topology alternative for different path lo exponent α and overhead energy τ value...62 Figure 5.2. Average packet delivery energy veru overhead energy...66 Figure 5.3. Average node energy veru overhead energy...67 Figure 5.4. Average hop count veru overhead energy...67 Figure 5.5. Network lifetime veru overhead energy...68 Figure 6.1. Sytem deign algorithm...83 Figure 6.2. Sample enor network with 200 enor and three ink...88 Figure 6.3. Energy and diconnected region map, until the 60 th day...90 Figure 6.4. Exhauted node veru time...91 Figure 6.5. Unreachable node veru time...91 Figure 6.6. Unreachable node veru time uing rerouting...92 Figure 6.7. Exhauted node veru time uing rerouting...92 Figure 6.8. Percentage of exhauted node veru time, with different number of ink.94 Figure 6.9. Percentage of unreachable node veru time, with different number of ink...94

13 xiii Figure Comparion of random placement with k-mean algorithm, with three ink...95 Figure Change in the number of ink for different network lifetime requirement.96 Figure A.1. Sample wirele enor network cenario Figure A.2. Senor node model Figure A.3. Proce diagram for the network layer Figure A.4. Proce diagram for the data link layer...106

14 xiv LIST OF TABLES Table 2.1. Optimal packet ize in link layer...13 Table 2.2. Length of binary BCH code with different t...14 Table 2.3. Path lo exponent for different environment...16 Table 4.1. Simulation parameter...53 Table 5.1. Average energy diipation at enor node...63 Table 6.1. Simulation parameter...86 Table 6.2. Expected network lifetime, with ρ =

15 xv LIST OF SYMBOLS/ABBREVIATIONS a k Adacency matrix of the minimum energy tree T min A b B B c D c r Set of arc in the enor network Branch ize of the relay node Set of branch node of the ink node Set of branch node of the relay node Speed of light Cot of deployment action of the r th redeployment N c Cot of a enor node at the r th redeployment r P c S c C D C N C N C r P C S C d d i D S Cot of placement of the ink node Cot of the ink node Total invetment cot Total cot of deployment action Total cot of enor node Total cot of enor node at the r th redeployment Total cot of ink node placement Total cot of ink node Euclidean ditance Euclidean ditance between two node having indexe i and Budget dedicated for the total ink invetment e i Energy cot of the arc ( i, ) ei Total energy diipation for a data packet on the path Pi e Relay energy load of the node e () t Total energy diipation of the node during the time interval (0,t]. e x Energy required for tak x E () t Reidual energy of the node at a given time t f G G x K Frequency Directed graph repreenting the enor network Antenna gain Service capacity of the ink

16 xvi l l x Length of a packet in bit Length of field x of a packet in bit l Path length of the path Pi i n G i () t Number of packet generated by the initiator node i n R () t Number of packet going through the relay node n r N N r p Number of enor node in the r th redeployment Set of enor node Set of enor node in the r th redeployment Bit error rate of the radio channel i p k Path matrix of the tree T min P Path from a enor node i to a ink node i P Minimum energy path from the enor node i to the ink node P x r min i i r Power required for tak x Number of redeployment in a enor network Relay matrix of the tree T min Ri Set of relay node of the path Pi S t t T min V Set of ink node Error correcting capabilitie in binary BCH code Time Minimum energy tree All poible node in the network Vi Vertex et of the path Pi min min Vi Vertex et of the minimum energy path Pi X i () t Number of packet generated during the time interval (0,t] ( ) Z n th interarrival time of packet i α δ E η λ Path lo exponent Energy aving Energy efficiency Wavelength of the ignal µ i Expected value of the interarrival time of packet ρ () t Senor meaurement reliability function

17 xvii ρ Predefined threhold for enor meaurement reliability Threhold τ Overhead energy ADC BCH BSL CA CLP EAR FDMA FEC FSM GPS IA IEEE ISM ISO MAC MEMS MSMNL MSPOP OSI SMACS TDMA Analog to Digital Converter Boe-Chaudhuri-Hocquenghem code Bet Sink Location Conider Algorithm Concentrator Location Problem Eavedrop-And-Regiter Frequency Diviion Multiple Acce Forward Error Correction Finite State Machine Global Poitioning Sytem Ignore Algorithm Intitute of Electrical and Electronic Engineer Indutrial, Scientific and Medical International Standard Organization Medium Acce Control ublayer Micro Electrical Mechanical Sytem Minimization of the number of Sink node while Maximizing the Network Lifetime Minimization of the number of Sink node for a Predefined minimum Operation Period Open Sytem Interconnection Self-organizing Medium Acce Control for Senor network Time Diviion Multiple Acce

18 1 1. INTRODUCTION Wirele enor node are combining the wirele communication infratructure with the ening technology. Intead of tranmitting the perceived data to the control center through wired link, ad hoc communication method are utilized, and the data packet are tranmitted uing multi-hop connection [1, 2]. Through advance in Micro Electrical Mechanical Sytem (MEMS) technology mall, low-cot, low-power electronic device coupled with ening and wirele communication capabilitie are contructed. Thee device form a elf-organizing ad hoc network to forward data packet toward ink node. There are everal urvey paper providing with in-depth background reearch on enor network [3-6]. The elf-organization feature of enor make it feaible to deploy them randomly over the region being oberved. Without needing a previou exploration, enor might be intalled to the environment in a random way, like dropping them from an aircraft. In thi manner, a large number of enor node are pread over the environment without having a prior knowledge of where each enor i being placed individually. The mot critical reource in the enor network i the available energy of the enor node. Whenever the enor node are not coupled with ome energy-cavenging tool, the only energy reource of them will be their intalled battery, and the enor with exhauted batterie cannot operate anymore. Moreover, ince enor node behave a relay node for data propagation of other enor to ink node, network connectivity decreae gradually [7]. Thi may reult in diconnected ubnetwork of enor, i.e., ome portion of the network cannot be reachable at all. Therefore, the level of power conumption mut be conidered at each tage in wirele enor network deign. Senor node have a hort tranmiion range due to their limited radio capabilitie. Therefore, the data mut be relayed uing intermediate node toward the ink. In addition, it may be more advantageou to ue a multi-hop path to the ink node coniting of horter link rather than uing a ingle long connection.

19 2 _In ome application, everal thouand of enor node might be deployed over the _monitored region. For example, in agricultural cenario, in environmental monitoring _application, uch large-cale enor network would be neceary. Moreover, the _diameter of the region might eaily be everal kilometer. In thi cae, calability of the _network become a very important deign iue. In order to obtain a calable network, the _enor node hould be divided into cluter. The node within a cluter will then be _connected to the ink node dedicated for that cluter. Beide finding the bet number of _ink node, their optimum placement within the field i alo an important point Contribution of the Thei In thi thei, we have introduced the multiple ink enor network deign problem. We have given a framework coniting of new formulation for the multiple ink enor network. Starting with the definition of the enor network, we have provided an infratructure that i independent from the routing algorithm, which ha been ued within the derivation of the problem. Then, we have invetigated the uage of an intermediate node forming multi-hop link, and it effect on energy gain. We have focued on uniformly deployed enor node, each having identical communication capabilitie. The enor node are aumed to be able to adut their tranmiion power. Therefore, each enor conume only the amount of energy that will uffice to reach for the tranmitted radio wave to the detined receiver antenna. We have tudied different multi-hop communication cenario and calculated the energy aving in each cenario. We have alo expanded thee cenario to general cae. The generalization can be applied into any arbitrary triangle and can be ued in energy optimized route calculation. We alo tried to quantify the effect of path lo exponent α, and overhead energy τ on energy aving. It i hown that the enor lifetime can eaily be doubled uing power adutable tranmitter circuitry. Thereafter, we have hown that neglecting the overhead energy during routing deciion could reult in uboptimal energy uage. The effect of overhead energy i uually ignored in traditional ad hoc network, where the tranmiion energy i much higher than the overhead energy. However, in enor network, due to hort communication range, we

20 3 have to include the overhead energy to the overall energy cot in the routing calculation. We have invetigated the ue of multi-hop communication link in routing and compared the amount of energy gain acquired by correct energy calculation. We how that neglecting the overhead energy and overemphaizing the importance of power adutable tranmitter circuitry could reult in coniderable energy lo. Finally, we have tated characteritic feature of the multiple ink location problem in large-cale wirele enor network. Several deign iue including different deign criteria, routing alternative and redeployment cenario are preented. The effect of locating ink node on the enor environment regarding the total network lifetime i analyzed. The predefined contraint tating the minimum required operational time for the enor network i incorporated with the deign problem. Solution technique that are finding the bet ink location and the quantity of the ink node are preented. Uing demontrative example and imulation, thee olution technique are evaluated Structure of the Thei In the next chapter, we give a brief introduction on wirele enor network. We introduce firt the enor device, how they phyically contructed. After that, we preent the underlying network architecture, and the energy model. In Chapter 3, multiple ink enor network framework i introduced. A mathematical formulation of the enor network are given, which i later ued to repreent the routing tree, to define the communication path and relay et, moreover, to calculate the overall energy diipation in the network. In Chapter 4, we provide a formulation to quantify energy aving uing multi-hop communication link. The reult are compared with imulation. We how that multi-hopping i not alway advantageou, and formulate whenever to ue multi-hopping. In Chapter 5, we analyze the effect of overhead energy to the network lifetime. We how that neglecting the overhead energy during routing calculation could reult in uboptimal routing tree, which caue higher energy diipation at enor node.

21 4 In Chapter 6, we introduce the multiple ink enor network deign problem. Several deign criteria and obective are preented. The effect of routing deciion and redeployment cenario of enor node are tated. Together with the definition of ink location problem, a olution technique i alo given. After that, computational experiment are preented. The energy map of the network and the map of unreachable region through it lifetime are preented within the imulation reult. Finally, we conclude the thei, and provide ome future reearch direction.

22 5 2. WIRELESS SENSOR NETWORKS Indutrial enor are reponible to perceive a phyical phenomenon in the environment. Thereafter, the data gathered through the enor ha to be forwarded to a control center for further proceing. Intead of tranmitting thi data through wired link, wirele enor node employ wirele communication technologie for data propagation. Advance in technology enabled contruction of mall, low-cot, low-power electronic device coupled with ening and wirele communication capabilitie. Thee enor element can eaily build a elf-organizing network for information propagation [1, 2]. There are everal urvey paper providing with in-depth background reearch on enor network [3-6]. In thi chapter, application pecific deign iue are dicued. Beide the ample cenario that thi work could be applied, network pecific technical detail are alo mentioned Current Senor Mote Recent advance in MEMS technology enabled mall ized electronic device coupled with enor and communication equipment. The main focu on thi production cycle i to achieve very low-cot device. Figure 2.1. Berkeley/Crobow Mica mote compared with a US quarter (25 mm) [8]

23 6 The Berkeley/Crobow Mica Mote (ee Figure 2.1) ha a ize of a US quarter (25 mm) coupled with a multi-channel tranceiver, on-board temperature enor, and a proceing unit [8]. The tranceiver i capable to work on 898/916 MHz or 433 MHz Indutrial, Scientific and Medical (ISM) band where the radio power i programmable. Figure 2.2. Smart Dut Mote (5 mm) [9] Another ucceful implementation i the Smart Dut Mote (ee Figure 2.2). Thee device are communicating uing laer beam, and are imagined to become one cubic millimeter of ize [9]. Location Finding Sytem Mobilizer Sening Unit Senor ADC Proceing Unit Proceor Storage Tranceiver Power Unit Power Generator Figure 2.3. General architecture of a enor node, redrawn from [6] The general architecture of a enor node i hown in Figure 2.3 (redrawn from [6]). The maor component are ening unit, proceing unit, tranceiver, and power unit. The environmental information i retrieved uing the enor and converted with an analog to digital converter (ADC) to digital data. Thi data i forwarded to the proceing unit to

24 7 become a data packet that i to be ent to the ink node for further examination. The communication between the enor node are carried out with the tranceiver. The power unit feed all thee component with the neceary operational power. The optional unit, uch a the location finding ytem, mobilizer and power generator may be embedded to the node depending on the application. Mot of the application require ome location information for the ened data when they reach the ink node. Mobility might alo be an application-pecific requirement. Although mot monitoring application utilize only tatic enor node, for ome tracking cenario mobility might be a maor deign criterion. Finally, in order to prolong the lifetime of a enor node, a power cavenging tool uch a olar cell can be attached to the node Sample Scenario Wirele enor network have many application area mentioned in the literature. A detailed lit can be found in [6]. Moreover, ome application require a more detailed analyi, ince there might be ome application pecific contraint to be conidered. The elf-organization feature of enor make it feaible to deploy them randomly over the region being oberved. Without needing a previou exploration, enor might be intalled to the environment in a random way, like dropping them from an aircraft. In thi manner, a large number of enor node are pread over the environment without having a prior knowledge of where each enor i being placed individually. Thee enor are aumed to be ditributed uniformly in the environment. Two other deployment trategie are mentioned in [10]. The enor may be regularly placed with ome geometric topology depending on the application, e.g., a grid. They can alo be placed with a prior knowledge of the phenomenon to be oberved, reulting in a biaed intallation. In place where the phenomenon i more likely to occur or appear more denely, a higher amount of enor might be neceary for an invetigation that i more precie. In order to reduce the cot of deployment, a path expoure method i propoed in [11]. Having deployed the enor in the environment, they tart to oberve the phenomenon. Data from the enor might be gathered in different way. Firt, the enor

25 8 might continuouly end report to the ink with an application-dependent predefined interval. Second, they might be polled by the control unit. In thi cae, all the enor might be under conideration or only a mall portion lying on the upected region might be queried a well. In the firt cae, the query i pread uing broadcat method to the network, wherea in the latter cae multicat communication technique mut be employed to ave reource. Third, enor can decide to end data when they oberve a pecific event [12, 13]. In many environmental application like foret fire detection, oil eroion monitoring, air pollution meaurement, or monitoring the altine level of the field, enor are ditributed randomly in the conidered environment. Due to the extreme ize of the area and application complete coverage need, a very large amount of enor mut be deployed. In thi cae, calability become a crucial iue. Therefore, the complete enor network hould be divided into cluter to achieve a more table ytem [14, 15], [16]. In thi manner, not only the ytem will be eaier to manage, but alo the total network lifetime will increae reulting in a more economical invetment. Several biomedical application can alo make ue of wirele enor node through incorporation of ening material with wirele communication circuitry, uch a a glucoe level monitor or retina prothei [17]. When we conider wirele networking of human-embedded mart enor array, the deign contraint are very different. The olution hould be ultra-afe and reliable, work trouble-free in different geographical location, and require minimal maintenance. Another intereting application i habitat monitoring. In [ 18 ], eabird neting environment i monitored. Thi experiment i accomplihed uing 32 enor node on a mall iland treaming live data onto the web. In [19], the concept of mart kindergarten i introduced where developmental problemolving environment for early childhood education are incorporated with wirele enor network. Here, enor-enhanced toy and claroom obect are connected with back-end middleware ervice and databae technique.

26 Location Awarene Since enor node are pread randomly over the field, they initially do not know their exact location. Many application, however, require location information to achieve the deired functionality. Extracting location information from a Global Poitioning Sytem (GPS) module attached to the enor i not a feaible olution [20, 21]. Firt, thee device are phyically large and energy enitive. Second, in many application, enor antennae cannot be in line-of-ight of the atellite. In addition, they are till very expenive device, producing a cotly olution for location etimation. Although GPS cannot be a olution for location etimation problem, current reearch on thi topic provided good alternative. In [22], a centralized method i propoed. Uing convex poition contraint, which have been derived from the connectivity information, the poition etimation i performed relative to node, whoe location information are known a priori. In [21], a radio frequency technique i ued to etimate location. Each beacon periodically ignal overlapping location information to the network. Depending on the connectivity metric, node localize themelve to the centroid of their nearby beacon. A imilar technique i given in [23], where a collaborative multi-lateration technique i preented. Uing thi method, ad-hoc deployed enor node can etimate their location by uing beacon location that are everal hop away and ditance meaurement to neighboring node. A different approach in [24] i baed on an angle of arrival etimation technique. In thi work, beacon node are equipped with a directional antenna, uing which they can end directional beacon ignal that are powerful enough to be heard by all enor node MAC Layer Interface For a careful deign of wirele enor network, one hould conider an appropriate MAC layer optimized for enor communication. One hould alway conider that enor

27 10 node are low-power device, and they do not contain a trong computational unit. Therefore, MAC layer deigned for traditional ad hoc network cannot be applied to wirele enor network. Several MAC layer alternative are propoed in the literature. For a detailed lit, the reader could refer to [6]. Self-organizing Medium Acce Control for Senor network (SMACS) i an infratructure building protocol that form a flat topology for enor network [25]. Thi i a ditributed protocol that enable a collection of node to dicover their neighbor and etablih tranmiion/reception chedule for communicating with them without the need for any local or global mater node. To reduce the likelihood of colliion, it require each link to operate on a different frequency. Thi frequency band i choen at random from a large pool of poible choice when the link are formed. In order to provide continuou ervice to mobile enor node, Eavedrop-And- Regiter (EAR) algorithm i propoed [25]. Thi algorithm enable eamle interconnection of mobile node in the field of tationary wirele node, and repreent the mobility management apect of the SMACS protocol. In [26], time diviion multiple acce (TDMA) and frequency diviion multiple acce (FDMA) cheme are dicued. In TDMA, the tranmiion time i minimized, a the full bandwidth of the channel i allocated for a ingle enor node. However, in thi cae, only one enor can be actively tranmitting. In order to enable imultaneou tranmiion, FDMA cheme can be ued where the bandwidth i divided into frequencie, which are aigned to different enor. In thi cae, the tranmiion time i maximized. A hybrid cheme involving both TDMA and FDMA i alo introduced. Thi thei i independent of the MAC layer. The ink location and related clutering mechanim can be applied into any MAC layer that the enor hardware i employing. Therefore, MAC layer i not conidered a a fundamental part of the olution. On the contrary, the olution can be ued with any MAC layer that will be found on the market.

28 Routing Technique In order to utilize the enor energy in the mot beneficial manner, power-aware routing method mut be ued. Since thee equipment are limited on battery reource, the underlying routing protocol hould pay attention to the power level of each enor in the network. Data that i extracted from the environment hould be forwarded to the ink node for further proceing. During thi phae, enor contitute an ad hoc network infratructure and data packet are routed to the ink node through intermediate node. Each node generate a mall data packet containing the knowledge gathered from the environment. Thi data packet i ent to the detination uing the underlying routing method with the help of intermediate enor node. Intermediate node have everal alternative. Thee alternative are application dependent and may be choen according to uer need. (i) They can directly forward the packet to the next relay node or to the detination, if it wa the lat hop on the way to the detination. (ii) They can delay the forwarding for a moment waiting for other enor, which might a well be generating a packet ent to the ame detination, o that all thee packet can be merged into one larger packet. (iii) Similar to (ii), but thi time the data in each packet might be extracted and aggregated into a new reult, and thi reult i forwarded to the detination. (iv) An intermediate node can alo add it own meaurement to the packet, uing method decribed in either (ii) or (iii). In Figure 2.4, enor node i 1 and i 2 tranmit data packet imultaneouly. Their packet are routed to the ink node through intermediate node. The underlying routing method may chooe to merge the data packet into one packet on the way to the detination at the intermediate node. All the other node in the environment may tay idle during thi communication.

29 12 i 1 i 2 idle node intermediate node initiator node ink Figure 2.4. Data delivery from ource to the ink uing intermediate node In thi routing mechanim, intermediate node that have enough reidual power hould be ued a relay. The choice of intermediate node can be performed in a ditributed manner at the node level, or centrally at the detination. In the latter cae, a global knowledge of node tatu information i aumed. Thi data i not unrealitic to be captured. Senor node are ending their meaurement to the detination. Supplementary information like their geographic location and battery level may be piggybacked to their data packet. A a reult, the detination node may retrieve all the neceary information about the current network infratructure and remaining reource from the field. Furthermore, ince thee node are more powerful in the ene computational power and battery reource, they can perform extenive computation like centralized routing deciion eaily Packet Structure Data packet need to be carefully deigned to carry the information gathered from the environment. Packet are originated from ource enor and are ent to intermediate node in order to be forwarded to the detination. In the previou ection, alternative routing, merging and aggregating mechanim are tated. Beide their effect on routing, thee requirement alo affect the underlying packet tructure. Header Payload Trailer l h l p l t Figure 2.5. Baic link layer packet tructure, redrawn from [27]

30 13 The baic link layer packet tructure i given in Figure 2.5, which i preented in [27]. Here, the packet i compoed of header, payload and trailer part, which are aumed to be of l h, l p and l t bit long repectively. The header field contain egment information correponding to higher layer packet and ource and detination identifier. Whenever the application doe not require the exact node identifier, a collection of event, location, and attribute identifier could alo eaily replace the header information, reulting with a much horter field of a few byte. The payload contain information bit and the trailer part contain error control bit. The ize of the payload depend on the information that the packet contain. The data gathered from the phenomenon hould be ent to the detination. For temperature, humidity or attribute enor, only one or two byte will be ufficient to code the information. Depending on the alternative routing and aggregating mechanim, thi data will be replicated for each intermediate enor in the routing tree. For centralized power-aware routing method, current battery level of the enor hould be ent to the detination node. Furthermore, again depending on the alternative routing and aggregating mechanim, thi battery information contain data for each enor in the routing tree. Thi information i extracted at the detination and ued in route calculation. Table 2.1. Optimal packet ize in link layer [27] FEC Method η Min max Without FEC BCH, t = BCH, t = BCH, t = In [27], a detailed analyi i preented to etimate the optimum payload ize conidering energy efficiency (η). The payload ize i found to lie between 50 and 500

31 14 byte depending on the bit error rate of the channel when no error control mechanim i ued. Thi ize increae up to a minimum of 500 and maximum of 3000 byte according to the error correcting capability that i employed. Here, binary BCH code are ued with different error correcting capabilitie (t), i.e., the maximum number of bit error that can be corrected eamlely. Approximate reult for raw bit error rate p = 10-3 are ummarized in Table 2.1. Table 2.2. Length of binary BCH code with different t [28] t Total packet ize BCH code length Data ize Uing BCH code, however, add extra error correcting bit to the data packet. A deigner hould conider thi overhead during etimating the neceary packet ize. Example for thee overhead-bit are given in Table 2.2. For a detailed decription of binary BCH code, the reader may refer to [28] Energy Model Efficient energy conumption i one of the mot important deign contraint in wirele enor network architecture [29]. The life of each enor node depend on it

32 15 power diipation. In application where the enor are not equipped with energy cavenging tool like olar cell, enor with exhauted batterie cannot operate anymore. Moreover, ince enor node behave a relay node for data propagation of other enor to ink node, network connectivity decreae gradually [7]. Thi may reult in diconnected ubnetwork of enor, i.e., ome portion of the network cannot be reachable at all. Therefore, the level of power conumption mut be conidered at each tage in wirele enor network deign Tranmitter Power Model A mentioned before, the main concern in wirele enor network deign i power. The underlying architecture mut conider power efficiency a a maor contraint. A good evaluation of the available technique can be found in [30]. To tart, conider the radio propagation model in a ingle-path free-pace channel. The relationhip between tranmitted power P t and received power P r i given by Pr P t 2 λ = GtGr 4πd (2.1) where G t and G r are the tranmitter and receiver antenna gain repectively, d i the ditance between the tranmitter and receiver, λ = c f i the wavelength of the tranmitted ignal, wherea f i it frequency, and c i the velocity of radio wave propagation in free pace, which i equal to the peed of light. Uing Equation 2.1, we derive 2 P t = ωd (2.2) where ω = ( P G G )( 4π λ) 2. Equation 2.2 can be further generalized a r t r α P t = ωd (2.3)

33 16 where α > 1 i known a path lo exponent. For free-pace channel, we have een in Equation 2.2 that α = 2. Table 2.3 give a lit of typical path lo exponent value obtained in variou radio environment [31]. In many enor application, it i aumed that α range between 2 and 4, ince the enor have hort antennae, which are very cloe to the ground. Table 2.3. Path lo exponent for different environment [31] Environment α Free pace 2 Urban area cellular radio 2.7 to 3.5 Shadowed urban cellular radio 3 to 5 In building line-of-ight 1.6 to 1.8 Obtructed in building 4 to 6 Obtructed in factorie 2 to 3 Power i defined by the rate of change in the energy with time [32]. Therefore, the amount of energy that i neceary to operate for time t conuming power P can be found a follow. E = P t (2.4) Energy Conumption Energy conumption in an arbitrary enor node ha in general the following component depending on the operation performed within the node: (i) Sening Energy: In order to activate ening circuitry within the node, and gathering data from the environment, an amount of energy mut be diipated, which i called ening energy, e S. The magnitude of thi energy depend on the tak that i aigned to the enor. Different enor require different level of energy during operation.

34 17 (ii) Tranmitter Energy: Afterward, thi data mut be tranmitted toward the detination. Therefore, the tranmitter circuitry mut be operated. For thi operation, the tranmitter energy, e T mut be conumed which depend on the tranmitter power, P t, ize of the data packet, and the data tranfer rate. (iii) Receiver Energy: A a relay node, a enor node i alo in charge of forwarding data packet of other enor node. For thi operation, enor mut be able to receive thoe data packet. The receiver energy, e R, will be conumed during thi operation, which i irrelevant of the ditance between node. During reception, receiver power, P r, will be pent during the reception of the data packet with the given data tranfer rate. (iv) Computation Energy: To operate thee circuitrie, enor proceing unit mut be activated. Moreover, whenever data aggregation i performed additional computation mut be realized. Compared to the previou item, computation energy, e C, i relatively low [33]. During the life cycle of a typical enor node, each event or query will be followed by a ening operation, performing neceary calculation to derive a data packet and tranmitting thi packet to the detination. In addition, enor node often relay data packet received from other enor. Thu, the total energy, e Total, in an arbitrary active time frame can be preented a the um of above energy requirement. e = e + e + e + e (2.5) Total T R S C Efficient ening circuitrie and computation algorithm help to reduce e S, and e C. The other two component e T, and e R are dependent on the communication architecture and underlying technique. Therefore, power aware method mut be employed in order to reduce the energy conumption during communication [33]. Only the tranmitter energy, e T, i related with the ditance between the communicating enor node. The other component of total energy remain contant with varying ditance between communicating pair. Therefore, we can rewrite Equation 2.5 a a function of d uing Equation 2.3 and Equation 2.4 a follow.

35 18 ( d ) = κd α + τ e Total (2.6) where τ = R κ = ω t e + e + e S C, with t being the duration of packet tranmiion proce, and, the overhead energy, which i a contant value with varying d. Any other energy conuming activity in the enor node can be added to the overhead energy component that do not depend on the tranmiion ditance [34]. A imilar energy model i propoed in [35] where the energy conumption for a meage i meaured a factor κ wa miing. d α + τ, with a comparable argumentation. However, the important

36 19 3. MULTIPLE SINK SENSOR NETWORK DEFINITIONS AND FORMULATIONS 3.1. Motivation The efficiency of the enor network invetment i directly related with the length of the reliable monitoring duration of the field. The better energy control mechanim are ued in the enor node firmware and in the network management technique, the longer the network will be erving their invetor. Therefore, the limited battery reource of the enor hould be handled efficiently. In ome application, everal thouand of enor node might be deployed over the monitored region. For example, in agricultural cenario, in environmental monitoring application, uch large-cale enor network would be neceary. The diameter of the region might eaily be a large a everal kilometer. In thi cae, calability of the network i a very important deign iue. In order to obtain a calable network, the enor node hould be divided into cluter. The node within a cluter will then be connected to the ink node dedicated for that cluter. Figure 3.1 how uch a enor network with everal node and three cluter with three ink node. Figure 3.1. A large-cale enor network with three cluter

37 20 During the deign phae of a large-cale enor network, the deigner hould decide on the number of cluter, and more important than that, the optimum location of the ink node. We call thi problem a the multiple ink enor network deign problem and try to provide ome olution. In the following ection, we give a new formulation for the multiple ink enor network. Starting with the definition of the enor network, we will provide an infratructure that i independent from the routing algorithm, which i going to be ued within the derivation of the problem. Thereafter, energy diipation formulation are derived, in order to calculate the node lifetime. Finally, the invetment cot formulation are preented Formulation of the Multiple Sink Network Deign Problem The wirele enor network conit of everal enor node and one or more ink node, each of which i connected through wirele link to other node. In thi ection, we try to derive formulation to quantify the lifetime of the enor network, which will later be ued a deign obective. In the following paragraph, we formalize the enor network uing graph theoretical viewpoint where the baic definition can be found in [36, 37] Preliminarie Definition 3.1: Let N = { enor node }, the et of enor node in the wirele enor network, and S = { ink node }, the et of ink node. Then let V = N S denote all poible node in the network. Let G = (V, A) be a directed graph repreenting the enor network. In thi graph, the vertex et V tand for the node, and the arc et A tand for valid communication link. Let ( i, ) A denote arc, where i, V. Let d i denote the Euclidean ditance between node i, V. If we aume that the radio tranmitter of the node have enough tranmiion power, where P t, then the radio ignal of each node can reach to every other node in the network, reulting in a fully connected graph. In the real world, however, there i a

38 21 phyical limit for the maximum tranmiion power, with P t Pmax. Therefore, we cannot expect G being fully connected. On the contrary, there might be ome diconnected node, whoe radio ignal cannot reach to any other node in the network. If we exclude thee diconnected node from the vertex et, we obtain a new vertex et V V, where G' = (V', A) form a connected graph. Since our aim i uccefully managing the connected node in the network, without lo of generality, we can aume that the graph G i connected. Definition 3.2: A path from a enor node ubgraph Pi 0 of G, where P = i ( Vi Ai ) 0 0 {( i i ), ( i, i ),...,( i, i ), ( i ) } A i 0 N to a ink node S i a non-empty, i, i 1,..., i N,, V { i i i } 0 i = 0, 1,..., n, 0 0 n, Ai = 0, n 1 n n,. The node i N 0 0 i called a the initiator node, and the node i 1, i 2,..., i N are called a intermediate node or relay node. n After the deployment phae, the ink node tart to collect information from the enor node. Thi data flow i performed through communication path from enor node toward the ink node. Pi 3.2 how uch a path where V = { i,...,, k } repreent thee data flow path in the network. Figure i,...,. i k Figure 3.2. A path from the enor i to the ink through intermediate node and k Definition 3.3: The energy cot of an arc ( i, ) A, e i i defined to be a real-valued function node e : A R. The energy cot of a path Pi from a enor node i N to a ink S i given by ( ) = e P i e (, k ) k A i.

39 22 Uing the energy cot function a the metric, energy aware routing algorithm might calculate the minimum energy path in the network, in order to achieve the maximum energy aving. In other word, each enor node i going to deliver it data packet through a minimum energy path to a ink node. In our energy model, we ue the energy cot function (ee Section 2.7.2) e κd α +τ (3.1) i = i where α i the path lo exponent, and κ, τ R are real number. In many enor application, it i aumed that α range between 2 and 4, ince the enor have hort antennae, which are very cloe to the ground. Definition 3.4: The minimum energy path S i a path with the vertex et P min i P from a enor node i N to a ink node min i P i V, where ( ) min i = arg min P i e i a minimum, i.e., { e( P )} The minimum energy tree T min = (V', A') i a ubgraph of G = (V, A), where T min = i N S i min { P } min. i. V V, A A, (a) (b) Figure 3.3. (a) A enor network graph, (b) Correponding minimum energy tree The minimum energy tree i a collection of all the minimum energy path from the enor node to their correponding ink node. Here, the enor node are matched with the ink node according to the energy cot meaurement of the path connecting them. Figure 3.3 (a) how an example enor network a a graph, where every communication

40 23 link i drawn. In Figure 3.3 (b), the correponding minimum energy tree for each ink i hown. Lemma 3.1: Let T min = (V', A') be the minimum energy tree of G = (V, A), then N V. Proof: The lemma follow directly from the definition of the minimum energy tree T min. Since for all i N, there exit a ink S, where we have a min min P i T, we have V i. Thi lemma i important a it tate that all enor node are included in the minimum energy tree. In other word, every enor node i connected to a ink node by a minimum energy path. The tatement i, however, not true for the ink node. Not every ink node hould omehow be ued in the minimum energy tree. A a counter example, aume a ink node lying at the border of the network, where it can be reached by a enor node, but there exit a better alternative for thi node to communicate. Then, thi enor node will not be connected to that ink node in the minimum energy tree. Definition 3.5: Let n = N. The adacency matrix M A = ( a k ) n v of the minimum energy tree T min = (V', A') i defined by a k (, k) 1 if A = 0 otherwie. Lemma 3.2: Let P min i be the minimum energy path from a enor node i N to a ink node S. Then for all all x V {} k. min V i, there exit k uch that a = 1 and a = 0 for min V i k x Proof: Let T min min min min = (V', E'), and aume P ( V A ) min and A = {( i, u),...,(, k ),...,( v ) } A a k i, min i =,, where V min { i u k v } V i i i i =,,...,,,...,,. Then from the definition of the adacency matrix, = 1. Since P i a path from i to, a = 0 for all x V {} k. It remain to prove x min i

41 24 min that a = 0 for all x V V {} k. But, thi i clear from the definition of the minimum x i min energy path. If there exited x V V {} k uch that a = 1, then thi would mean i x that e e, which i a contradiction. Hence, the lemma i true. x k Theorem 3.1: For all, where i N and S, we have V i x V a = 1. x Proof: For all, the reult follow directly from the definition of the path i, and min V i min Lemma 3.2. There exit k uch that V i x V a x = a k + a x V {} k x P = = 1. For all other path between i and, where P i P, we know from Lemma 3.1 that there exit a min i enor node n N and a ink node t S, where lie on the minimum energy path P. min n t Thu, there exit k uch that a = 1, and the reult follow. min V n t k Thi theorem tate through the adacency matrix that each enor node i connected to one and only one other enor node toward a ink node. Thi concluion i trivial from the definition of the tree, but the formula i neceary in the following formulation Routing The energy diipation i directly related with the underlying routing technique. Depending on the application requirement, different routing trategie might be implemented on the ame network. The route might form tree tructure where the root are the ink node, or imilarly, multi-path routing trategie could alo be employed when the communication link are le reliable, while generating multiple copie of the ame data packet. In order to handle any type of routing alternative, we repreent the routing deciion uing path matrice in a generalized manner, where the reult of any routing algorithm eaily can be applied.

42 25 Definition 3.6: Let the tree T min i defined by n = N, m = S, v V = n + m =. The path matrix ( ) i M P p k n m n v = of p i k 1 = 0 if (, k) A otherwie. min i, i N, S The path matrix how the reult of the underlying routing algorithm. The element of the form i p k hould be read a follow: If we conider a path from a enor node i to a ink node, and if the link connecting the node and k lie on that path, then the value of the element i 1, otherwie 0. In multi-path routing algorithm, the binary value of the matrix howing the preence of the link could eaily be extended to how the probability i for a packet to chooe that link, where p = P{, k) A i N, S} k (. In thi work, we focu on tree algorithm, and therefore the path matrix repreent the connection for the minimum energy tree T min. Thi matrix i later ued for network-wide energy calculation. i There i a cloe relation between the definition of the adacency matrix and the path matrix. The following lemma tate thi relationhip. Lemma 3.3: Let T min = (V', A') be the minimum energy tree in a enor network G = (V, A). For any i N, and S, we have min P T p = a i i k k, for all, k V i. Proof: The reult i achieved uing Lemma 3.2 and the definition of the matrice. min i (i) P T, k V p = 1 (, k) A A (, k) A a = 1. i i k i k (ii) a k = 1 (, k) A There exit a path Pi uch that i A and (, k) A i A i min p k = 1 Pi T.

43 Path Length Next, we try to calculate the number of enor node on the path that are connecting a enor node to a ink node. Thi value can be ued for calculating the average energy diipation for an arbitrary path in the network. Definition 3.7: Let i N, S. The et of relay node or the relay et of the path Pi i defined a { N V {} } Ri = : i, or equivalently {} N Ri = Vi. In order to viualize thi et, conider Figure 3.4. Here, the path from the enor node i to a ink node i hown, where V i = { i,,..., k, }. Then we have R i = { i,,..., k}. Including the initiator enor node to the et of relay node may be confuing, and the et could be redefined by excluding the initiator node from the et. In our work, however, we include thi node to the et. The reaon i that even thi node ha to relay it own data through the network layer to the next-hop node. Ri i k Figure 3.4. The et of relay node of the path Pi Definition 3.8: The path length of the path P i defined a i l i = Ri. In order to calculate the number of enor node in the path, we require one final definition, the relay node matrix.

44 27 Definition 3.9: Let the tree T min i defined by n = N, m = S, v V = n + m =. The relay matrix ( i M ) R r n m n = of r i 1 if Ri, i N, S = 0 otherwie. An element of the relay matrix of the minimum energy tree i et to 1, if and only if that node i included in the minimum energy path from a enor node i to a ink node. Lemma 3.4: Let P be the minimum energy path from a enor node i N to a ink min i node S. Then, we have l r. = i N i Proof: For all R r i N i = i, the definition of the relay matrix tate, r = 1. Therefore, R i R i = l i i. Similarly, for all N R i, we have r = 0, where i i i i r = 0. Therefore, r r + r = li + 0 = li. R i N = R i N R i Theorem 3.2: Let i For the relay matrix ( ) N be an arbitrary node in the enor network, and i N, S. M = of the tree T min, we have R r i i r = p. k V k Proof: Let R denote the relay et of the path i min P = ( V, min i i A ). min i (i) If have, i R i, we know from Lemma 3.3 that k a k k V k V p =, for all k V. Therefore we i p = a. And from Theorem 3.1, we have a = 1. k Hence, we have k V k p = = i k i 1 r, for all R i. k V k

45 28 (ii) If k V N R i, and hence,, we have k V p = = i k i, for all k V. Therefore p = 0, for all min (, k) A i i 0 r, for all N R i. k Combining the reult (i) and (ii), we have i p = k k V r i, for all N. Corollary 3.1: Let P be the minimum energy path from a enor node i N to a ink min i node S. Then, we have l p. = i N k V i k Proof: From Lemma 3.4, and from Theorem 3.2, the reult follow. i i i l i = r = p k = p k N N k V N k V The reult of thi corollary can be ued to calculate the length of each path in the minimum energy tree. Depending on the deign criteria of the underlying routing algorithm, we may have different path matrice. However, the reult here can be applied on any routing tree Branch Node The energy diipated by an intermediate node depend on the number of node that are connected to the ink through itelf. The packet of initiator node are forwarded toward ink node through intermediate node. The node that are cloe to the ink node carry a higher load. When the batterie of uch a critical node run out of energy, then the whole branch that i connected through thi node may become unreachable. Although there are technique to recontruct the tree to connect thi branch to the ink [38], the routing tree hould conider balancing thi relaying load throughout the network, in order to maximize the total lifetime of the network.

46 29 Definition 3.10: Let N i defined a S. The et of branch node or the branch et of a relay node B { i N R } = :. i Similarly, the et of branch node or the branch et of a ink node B t = B. N S i defined a The branch et of a relay node include all node in the routing tree, which are connected to a ink node through a path that i paing over thi relay node. In Figure 3.5, an arbitrary relay node i given. Thi node i an element of the path connecting the initiator node { i i,..., } 0, 1 i n to the ink node. i 0 B i 1 k i n Figure 3.5. The et of branch node of the relay node Becaue of the definition of the relay et, we aume that alo relay it own packet to the ink. Therefore, i an element of it branch et. If an initiator node reache the relay node through a multi-hop link, ay through another intermediate node k, then from the definition, k i alo an element of the branch et of, becaue the node k i an initiator of a different path to the ink a well. The following lemma tate the relation between the relay et and the branch et. Lemma 3.5: Let i, N, S. Then, we have i B R. i Proof: The lemma i obviou from the definition of thee two et. Aume exit a ink node i B, then there S, where i N i the initiator node of the path Pi, and R i.

47 30 Hence, i B R. i Aume now, R i. Then, there exit a path i P, with the initiator node i N and ink node S. Then, i B. Hence, R i B. i Lemma 3.6: Let N be an arbitrary enor node, and S a ink node in a enor i network. For the relay matrix ( ) M = of the tree T min, we have R r i B = r. i N Proof: From the definition of T min, there exit a ink node S, uch that P min T min. For i N, the definition of the relay matrix tate, r = 1, if i P min i T min, i.e., i min V i, and i we have r = 0, for all Therefore, B = i N ' r i i N. min V i i i N N ' i i + 0 = r + r = r, where i N ' i N N =. min V i In order to calculate the total number of node that are connected to a ink node, it i ufficient to count all branch et of the relay node, which are immediate predeceor of thi ink node, i.e., which are only one hop away from the ink node. Lemma 3.7: Let be S an arbitrary ink node in a enor network. Then, i B = p p. N i N k V k Proof: For S, = B B, where N = { N : a = 1 } N which are directly connected to the ink node. Therefore, For the minimum energy tree, we have, i.e., N' i the et of enor node B = B a. N a = p, from Definition 3.6.

48 31 Then, uing Lemma 3.6, and from Theorem 3.2, we have i i i B = r p = p k p = p k p. N i N N i N k V N i N k V Definition 3.11: The branch ize of a relay node b =. B S N i defined a Corollary 3.2: Let T min be the minimum energy tree in a enor network, and arbitrary enor node. Then, we have b =. i p k S i N k V N an Proof: From Lemma 3.6, and from Theorem 3.2, the reult follow. i i i b = B = r = p k = p k. S S i N S i N k V S i N k V The routing algorithm hould conider the number of node that are connected to a ink node b, whenever a capacity contraint related with the ink node i tated. The routing tree hould be contructed o that thee limitation are not exceeded Energy Diipation One of the maor deign concern in wirele enor network i the energy diipation at the enor node. Routing algorithm hould conider efficient management of the limited energy reource to increae the lifetime of individual node, therefore reulting in a network that i operational much longer. Here, we derive formulation for total energy diipation at the node level and each data path in the network.

49 32 Definition 3.12: The total energy diipation e for a data packet, which i generated at i an initiator node i N arriving at a ink node S, i defined by e min ( P ) = i e. i Similarly, for the minimum energy tree T min = (V', A'), and N, k V where ( k) A,, the relay energy load e of a node i defined by e = e b. k We aume that the data packet chooe to travel along the minimum energy path in the network. If alternative path can be ued depending on the underlying routing algorithm, thee definition can be extended accordingly. Now, we calculate the total energy diipation value. Lemma 3.8: Let network. Then, i N be an arbitrary initiator node, and S a ink node in a enor e e p. = i N k V k i k Proof: Let i N, S min. Then we have e = e( P ) of the path. Let M A ( a k ) n v Then A e k = i i = (, k ) e k min A i = be the adacency matrix of T min. e k min min min (, k ) A (, k ) A (, k ) A (, k ) A ( k ) from the definition of energy cot k N V + 0 = e a + e a = e a = e a where i i i, k k k k k N k V min = N V A i. Finally, uing Lemma 3.3 we have i = e ka k = N k V N k V e e p k k k i k The total energy diipation value e give the energy cot of the communication i path P in the enor network. Energy aware routing algorithm hould chooe better i ink alternative uch that thi cot i minimized. Next, we calculate the relay load of enor node.

50 33 Lemma 3.9: Let network. Then, N be an arbitrary relay node, and S a ink node in a enor i e = e p. S i N k V k k Proof: Let i N, V Then we have Therefore, we have,. k, T min = (V', A'), and ( k) A = = = i e e kb e ka k b e ka k p v from Corollary 3.2. k V k V S i N v V k V S i N v V i i i e = e a p = e p p from Lemma 3.3. k k v k V S i N v V i i i i Here, p = 1 only when k = v, k, v V, and p = 0 otherwie. Therefore, by k p v changing the index, we have S i N k V k p v i e = e p. k k k k v The relay energy load of enor node hould be controlled efficiently, o that the relay traffic i equally ditributed among all relay node. An upper limit could be determined for thi load, o that premature node failure could be prevented Counting the Packet In order to manage the energy reource of enor node efficiently, we mut have a mechanim to quantify the number of packet that thee enor node deal with during a time frame. Definition 3.13: The number of packet going through a relay node N during a time interval (0,t] i denoted a n R () t. Similarly, the number of packet generated by an initiator node i N during a time interval (0,t] i denoted a () t. Equivalently, n R G () t = n () t i. S i B n G i

51 34 Lemma 3.10: Let N be an arbitrary enor node in a enor network. Then, R G () t = n () t n r. S i N i i Proof: Let i B be an arbitrary initiator node in the branch et of, and S a ink node. Then from Lemma 3.5, we know R G () t = n () t n r. S i B i i i, and therefore, r = 1 R i. Then, we have For i i N, with a imilar argumentation we have r = 0. Hence, B R G i G i G i () = () + = () + () = G i G t n t r n t r n t r n () t r + n () t n 0 R i i i i i i S S S i N B S i B i B i B i N B G () t = n () t n r. S i N i i r Corollary 3.3: Let N be an arbitrary enor node in a enor network. Then, we have R G () t = n () t n p. S i N k V i i k Proof: From Lemma 3.10 and from Theorem 3.2, the reult follow. R G i G i G i n () t = ni () t r = ni () t p k = ni () t p k. S i N S i N k V S i N k V In order to quantify the number of packet generated during a time period n G i () t, we have to clarify the packet generation proce, which i a random proce whoe behavior i not predictable in all it detail. Thi proce may have an arbitrary probability ditribution, which i poibly known a priori, a it i cloely related with the underlying enor application.

52 35 Definition 3.14: Let i N be an arbitrary initiator node. Let X i () t denote the number of packet generated during the time interval (0,t]. Then { X i () t, t 0} i a family of random variable, forming a tochatic proce. Let ( n) Z denote the n th interarrival time, n 1, i Z ( n) i = tn tn 1 with a known cumulative ditribution function, and known expected value P ( n) ( Z x) F ( x) i = ( n) [ Z i ] i E = µ. i n =1 n =2 n =3 0 t 1 t 2 t 3 (1) Z i (2) Z i (3) Z i t Figure 3.6. The packet generation interarrival time ( n) Z for the initiator node i i Recall 3.1: For t, we have E [ X ] i t =. µ i Proof: For the proof, the reader may refer to [39]. Corollary 3.4: Let interarrival time µ. For t, i i N be an arbitrary enor node, having an average packet n G i () t t =. µ i

53 36 A an example, aume a Poion packet generation proce with parameter λ i, λi x where the interarrival time ha a cumulative ditribution function F ( x) e i =1. Then, we know that µ 1 λ i G =, hence n () t λ t i i =. i We further aume that the packet generation procee of each individual enor node are independent of each other. For general-purpoe continuou monitoring application, thi aumption clearly hold. Senor are going to end their meaurement in independent moment in time. For ome application, like eimic meaurement, thi aumption might not hold. That i, when a pecial event occur in the field, then every node that i cloe to thi node will try to end a packet to inform the ink node. Mot of thee application, however, ue a data aggregation mechanim where the data packet that are generated eparately are oined into a ingle packet. Then, only thi packet i forwarded to the ink. Conidering only thoe packet a real packet generation for the enor network, the aumption hold for thee type of enor network too. The number of packet that a relay node ha to forward toward a ink node can be found a follow. Lemma 3.11: Let N be an arbitrary node in a enor network where the packet generation of the enor node i independent. Then, for R () t = ( t ) n µ p. S i N k V i t, i k Proof: Let { X () t, t 0} R be the random proce counting the number of packet going through a R relay node N during a time interval (0,t], where X () t = X () t. Then we have R E [ X () t ] = E X i () t = E[ X i () t ], ince X i () t, S S i B i B Therefore, for S i B [ ] ( i ) R R t, we have n () t = lim E X () t = t µ. t S i B i B are independent. i

54 37 Uing the ame technique in Corollary 3.3, we have n R i () t = ( t ) = ( t µ ) r = ( t ) µ p i i µ i S i B S i N S i N k V i k Corollary 3.5: Let N be an arbitrary node in a enor network. When all initiator node have the ame average packet interarrival time µ, that i µ = µ i, for all i N, then n R t µ () t = S i N k V p i k. Proof: The reult follow directly from Lemma Node Lifetime The lifetime of the enor network i cloely dependent to the lifetime of each individual enor in the network. Whenever a node failure occur, all the branch node would be unreachable until a new route dicovery proce i initiated. Therefore, we have to control the lifetime of each enor node and try to prolong it a much a poible, in order to maximize the network lifetime. Definition 3.15: Let E () t be the reidual energy of a node N at a given time t. Then ( 0) E denote the initial battery capacity of the node N. The node N i aid to be alive whenever () t > 0 whenever () t = 0 E. Similarly, the node N i aid to be exhauted or dead E. Let e () t denote the total energy diipation of a node N during a time interval (0,t]. Then we have E () t E ( ) e () t = 0. Clearly, the reidual energy of a enor node E () t i a monotonically decreaing, real-valued function of time. We have to find the approximate time when an operational node become exhauted.

55 38 Lemma 3.12: Let N be an arbitrary node in a enor network where the packet generation of the enor node i independent. Then, for () t = ( t ) e µ p e. S i N k V i i k t, k Proof: Obviou from Lemma 3.9, and Lemma Corollary 3.6: Let exhauted when N be an arbitrary node in a enor network. Node become t = E ( 0) ( 1 µ i ) S i N k V p i k e k. Proof: The derivation i obviou from Lemma We want to find t uch that () t = 0 i i, ( t) E ( 0 ) e ( t) = E ( 0) ( t ) p e = 0 E µ. = Hence, E ( ) = t ( 1 µ ) S i N k V i S i N k V i k k i k k E. That 0 p e and the reult follow. If we are uing ame enor node throughout the enor field, then we can eaily aume that their initial battery capacitie are equal. Therefore, we can rewrite the maximization obective where we try to maximize the lifetime of enor node, a a impler minimization problem, where we try to minimize the denominator, i.e., ( µ i ) S i N k V 1 p e. i k k Invetment Cot The mot important deciion point of an invetor i the total invetment cot, i.e., the total budget of the ytem. Therefore, we have to define parameter to calculate the total outcome to build an operational enor network accompanying multiple ink node.

56 39 During the lifetime of the network, redeployment of additional enor node might be neceary. Thi requirement might be becaue of node failure having exhauted batterie, a well a becaue of changed monitoring need where meaurement that are more precie become neceary. The number of deployed enor node i the mot baic budget entry. Here, we make an extenion on Definition 3.1 where we define the et of enor node. Definition 3.16: Let where = { 0,1, 2,... } r Ζ repreent the number of redeployment in a enor network, Ζ. Let N r denote the et of enor node in the r-th redeployment. Let n = N denote the number of enor node in the r-th redeployment. Then r r N = n = t r N i i=0 r n i i= 0. From the definition, it i clear that r = 0 repreent the initial deployment of the enor node, and r 1 repreent additional redeployment to the network. Definition 3.17: The cot of a enor node at the r-th redeployment i given a c R. N r The cot of deployment action of the r-th redeployment i given a D c r R. The cot of a S ink node S i given a c R. The cot of placement of a ink node S i a real-valued function c :R 2 R, having the coordinate ( x, ) of the ink node a argument. P y Thee unit cot parameter will be ued to calculate the total budget of the enor network operation. The cot of individual enor node could vary between redeployment attempt becaue the number of deployed enor will vary. Conidering the cale of economy, the more enor node are deployed, the le i the unit price. At each deployment phae, a contant cot will be given depending on the labor and the vehicle ued. If the enor are cattered to a large region from an aircraft then a much higher deployment action cot hould be paid, compared to a deployment where only a maller

57 40 region and manual placement i conidered. For the ink node, a the ink node might have different capabilitie, their cot might be different. If the invetor would chooe identical ink node, then S S c = c, for all S. Finally, the placement of the ink node might be dependent on environmental retriction, where the cot i related with the geographical coordinate of the location. Then the regional placement cot function P ( x y ) c, of the ink S will be different for uch location. Now, we can define the total cot for the enor network invetment. Definition 3.18: The total cot of enor node at the r-th redeployment i given a N C r R, where C = n c. Then, the total cot of enor node i given by N r r N r N C R, where C N = r i= 0 C N i = r i= 0 n c N i i. The total cot of deployment action i given by D C R, where C D = r i= 0 c D i. The total cot of ink node i given by S C R, where S S C = c. S The total cot of ink node placement i given by The total invetment cot i given by r i= 0 S P C R, where ( x y ) P P C = c,. C R, where r i= 0 S S ( x y ) N D S P C = n c + c + c + c, i i i. The total invetment cot i the um of all deployment cot of a enor network operation. For an economically feaible operation, the invetor need to minimize thi cot a much a poible, regarding the other contraint in the network.

58 Summary In thi chapter, we have derived everal new formulation that are neceary to build a framework for the multiple ink enor network deign problem. Important characteritic of the enor network infratructure have been analyzed and the neceary definition have been introduced. Thee definition and formulation will be ued in the following chapter to quantify the energy diipation at the enor node. Thereafter, deign obective related to the multiple ink enor network deign problem will be preented baed on thee formulation.

59 42 4. QUANTIFYING SAVED ENERGY BY MULTI-HOPPING Senor node have a hort tranmiion range due to their limited radio capabilitie. Therefore, the data mut be relayed uing intermediate node toward the ink. In addition, it may be more advantageou to ue a multi-hop path to the ink node coniting of horter link rather than uing a ingle long connection. The energy conumption at the tranmitter i known to be proportional to α d where d i the range of the radio ignal and α i the path lo exponent [7, 40-43]. In [40], a minimum energy connection protocol baed on the ditributed Bellman-Ford algorithm i invetigated. The effect of mobilization i alo analyzed. In [41], a power-aware routing algorithm for wirele ad-hoc network i preented, which help to minimize the tranmiion power needed to forward data packet. In [42], directional antennae are ued to contruct the minimum energy tree. Here again, the cot of a link i aumed to conit of only the dominant component, i.e., the tranmitter energy. Energy efficiency on contructing multicat tree on wirele network i conidered in [44], where the energy gain i focued on tranmitter energy. There are alo different tudie for energy baed optimization. In [45], optimum one-hop tranmiion ditance i calculated that will minimize the total ytem energy. In thi work, it i aumed that each node i communicating with it next-hop node in a linear network topology. In [46], a communication protocol for wirele enor network i propoed, baed on energy efficiency. Here, only free pace propagation model i aumed and the effect of different path lo exponent value are not invetigated. A different minimum energy routing model i propoed in [47], where the effect of hadowing and fading i alo conidered. Although the importance of the receiver energy i not oppoed, thi factor i neglected in detailed analyi. When only the tranmiion energy i conidered, uing horter multi-hop link eem to be more advantageou. However, due to other energy conuming activitie on the enor node, uch a reception of relayed meage, ening and computation tak, a coniderable overhead energy might be diipated during forwarding a meage. Therefore, multi-hopping i not alway advantageou in wirele enor network.

60 43 In thi ection, we try to invetigate, when the uage of an intermediate node reult in energy gain. We analyze the amount of energy gain uing multi-hop link to contruct a communication path. We focu on uniformly deployed enor node, each having identical communication capabilitie. The enor node are aumed to be able to adut their tranmiion power. Therefore, each enor conume only the amount of energy that will uffice to reach for the tranmitted radio wave to the detined receiver antenna. A imilar tranmitter model i propoed in [48] Network Model Aumption The enor network conit of enor node and one or more ink node where the reult of enor meaurement are collected. If the enor are equipped with undirected antennae then each node i connected to every other node within the tranmiion range of it radio ignal. Thi ituation i preented in Figure 4.1. Senor node i 0 i able to tranmit radio ignal at three different power level P 1, P 2, and P 3. Depending on the power level, enor node in varying ditance to the originator node tart to receive ignal. i2 i2 i2 i2 P1 P2 P3 P1 P2 P3 i5 i0 i5 i0 i5 i0 i5 i0 i1 i1 i1 i1 i3 i3 i3 i3 i6 i4 i6 i4 i6 i4 i6 i4 (a) (b) (c) (d) Figure 4.1. Radio tranmiion with different power level reult in different tranmiion range The enor are aumed identical having the ame radio equipment. Therefore, ignoring the environmental obtacle, whenever a node i can reach to another node, it i

61 44 evident that backward communication i alo poible, i.e., node i can be reached by node. Routing deciion will dictate enor node with different tranmiion power level in order to ave energy. Therefore, it may eaily happen that node i tranmitting with a high power level to reach to a ditant node, and node tranmitting with a lower power level to a cloer node k. In thi cae, it i clear that node cannot be heard by node i. Therefore, we aume directed edge in the network graph G Multi-Hop Link During election of the mot energy effective route, alternative link mut be conidered. In the implet cae, one ha to chooe between a direct link from ource to detination and a multi-hop link uing intermediate node, if available. Figure 4.2 how uch a ubproblem during routing deciion. A communication requet between node i and may trivially reult in a direct link (i, ) between thoe two node, wherea a good alternative would be found by uing the intermediate node k reulting in the path <i, k, >. i Figure 4.2. Uing multi-hop link in routing deciion k 4.2. Energy Saving Routing algorithm in enor network hould conider communication link with le energy conumption among other alternative. Suppoe that we have two enor node i and within the enor field where node i want to end a data packet to node. Thi ituation i repreented in Figure 4.3 (a). Trivially, node i hould adut it tranmitter circuitry power o that node will receive the tranmitted ignal. Alternatively, the routing algorithm may decide to ue an intermediate node k, which i lying between both

62 45 the tranmitter and the receiver node. Energy aving, δ E, can be formulated a the difference of total energy conumption between two alternative E (1) Total (2) Total δ = e e (4.1) where (1) e Total and alternative, repectively. (2) e Total give the total energy conumption value of thee two Here, we will conider three different cenario where an intermediate node can be ued, and compare the energy aving achieved at each cenario. i i k d i d ik d k (a) (b) k (3) k (2) i k (1) d i / 2 (c) d i / 2 Figure 4.3. Routing deciion alternative, (a) direct communication, (b) and (c) uing an intermediate node D Communication Link In the implet cae, we aume a one-dimenional environment. Here, the intermediate node k lie on the line connecting the ource and the detination node, a given in Figure 4.3 (b). It i clear that energy lo would occur when node k would be beyond node i or node. Therefore, we conider have 0 d, d d. Uing Equation 2.6, we ik k i

63 46 (1) Total e (2) Total e = e i = e ik = κd + e k α i = + τ α α ( κd + τ ) + ( κd + τ ) ik k (4.2) where (1) e Total give the total energy conumption when a direct communication link between node i and i etablihed, and (2) etotal give the total energy conumption when an intermediate node k i ued. Therefore, a two-hop communication path i utilized, the firt link connect node i with node k, and the econd link connect node k with node. By uing Equation 4.2, energy aving can be found a follow. δ E α α α = i ik k κ [ d d ] τ d (4.3) δ E (1) e Total δ E(max) Energy Saving τ 0 0 di / 2 d i d ik Intermediate Node Poition Figure 4.4. Energy aving in 1-D communication cenario Here, uing the fact that d = d + d, we get i ik k δ E α α α κ [( d ) ( d d ) ] τ = i ik i ik d (4.4)

64 47 We keep the ditance between node i and node contant and oberve the energy aving behavior. An intermediate node k i ued that i found on the line between node i and node. For implicity, we take τ = τ 0, an arbitrary fixed energy requirement at each enor node. The behavior can be oberved in Figure 4.4. When node k i cloe to the ource or the receiver, a ignificant amount of energy lo occur. Uing an intermediate node become only meaningful when thi node i ditant from both the ender and the receiver. For different value of path lo exponent α, thi behavior remain the ame. However, the amount of energy that i required for ucceful data tranmiion increae exponentially a we can ee in Figure 4.5. δ E α = 6 Energy Saving α = 5 α = 4 α = di / 2 Intermediate Node Poition d i d ik Figure 4.5. Effect of α on energy aving in 1-D communication cenario E dik The point of maximum energy aving can be found by etting ( ) 0 δ =. The firt derivative of energy aving with repect to ditance between node i and node k can be written a follow. dδ dd E ik = ακ α 1 1 [( ) ] α d d d i ik ik (4.5)

65 48 E ik Here, we have ( d ) = 0 δ if d = 2. In other word, maximum energy aving ik d i would be achieved when node k i exactly on the midpoint between node i and node. Uing thi reult, we can find the place for an intermediate node where energy i aved when thi node i ued a a relay node. In other word, we want to find d ik, o that δ E > 0. Setting di = 2dik in Equation 4.4, we get δ = 2 α 1 α ( 2 1) κ τ E d ik (4.6) Therefore, we can ay that δ > 0, whenever we have an intermediate node whoe ditance from the ource node i found a follow. E 1 α τ d ik > α 1 (4.7) 2(2 1) κ Equation 4.6 provide with another important reult. We know from Equation 2.6 that ( ) α e d =. Therefore, we can conclude with an energy aving, whenever the T ik κd ik following inequality between the overhead energy τ and tranmitter energy e T hold. α ( 2 1 1) e T τ < 2 (4.8) Iocele Triangular Communication Link In the econd cenario, we let the intermediate node lie on the top corner of an iocele triangle whoe other two corner are the ource and the detination node. Thi cenario i preented in Figure 4.3 (c). Obviouly, the ditance between the intermediate node and either the ource or the detination cannot be larger than the ditance of a direct link between the ource and the detination. Therefore, in thi cae, we conider d i 2 d, d d. ik k i

66 49 Since the routing triangle i iocele, we know d = d. Therefore, the energy ik k aving defined in Equation 4.3 can be repreented a follow. δ E α α = i ik κ ( d ) τ d 2 (4.9) δ E δ E (max) Energy Saving 0 d i / 2 d i d ik (1) e Total Intermediate Node Poition Figure 4.6. Energy aving in iocele triangular communication cenario The energy aving with repect to increaing d ik can be een in Figure 4.6. It i monotonically decreaing becaue the total ditance of data link i increaing and more tranmitter energy would be neceary to communicate. Maximum energy aving i achieved when the intermediate node k lie on the line connecting node i and node. In Figure 4.7, we oberve imilar behavior for different value of path lo exponent α, although the amount of energy increae exponentially. In order to find the place where the amount of energy aving i poitive, we put δ > 0 in Equation 4.9 and derive the following inequality. E 1 α 1 α τ d ik < di 2 κ (4.10)

67 50 δ 10 7 E Energy Saving α = 3 α = 4 α = 6 α = / 2 d i di Intermediate Node Poition d ik Figure 4.7. Effect of α on energy aving in iocele triangular communication cenario Arbitrary Triangular Communication Link In real life ituation, however, arbitrary triangular routing alternative will be found, and the routing algorithm ha to decide whether to chooe the direct link or to chooe the multi-hop one. Figure 4.8 how thi cenario. k (x, h) h (0, 0) (d i, 0) i x d i x Figure 4.8. Arbitrary triangular communication cenario Here, we aume that the node are lying on a 2-D plane where node i i at the origin, and node lie on the x-axi with coordinate (d i, 0). Then, the intermediate node k ha coordinate (x, h), where h i the height of the triangle. In thi cae, energy aving can be found a follow, uing d ik h + x =, and d 2 h 2 ( d x ) 2 k + i =.

68 51 δ α 2 ( ) 2 2 α 2 2 ( h + x ) h + ( d x) E = κ [ di i ] τ (4.11) α 2 Thi equation i plotted in Figure 4.9. We have een thi behavior in the firt two cenario. The generalization can eaily be reduced to thee cenario by putting h = 0 or x = 2 for the firt and econd cenario repectively. d i Figure 4.9. Energy aving in arbitrary triangular communication cenario Generalization Until now, we have preented technique for two-hop cenario. However, thee technique can eaily be applied recurively on ituation where a multi-hop communication link hould be conidered a an alternative. Conidering the ituation in Figure 4.10 (a), when node i want to reach node, there might be more than one intermediate node, uch a node k and l. In thi cae, the

69 52 underlying routing algorithm hould conider the amount of energy aving when node k and l are ued a relay node. k l k i i (a) (b) Figure Generalization into a multi-hop path When a ditributed routing algorithm i ued, node i will decide on it output power level according to it neighbor. Therefore, node i will compare the alternative (i, ) with the path <i, k, >, a in Figure 4.10 (b). node i i not reponible on the routing deciion of node k. Therefore, node k hould decide whether to end packet through node l or ending it directly to node Simulation on the Energy Saving by Multi-hopping In order to validate the effect of utilizing multi-hop communication link in energy aving, we performed imulation uing Opnet Modeler [49] on different cenario Simulation Setup We focu in our imulation on three different type of enor node varying on their tranmiion power adutment capability. The firt node type, P max, i unable to make any power control on tranmitter circuitry. Thi type of node hould alway end packet with the maximum tranmiion power, independent of the ditance between ource and detination node. The econd node type, P 3, can adut it tranmiion power at three different power level, wherea the third node type, P cont, ha a continuou power level adutment capability. In imulation, however, we have ued 20 dicrete power level intead of a continuou cale. P 3 and P cont type enor try to change their tranmiion power to the minimum level that will be ufficient for their radio packet to reach to their detination. For each experiment, 10 different random enor network are generated. The

70 53 graph are plotted uing the average value derived from thee network, with a 95 per cent confidence interval. Each enor network conit of one ink node and 100 enor node. The ink node i located in the middle of the area, wherea the enor node are ditributed uniformly. We have alo conidered locating the ink node to one of the corner of the area, which did not change the overall behavior of the ytem. Table 4.1. Simulation parameter Parameter Sample tranmiion power Sample tranmiion range Data rate Packet ize Minimum tranmiion power Maximum tranmiion power Default area ize (A) Value 800 mw 200 m 20 kbp 1024 bit 100 mw 2,000 mw 200 m x 200 m Default path lo exponent (α) 3 Number of enor node 100 The enor are aumed to ue 800 mw tranmiion power for a 200 m radio range in open air ( α = 2 ). Thee value are choen, a they are very cloe to the Berkeley/Crobow Mica Mote pecification [8]. Thi data i ued to calculate the correponding radio range for each different environment type with different path lo exponent value. Thee aumption are ummarized in Table 4.1. The energy model in Equation 2.6 i ued to calculate the average energy pent at each enor node for one packet tranmiion. Here, the overhead energy τ ha a typical value of 20 mj per packet where 400 mw receiver power i aumed, and both ening and

71 54 computation energy i neglected. However, we have conidered τ = 0 mj to 50 mj to examine the effect of different overhead energy level. In thi work, we monitor the average hop count and the average energy pent per packet at each node. Thee value are calculated a follow. After the network etup phae, a communication tree i formed. Thereafter, for each enor, the communication path from itelf to the ink node i travered, and both the number of hop and the neceary energy i recorded Reult In the firt experiment, the default imulation parameter are ued. The reult are preented in Figure 4.11 and Figure P (cont) P (3 level) P (max) Average Hop Count Overhead Energy (mj) Figure Average hop count veru overhead energy τ (A = 200 m x 200 m, α = 3) Multi-hop communication path are utilized whenever the overhead at each hop i mall. Therefore, at higher overhead energy value, direct link are preferred to multi-hop path. When the enor are communicating with the maximum tranmiion power, then the reulting routing tree will be independent of the overhead energy, i.e., each enor will

72 55 try to communicate with the one that i furthet away from itelf. Hence, we have a contant average hop count for P max node. Since P cont node can make a finer power adutment than P 3 node, thi optimization reult in a higher average hop count. Average Node Energy (mj) P (max) P (3 level) P (cont) Overhead Energy (mj) Figure Average node energy veru overhead energy τ (A = 200 m x 200 m, α = 3) It i evident that average node energy hould increae when the overhead energy increae (ee Figure 4.12), ince thi i a contant additive of the total energy per node. The increae in the total energy, however, i more than the additional overhead. The reaon for thi i that the tendency to ue direct link increae a the overhead energy increae, which require more energy than multi-hop path coniting of horter link. A the amount of power adutment level increae, the energy pent at each node decreae. In other word, enor node can ue their energy more effectively. A an example, for the typical cae where τ = 20 mj, P max node pend on the average e Total = 282 mj, wherea P cont node pend on the average e Total = 137 mj. Thi reult in an improvement of more than 50 per cent energy aving, which double the lifetime of each enor node. In Figure 4.13, we conider only the P cont node. Here, the reult of all experiment with different overhead energy value are plotted. The trendline indicate clearly that whenever the network i able to ue multi-hop link, average node energy decreae. The

73 56 uage of multi-hop link, however, i determined by conidering the amount of the overhead energy, a we have een in Figure Average Node Energy (mj) Average Hop Count Figure Average node energy veru average hop count (A = 200 m x 200 m, α = 3, only P cont node are ued) Average Node Energy (mj) P (max) P (3 level) P (cont) Overhead Energy (mj) Figure Average node energy veru overhead energy τ (A = 400 m x 400 m, α = 3)

74 57 In the econd experiment, the effect of enor denity i analyzed. Therefore, the area ize i increaed to 400 m x 400 m while the number of enor i kept the ame. A hown in Figure 4.14, the network how the ame behavior a in the dene cenario, with a difference that the average node energy requirement become larger. Thi i becaue the average ditance between each enor node ha been increaed. For our typical cae where τ = 20 mj, the improvement achieved by uing P cont node intead of P max node i found a 42 per cent, which again approximately double the lifetime of each enor node. The third experiment focue on different environmental condition by varying path lo exponent α. In thi experiment, only P cont node are ued which are proven to provide with the mot efficient energy management cheme. Average Hop Count Overhead Energy (mj) α = 3.5 α = 3 α = 2.5 α = 2 Figure Average hop count veru overhead energy τ (A = 200 m x 200 m, only P cont node are ued) We know that in urban area or in more obtructed environment, the value of α increae. Therefore, radio tranmiion range decreae for the ame tranmiion power value. A a reult, the enor node can be connected to the ink node only with horter link, and therefore uing more hop (ee Figure 4.15). Moreover, we can clearly oberve that the degree of multi-hopping reduce when the overhead energy at each enor node

75 58 increae. Thi how that the node prefer rather direct link than multi-hop path. For α value greater than 4, even the maximum tranmiion power that our enor node are capable become inufficient to form a connected network. In rural area (α = 2), however, the enor can be more denely deployed, a the radio range i higher. In our experiment, each enor node tart to communicate via a direct link with the ink node, a the overhead for uing a multi-hop link i relatively high. Only for the cae where the overhead i omitted (τ = 0 mj), ome multi-hop link are etablihed. In Figure 4.16, we oberve that the energy diipation of each enor node i exponentially related with the path lo exponent. Therefore, in more obtructed environment, one mut expect horter enor lifetime, which i exponentially related with α. Average Node Energy (mj) α = 3.5 α = 3 α = 2.5 α = Overhead Energy (mj) Figure Average node energy veru overhead energy τ (A = 200 m x 200 m, only P cont node are ued) An intereting reult i that, the average hop count i alo exponentially related with the path lo exponent. The typical cae with τ = 20 mj i hown in Figure Here, we have a larger confidence interval for larger α value, ince the interconnection degree of the network decreae, which reult in more deviated value. However, the exponential trend can eaily be een, ince we ue a logarithmic cale. Therefore, the degree of

76 59 multi-hopping increae with increaing path lo exponent exponentially, which i increae the end-to-end delay and packet lo rate, but decreae the total energy diipation. 10 Average Hop Count.. 1 1,5 2 2,5 3 3,5 4 Path Lo Exponent Figure Average hop count veru path lo exponent α (A = 200 m x 200 m, τ = 20 mj, only P cont node are ued) 4.4. Concluion on the Energy Saving by Multi-hopping In order to maximize the network lifetime, energy reource of each individual enor node mut be conumed effectively. Uing multi-hop path that conit of horter link intead of one long link might reult in coniderable energy gain. In thi chapter, we propoed a new analytical approach to quantify energy aving uing multi-hopping and power level adutment. We have tudied different multi-hop communication cenario and calculated the energy aving in each cenario. We have alo expanded thee cenario to general cae. The generalization can be applied into any arbitrary triangle and can be ued in energy optimized route calculation. We alo tried to quantify the effect of path lo exponent α, and overhead energy τ on energy aving. Thee analytical method can be ued for developing fater power aware routing algorithm. We have alo validated our analytical tudy uing imulation.

77 60 Although the tranmitter energy reduce by uing multi-hop communication link, we have hown that the total communication energy might increae depending on the overhead energy that ha to be diipated at every hop in the network. Therefore, the degree of hopping hould decreae whenever higher overhead energy value are under conideration. We have compared the effect of overhead energy with average hop count and with average node energy per packet on different cenario. It i hown that the enor lifetime can eaily be doubled uing power adutable tranmitter circuitry.

78 61 5. THE EFFECT OF OVERHEAD ENERGY TO THE NETWORK LIFETIME Although the tranmitter energy i one of the maor factor of total energy diipation in a enor node, neglecting the overhead energy in energy aware routing deciion could reult in uboptimal energy uage. Routing algorithm hould be concerned about the overhead energy, which i wated at each hop of data tranfer. When only the tranmiion energy i conidered a the communication cot, uing horter multi-hop link eem to be more advantageou. However, due to other energy conuming activitie on the enor node, uch a reception of relayed meage, ening and computation tak, a coniderable overhead energy might be diipated while forwarding a meage. Therefore, multi-hopping become not alway advantageou in wirele enor network. In thi chapter, the ue of multi-hop communication link i invetigated, and the amount of energy gain that i acquired by correct routing energy calculation i compared. We how that neglecting the overhead energy and overemphaizing the importance of power adutable tranmitter circuitry could reult in coniderable energy lo Motivation for Overhead Energy Conideration The path lo exponent α ha a great impact on energy diipation at the enor α node, ince the tranmitter energy i proportional to d where d i the range of the radio ignal. On the other hand, the route calculation hould alo conider the overhead energy diipation at the enor node, which include the receiver energy, the computation energy, and the ening energy. Thee overhead energy requirement and path lo exponent value may reult in different minimum energy tree tructure, conequently different routing topologie. Conider a mall wirele enor network with three enor node i 1, i 2, i 3 and one ink node whoe layout i given in Figure 5.1. Even in uch a mall network, we can ee that routing deciion baed on energy calculation may reult in different route

79 62 depending on the aumption about the underlying model. Figure 5.1 (a) and (c) how the minimum energy routing tree where the overhead energy τ i neglected during routing calculation auming τ = 0 mj, for different environmental ituation with α = 2 and α = 3 repectively. In real world enor node, however, we mut not forget the overhead energy, which i diipated at each hop of data tranfer. Auming a realitic overhead energy value with τ = 20 mj, different routing topologie would be found which are preented in Figure 5.1 (b) and (d). Thee alternative how that the actual minimum energy route are different from the initial one. The mot important point i that, neglecting the ignificance of the overhead energy diipation would reult in a coniderable amount of energy wate. i 1 i 1 i 2 i 2 i 3 (a) α = 2, τ = 0 mj i 1 i 3 (b) α = 2, τ = 20 mj i 1 i 2 i 2 i 3 i 3 (c) α = 3, τ = 0 mj (d) α = 3, τ = 20 mj Figure 5.1. A ample network repreenting different topology alternative for different path lo exponent α and overhead energy τ value In In ummary, the overhead energy i an intrinic component of energy diipation at enor node. Neglecting thi important factor during routing deciion may reult in wore routing alternative while promoting meaningle multi-hop communication link and reulting in a ignificant amount of energy wate. Table 5.1, the average energy diipation at enor node are compared for the mall enor network given in Figure 5.1. The routing topologie where only the tranmitter

80 63 energy i conidered and the overhead energy i not taken into account will caue an obviou energy wate on enor node. In ummary, the overhead energy i an intrinic component of energy diipation at enor node. Neglecting thi important factor during routing deciion may reult in wore routing alternative while promoting meaningle multi-hop communication link and reulting in a ignificant amount of energy wate. Table 5.1. Average energy diipation at enor node Explanation E (mj) Topology at Figure 5.1 (b), where τ i conidered α = 2 Topology at Figure 5.1 (a), where τ i ignored Relative energy lo (%) 62 % Topology at Figure 5.1 (d), where τ i conidered α = 3 Topology at Figure 5.1 (c), where τ i ignored Relative energy lo (%) 16 % 5.2. Simulation on the Effect of Overhead Energy In order to viualize the effect of neglecting the overhead energy parameter during routing calculation, we performed imulation uing Opnet Modeler [49]. We have implemented two imilar minimum energy tree contruction algorithm baed on the Ditributed Bellman-Ford Algorithm [50]. In the firt cae, the Ignore algorithm (IA) conider only the tranmitter energy and trie to etablih connection between node where the tranmiion power i minimized, while ignoring the overhead energy diipation at each hop. In the econd cae, the Conider algorithm (CA) conider the total energy cot a given in Equation 2.6 while contructing the routing tree.

81 Simulation Setup The enor node are aumed to be capable of aduting their tranmitter power to the minimum required level that will be ufficient for their radio packet to reach to their detination. In imulation, however, we have ued 20 dicrete power level intead of a continuou cale. For each experiment, 10 different random enor network are generated. The graph are plotted uing the average value derived from thee network, with a 95 per cent confidence interval. Each enor network conit of one ink node and 100 enor node. The ink node i located in the middle of the area, wherea the enor node are ditributed uniformly. We have alo conidered locating the ink node to one of the corner of the area, which did not change the overall behavior of the ytem. The enor are aumed to ue 800 mw tranmiion power for a 200 m radio range in open air ( α = 2 ). Thee value are choen, a they are very cloe to the Berkeley/Crobow Mica Mote pecification [8]. However, we have caled the radio range for our imulation environment where we ued a contant path lo exponent value with α = 3. The initial battery capacity of the enor i choen to be 200 J. In [51], it i given that for an alkaline-manganee dioxide battery, the typical volumetric energy denity i 428 Watt hour per liter. In other word, a battery of ize one cubic centimeter would have the capacity 1540 J. However, we have choen a maller value to horten the imulation time. The behavior of the imulation will not change, ince the battery capacity only caue the reult to appear earlier. The enor are aumed to perform independent reading, and therefore independent packet generation. The packet generation proce i aumed to be a Poion proce with rate λ = 1 packet per hour, where we aume a continuou monitoring application. Neverthele, here a periodic proce could alo be choen where the enor are polled

82 65 with a predefined frequency. The energy model in Equation 2.6 i ued to calculate the average energy pent at each enor node for one packet tranmiion. We have conidered τ = 0 mj to 100 mj to examine the effect of different overhead energy level. The network lifetime i defined a the length of time until the firt battery drain-out among all enor node occur [52] T { t : E () t = 0, R } = min t (12) N where the enor energy reerve E () t i defined a a monotonically decreaing function of time. Other alternative for the network lifetime are dicued in Section Reult In thi work, we monitor the network lifetime, the average hop count and the average energy pent per packet at each node. Thee value are calculated a follow. After the network etup phae, a communication tree i formed. Thereafter, for each enor, the communication path from itelf to the ink node i travered, and both the number of hop and the neceary communication energy i recorded. IA generated alway the ame routing tree in pite of varying overhead energy level becaue it ignored the effect of overhead energy during routing tree formation phae. For the effect of other imulation parameter like node denity and path lo exponent, the reader may refer to Chapter 4.

83 66 Average Packet Delivery Energy (mj) Ignore Conider Overhead Energy (mj) Figure 5.2. Average packet delivery energy veru overhead energy In Figure 5.2, we have compared the average energy load of a packet on the network. For each data packet generated at any enor node, the total energy diipation on the path toward the ink node i calculated. The graph how the average of thi total energy over all enor node in the network with repect to increaing overhead energy value. Since IA produced the ame routing tree, the average energy diipation increae linearly. However, CA wa able to find more energy efficient route reducing the total energy diipation for a packet to reach to the detination.

84 Ignore Conider Average Node Energy (mj) Overhead Energy (mj) Figure 5.3. Average node energy veru overhead energy 6 5 Average Hop Count Ignore Conider Overhead Energy (mj) Figure 5.4. Average hop count veru overhead energy In Figure 5.3, the energy diipation at each enor node i compared individually. In thi graph, we can clearly ee that enor node pend more energy when they are connected uing the routing tree found by CA. Although individual energy diipation i higher compared to IA, we have een in Figure 5.2 that the total energy diipation i le. Whenever the overhead energy become a ignificant element in the energy cot, the routing algorithm prevent unneceary hop and therefore the energy wate becaue of

85 68 overhead energy that i pent at each hop. The reult can eaily be een in Figure 5.4, where the average hop count in the routing tree i compared. The larger the overhead energy that i pent at each hop i the maller i the average number of hop in the network. 15 Ignore Conider Network Lifetime (day) Overhead Energy (mj) Figure 5.5. Network lifetime veru overhead energy In Figure 5.5, the network lifetime i oberved. It i obviou that increaing the overhead energy horten the lifetime, ince the energy diipation at the enor node become higher. In addition, we can oberve undoubtedly that ignoring the overhead energy parameter in routing calculation reult in uboptimal routing tree. A an example, conider τ = 50 mj. The network would be alive only 3.6 day where the routing tree i contructed uing IA. At the ame overhead energy level, CA would create a more efficient routing tree where the lifetime would increae up to 5.5 day, with a gain of more than 50 per cent. For a larger overhead energy value with τ = 100 mj, thi gain in network lifetime i nearly 65 per cent Concluion on the Effect of Overhead Energy The overhead energy i an intrinic component of energy diipation at enor node. In thi work, we have analyzed the effect of neglecting the overhead energy diipation in

86 69 routing deciion. Neglecting thi important factor during routing deciion may reult in wore routing alternative while promoting meaningle multi-hop communication link and reulting in a ignificant amount of energy wate. The network lifetime would decreae ignificantly if the routing algorithm doe not conider overhead energy diipation.

87 70 6. MULTIPLE SINK SENSOR NETWORK DESIGN PROBLEM One of the mot important deign criteria in wirele enor network i energy efficiency. The ytem deigner hould alway conider the limited battery power of the enor node at each network deciion. In thi chapter, everal network deign obective are preented. Each cae repreent another point of view to the energy aving conideration. Becaue of the deciion prioritie of thee obective, each of them require a different approach to derive an optimized olution. Here, we will tate deign iue that might be important for large cale wirele enor network, including everal deign criteria, routing alternative and redeployment cenario. After that, the imilaritie and difference with the claical concentrator location problem are preented. Finally, our problem i tated together with the olution technique Deign Criteria Before going into the deign obective, we have to introduce the criteria that are important in multiple ink enor network deign, uch a the number of ink, aignment of the enor node to the ink, bet location of the ink, and the underlying routing algorithm Number of Sink Since the ink node are expenive device, they hould be inveted economically. To explore the problem, we analyze the two extreme point. On one hand, we can ue only one ink node for the whole enor network. When the ize of the network increae, however, the average length of the path, or imilarly, the number of hop from the enor to the ink node will increae. Therefore, the energy diipation for each packet delivery increae a well. Thi will reult in a decreae in the network lifetime. On the other hand, we can aociate one ink per enor node, and locate thee ink very cloe to their aociated enor node. Thi time, the tranmiion energy requirement at the enor node will be at the minimum, which reult in the theoretical maximum enor network lifetime. Thi deployment trategy i clearly not meaningful in term of economical

88 71 invetment. The cot of each ink node i more than the cot of a enor node in the order of hundred or even thouand. Therefore, the number of ink node i an important deign criterion, which i directly dependent on the available budget reerved for the ink node, S c S D S (6.1) where S i any ink node, dedicated for the total ink invetment. S c i the invetment cot for that ink, and D S i the budget Network Lifetime Depending on the underlying application, the network lifetime can be defined differently. In a miion critical application like medical urgerie, healthcare ytem, or military application, the failure of even a ingle enor might be important. The lifetime i defined in thi cae a the length of time until the firt battery drain-out among all enor node occur [52]. T { t : E () t = 0, R } = min t (6.2) N where the enor energy reerve E () t i defined a a monotonically decreaing function of time (ee Definition 3.15). For general purpoe monitoring application, the reliability of the data retrieved from the environment become a good metric to define the network life. For example, we can define the ratio of the uncovered area to the whole area under invetigation a the reliability metric. Thi ratio ρ () t i a monotonically increaing function, ince the A uncovered area increae with time. When a predefined threhold value i reached we ay that the network i not reliable anymore. For critical application, we can et thi threhold value to a lower value, for inignificant application to a larger value.

89 72 ρ t uncovered area at time t = ρ total area A () Threhold (6.3) The etimation of the uncovered area i not traightforward, a the ening region of the enor node overlap. Therefore, ome approximation can be derived for the reliability ratio. For example, the number of unreachable node or imilarly the number of exhauted node can be ued for the etimation a given in Equation 6.4 and Equation 6.5. number of unreachable node at time t ρ U () t = (6.4) total number of node number of exhauted node at time t ρ E () t = (6.5) total number of node Routing The underlying routing method i another important deciion point. The energy diipation i cloely related with the routing method. On one extreme, the application might not be uing any routing method at all, ending the data packet directly to the ink node. Thi kind of communication will either require very powerful radio tranmitter at the enor node providing with a large radio range, or many number of ink node that are in the cloe neighborhood of the enor node. A more common alternative i uing a multi-hop ad hoc network infratructure. In thi cae, enor node forward the data packet of other enor node toward the ink node. The route are found conidering their correponding energy requirement. In order to handle the reult of any routing algorithm, we have defined in Section the path matrix given in Equation 6.6. i 1 if (, k) i ued on the path Pi p k = (6.6) 0 otherwie. where i N i an arbitrary initiator node, and S i an arbitrary ink node.

90 Cluter Member Whenever the deigner ha a prior knowledge on the available invetment budget for the ink node, the number of ink node that will be deployed can eaily be found. At thi time, the cluter hould be formed, indicating the enor-to-ink aignment. The enor within a cluter will be communicating with the ink node that i allocated for them. Thi cluter formation hould be performed according to the energy diipation of the enor. The ink node may have an internal boundary that limit the number of connected enor to themelve. The data that i queried from the enor and being forwarded to the control center may be exceeding the communication capacity of the ink node. Therefore, the cluter ize could have a practical limit a given in Equation 6.7 B K (6.7) where B i the branch et of the ink node S (ee Definition 3.10), and K i the ervice capacity of that ink. Uing Lemma 3.7 we can rewrite the obective a given in Equation 6.8 i p p k N i N k V K (6.8) where i p k i the path matrix Location of Sink We know that the number of the ink mut be kept a low a poible becaue of their invetment cot. Having decided on the number of the ink node, we form the cluter where thee ink are going to be reponible. In the mean time, we alo try to find the optimum placement for thee ink node within each cluter. Evidently, thee ink node hould be located cloe to the center of the enor node in each cluter.

91 74 Due to environmental retriction, there might be region where the ink node cannot be placed at all. Prior knowledge on uch location limitation hould alo be incorporated to the optimization problem. Moreover, the cot of placement on ome region may be different. Therefore, thi cot hould alo be incorporated into the optimization problem. Aume that ( x y) where c P, i a real valued regional placement cot, x, y R give the coordinate of the location. Then the total placement cot i given in Equation 6.9. S ( x y ) P P C = c, (6.9) Data Generation Rate The enor node generate monitoring reult with different rate for different application. For example, an agricultural or environmental monitoring application might require periodic data generation, where the up-to-date tatu of the field hould be monitored continuouly. However, on a warehoue management application, the data generation could be initiated on-demand at the data center. Thee on-demand querie could be detined to the whole network or to ut a ubet of the region a well. In addition, the data generation rate in a continuou monitoring application could alo be different throughout the region. When the deigner ha a prior knowledge on the environment, he may chooe to intall ome pecially tuned node, which generate more often meaurement at critical place. Therefore, the ink node might have been intalled cloer to thoe critical place, where more data packet are generated Energy Model Efficient ening circuitrie and computation algorithm help to reduce the ening energy and computation energy diipation on the enor node. The maor energy diipation component are tranmitting and receiving energy, which i dependent on the communication architecture and underlying technique. Therefore, power aware method mut be employed in order to reduce the energy conumption during communication. In

92 75 our work, we ue the energy model given in Section Thi energy model i very imple in the ene that it doe not provide detail on attenuation, fading, and multi-path propagation. The reader may refer to [53] if more detailed empirical and emi-empirical path lo power model are needed Routing Deciion Minimum Energy Tree Data flow from enor node to the ink node form a tree architecture, where the root of the tree i the ink node. When we conider a network with multiple ink node, then the tree i going to be diconnected, forming a foret. Every connection in the tree will be etablihed depending on the energy cot meaurement of that link. Uing thee connection, minimum energy path from every enor node to their correponding ink node are contructed. The collection of thee path form the minimum energy tree. In thi tree, we guarantee that each data packet reache to a ink node with the overall minimum energy diipation caued at the enor node. The obective i to find the minimum total energy diipation in Equation min E = a e (6.10) Total N k V k k where a k repreent the element of the adacency matrix of the minimum energy tree (ee Definition 3.5), and e k i the energy cot of the link between the node the network (ee Definition 3.3). N, k V in After the deployment of the enor network together with all the enor node and the ink node, the minimum energy tree can be calculated according to an energy cot metric. Thi tree, however, may need ome modification during the lifetime of the network. The enor node that are cloe to the ink node are loaded more compared to the leaf node, reulting in relatively higher energy conumption. The tree may be recalculated periodically, where only the node that have ufficient reidual energy will

93 76 participate a relay node. Thi retructuring can alo be triggered on demand, whenever a large area cannot be monitored due to ome node failure. Moreover, we can alo deploy additional node in the neighborhood of the failed enor node, or even replace thee node, whenever the underlying application allow Minimize the Maximum Energy Diipation at Senor Node The energy diipation at a enor node depend on the activitie performed by thi node. In our model, thee activitie include generating data packet and tranmitting them toward the ink node, and forwarding data packet that are generated by other enor node toward the ink node (ee Section 2.7.2). When we try to minimize the energy diipation at each node, the reulting connection form a minimum energy tree, a we have een above. In order to etablih a fair energy controlling mechanim on the network, we may rather try to pread the load over the network. A good mechanim to formulate thi obective i to try to minimize the maximum energy diipation at each enor node in the network. Therefore, whenever a node ha a large relaying load cauing more energy diipation, ome of the load i going to be tranferred to ome neighboring enor node, where the relaying load i le. The obective i given in Equation 6.11 min max { e } N (6.11) where e i the relay energy load of a enor node Lemma 3.9 we can rewrite the obective a given in Equation 6.12 N (ee Definition 3.12). Uing min max N S i N k V i p ke k (6.12) where i p k i the path matrix, and e k i the energy cot. Whenever the packet generation rate of the enor node are known, we can incorporate it into the obective to minimize

94 77 the maximum energy diipation during a given time period. Then the previou obective will be modified to reflect the time parameter a given in Equation 6.13 min max { () t } N e (6.13) where e () t i the total energy diipation of a enor node N during the time period t (ee Definition 3.15). Uing Corollary 3.6 we can rewrite the obective a given in Equation 6.14 min max N S i N k V i µ i p ke k (6.14) ( 1 ) where µ i i the average packet interarrival time (ee Definition 3.14), matrix, and e k i the energy cot. i p k i the path Thi mechanim will prolong the network lifetime, while preading the energy load over the whole network. In [52], a imilar approach i preented where the lifetime of each individual enor node i tried to be maximized, conidering the data flow in the network. A maor diadvantage of thi method i, however, the batterie of every enor node are going to be exhauted in a imilar manner. Therefore, the idea of redeploying additional enor node will not be economically feaible Minimize the Maximum Energy Path Another method to pread the energy load over the whole network could be to eliminate long path on the routing tree. A a reult, each enor packet could reach to the ink node through path where the total energy diipation for the packet to reach to a ink node i the obective function. In thi cae, we try to minimize the maximum total energy diipation for a data packet a given in Equation 6.15

95 78 min max i N, S { } ei (6.15) where e i the total energy diipation for a data packet from an arbitrary initiator node i i N arriving at a ink node S. (ee Definition 3.12). Uing Lemma 3.8 we can rewrite the obective a given in Equation 6.16 min max i N, S N k V i p ke k (6.16) where i p k i the path matrix, and e k i the energy cot Maximum Reidual Energy Path Whenever the routing tree in the enor network can be modified everal time during the lifetime, then the reidual energy at the enor node can alo be ued in routing deciion. The idea i to ue only thoe enor node a relay node, which have more energy compared to the other node. The obective i then to maximize the minimum reidual energy path in the routing tree. However, thi obective i contradicting with the minimum energy tree obective. The node that are on the minimum energy tree are going to be utilized more, where they cannot be ued in the maximum reidual energy path. Therefore, thi path will be more cotly in term of energy diipation at the relay node. The idea of conidering the reidual energy in routing deciion could be ued a a contraint, where only the node with ufficient energy are conidered a relay candidate Redeployment Scenario The network lifetime i cloely related with the number of enor node whoe batterie are exhauted. Therefore, in order to prolong the network lifetime, the invetor might chooe ome redeployment mechanim, whenever the underlying application doe

96 79 not phyically prevent it. After the redeployment phae, routing path hould be recalculated. There are everal alternative for the redeployment Random Redeployment The enor node could again be intalled without any electivity. The whole region will be under conideration. The number of new enor node will be a deign parameter, where eaily a percentage of the initial enor node could be ued Neighborhood Redeployment The new enor node could be intalled in the cloe neighborhood of the enor node having an energy hortage. Here, both the hortage and the neighborhood hould be defined before the redeployment phae. Moreover, the number of new enor node hould alo be clarified Replacement In thi cenario, the enor node, or only the batterie of the enor node are replaced one by one. Thi replacement could be performed periodically, conidering node that are cloe to be exhauted, or imilarly it could be on demand, whenever a node fail. The feaible replacement period and the level of battery hortage hould be clarified Redundant Deployment Whenever the redeployment of additional enor i not poible becaue of environmental contraint or high redeployment cot, the deigner might chooe to deploy redundant enor node, which tay idle until any neighboring enor die out. In thi cae, the deigner hould control the deployment of thee additional node while forecating the region where an energy hortage will occur.

97 Sink Location Problem Find the Bet Sink Location (BSL) In many real world deployment cenario, the deigner will have a predefined budget granted for the invetment. Therefore, the number of ink node i known prior to the deployment phae. Since we know the number of ink node, which repreent the number of cluter in the network, the only problem remain i the efficient clutering of thee enor node. We call thi problem a finding the Bet Sink Location problem (BSL). There are many good clutering algorithm in the literature. Several technique are preented in [54], and [55]. Mot commonly ued clutering algorithm are claified a hierarchical and non-hierarchical method. The non-hierarchical method are uually referred to a k-mean clutering. For an implementation of thi algorithm, the reader may refer to [ 56 ]. Another generic method i the elf-organizing map, which i a general-purpoe unupervied learning algorithm [57, 58]. None of thee method provide the optimum number of cluter that hould be formed. The number of cluter hould be given a a deciion parameter to the algorithm. Exact location of the ink node are eaily found when the clutering algorithm complete. Whenever the Euclidean ditance i ued a the clutering metric, then the center of ma of the node within a cluter would give the location of the ink node. Depending on the prioritie of the routing algorithm, power aware ditance metric, like Equation 2.6, could alo be ued Minimize the Number of Sink for a Predefined Minimum Operation Period (MSPOP) In ome application, the invetor might requet the enor network be operational for a predefined duration. For example, in agricultural application, the field mut be monitored until the harvet. Therefore, the enor network hould be reliable until the crop grow up, and are reaped from the field. The farmer i definitely going to deploy a

98 81 new enor network in the next eaon. We call thi problem a Minimization of the number of Sink node for a Predefined minimum Operation Period (MSPOP). In order to olve thi problem, we have to calculate the enor network lifetime for any number of ink node. Then, only the olution will be elected, where the network lifetime exceed the predefined limiting contraint, with the minimum number of ink node. The maor iue in thi problem i to elect the correct number of ink node. The brute force technique i to tart with only one ink node, a tated in [54]. While incrementing the number of ink node by one, the network lifetime i evaluated. The earch will top, whenever the deired lifetime i reached. Thi incremental earch might be too long, when the actual number of required ink node i large. In thi cae, the earch might tart at any point where the deigner ha a prior knowledge, where the reult nearly lie. Similarly, a binary earch technique could alo be ued. Starting initially from one, the number of ink node are doubled until a feaible olution i reached. Thereafter, the olution pace i narrowed down, by halving the interval, until the minimum number i found Find the Minimum Number of Sink while Maximizing the Network Life (MSMNL) We may alo try to extend the network lifetime a much a poible with the mot economical invetment. We call thi problem a Minimization of the number of Sink node while Maximizing the Network Lifetime (MSMNL). When we do not have a prior knowledge on the number of ink node nor the lifetime contraint, then we bring up a combinatorial optimization problem. In thi cae, the obective hould combine the two alternative within one function, where the budget reerved for the ink node hould omehow be connected with the lifetime of the enor node. The initial invetment for the enor node hould be utilized for the longet period. Here, the cot per unit time metric could be ued. In order to

99 82 reach the required timeframe, we may need to perform ome redeployment within the network. We hould add the cot of the redeployment to the initial invetment cot, which include both the enor and the ink node. The near-optimal olution for thi problem could be found uing ome heuritic technique, like imulated annealing or genetic algorithm Difference with Concentrator Location Problem The problem of finding the number and the location of the ink node reemble ome claical problem like plant location problem [59], warehoue location problem [60], and the concentrator location problem (CLP), which ha been received a great interet in the literature [61-67]. There are, however, everal difference between thee problem and the multiple ink location problem. In thee problem, although the location of the central node are unknown, a lit of poible location i given. Locating the central node to thee place ha a varying cot, which i combined with the cot of the central node, hindering the deigner from chooing many number of them. In our problem, however, the ink can be placed everywhere in the environment, without having a prior knowledge. Therefore, enumeration of the location alternative i not poible. The communication between the enor node and the ink node are performed uing multi-hop link, which are going through other enor node in the network, wherea in CLP, the connection are through direct link. In addition, all thee intermediate enor node hould alo be connected to the ame ink node. The capacity of the central node i a contraint in CLP. Direct connection to the central node cannot exceed their capacity. In our problem, the ink node alo have a predefined capacity, a the enor node are communicating with the ink node through wirele link. However, the capacity i only related with the ize of the data proceing power of the ink node, rather than the direct communication link between the enor node and the ink node. Uing multi-hop connection, the number of enor node that are actually connected to any ink node i more than the number of direct connection.

100 A Solution Technique for the MSPOP Problem After dicuing the iue related to the multiple ink enor network deign and liting alternative problem, in thi ection, we will conider particularly the MSPOP problem and propoe a olution technique. 1. Deploy the enor node 2. Wait until the enor node find their location information 3. Collect the location information from the field 4. k = 0 5. Repeat i. k = k + 1 ii. Find the bet location for k ink node iii. Etimate the network lifetime 6. Until required network lifetime i reached 7. Output the ink location, and the etimated lifetime Figure 6.1. Sytem deign algorithm Thi problem i by nature an off-line problem, which hould be olved by the ytem deigner at a central location. Therefore, the location information of the enor node hould be collected from the field, before the olution phae. The algorithm of the ytem deign phae i given in Figure 6.1. In the following ection, each tep of thi algorithm i explained in detail Deployment of the Senor Node Depending on the underlying application, there may be everal alternative on enor network deployment. In an agricultural application, they might be cattered by the farmer, in a nearly uniform manner. In an environmental application like foret fire detection, they might be dropped from an aircraft. In in-houe application, they might be intalled by the contruction worker by hand. Neverthele, the clutering algorithm that i ued in Step 5.ii in Figure 6.1 hould be able to deal with thee deployment cenario. In addition,

101 84 we alo might be uing everal different clutering algorithm, each one optimized for another deployment type Finding Location Information In order to calculate ink location, we mut know the location of each individual enor node. Location information can eaily be derived, uing central or ditributed method (ee Section 2.3). If we ue a central approach, we can continue our algorithm with Step 3 in Figure 6.1, where the central agent can perform an off-line location etimation. The energy diipation at the enor node for the location finding proce i not conidered in thi problem Collecting the Location Information from the Field After the deployment of the enor node, we can ue a mobile terminal to collect the location data, which travere the field. If we do not have uch a pecial purpoe terminal, then we have to intall a ink node temporarily. We can take thi ink node back during final deployment phae. When thi i not poible due to phyical limitation of the application, then we can chooe to ue thi node a a fixed ink node in the final deployment, and conider thi node in the clutering algorithm, without moving it Finding the Bet Location for K Sink Node If the number of ink node i known, then we have the problem defined in Section The clutering algorithm i reponible to locate the ink node uccefully. Depending on the deployment ditribution, we can chooe different clutering algorithm at thi tep. In our implementation, we have ued the well known k-mean clutering algorithm [55, 56] Etimating the Network Lifetime In order to fulfill the time contraint, we have to etimate the network lifetime, with the ink location propoed at Step 5.ii in Figure 6.1. The detail on network lifetime are

102 85 given in Section 6.1.2, where we have defined everal reliability metric. In our implementation, we have ued the ratio in Equation 6.4. We ue a imulator to find out when the predefined reliability threhold i exceeded for the etimation of the lifetime. Thi imulator hould conider the packet generation rate, which i an application criterion, enor node hardware pecification, like the battery capacity, communication data rate, overhead energy, tranmitter power requirement, and environmental characteritic, like the path lo exponent Computational Experiment on Multiple Sink Senor Network Problem In thi ection, we try to give two example of multiple ink enor network deign problem. Firt, we will provide a demontrative example for the BSL problem on a ample enor network with three ink node. After that, we will conider the MSPOP problem and how the application of the olution technique decribed in Section 6.6 with everal enor network deployment Simulation Setup In our imulation, we only ue enor node having power adutable tranmitter circuitry, P cont node. Thee node have a power level adutment capability on a continuou cale. In imulation, however, we have ued 20 dicrete power level intead, to approximate continuity. In Chapter 4, we have hown that uing thi type of circuitry, we can eaily double the lifetime of each individual enor node. Here, we focu on the number of ink node, and try to derive a relation between the network lifetime. The imulation are performed on the tet bed developed in Chapter 4, uing Opnet Modeler [49]. The ample enor network conit of 200 node, which are ditributed uniformly over a planar quare region with 200 m x 200 m dimenion. Although the amount of node and the area ize are rather mall, the technique can be applied eaily to larger network both in area ize and node quantitie.

103 86 The enor are aumed to ue 800 mw tranmiion power for a 200 m radio range in open air ( α = 2 ). Thee value are choen, a they are very cloe to the Berkeley/Crobow Mica Mote pecification [8]. However, we have caled the radio range for our imulation environment where we ued a contant path lo exponent value with α = 3. For the effect of different path lo exponent value on energy diipation, the reader may refer to Chapter 4. Here, the overhead energy τ i choen to be 20 mj per packet, where 400 mw receiver power i aumed. Here, both ening and computation energy are neglected, ince they do not affect our deign deciion. The data rate of the communication channel i choen to be 20 kbp, and a fixed packet ize of 1024 bit i ued. Thee imulation aumption are ummarized in Table 6.1. Table 6.1. Simulation parameter Parameter Sample tranmiion power Sample tranmiion range Data rate Packet ize Minimum tranmiion power Maximum tranmiion power Initial battery capacity Simulation time Area ize (A) Value 800 mw 200 m 20 kbp 1024 bit 100 mw 2,000 mw 200 J 60 day 200 m x 200 m Path lo exponent (α) 3 Number of enor node 200 Reliability threhold (ρ) 0.25

104 87 The lifetime i defined to be related with the number of unreachable enor in the network. We conider the reading of the network to be unreliable anymore, whenever the ratio of the unreachable enor exceed thi threhold value, with ρ = The initial battery capacity of the enor i choen to be 200 J. In [51], it i given for an alkaline-manganee dioxide battery that the typical volumetric energy denity i 428 watt hour per liter. In other word, a battery of ize one cubic centimeter would have the capacity 1540 J. However, we have choen the maller value to horten the imulation time. The behavior of the imulation will not change, ince the battery capacity only caue the reult to appear earlier. A a conequence, we have alo choen a hort imulation time, 60 day. The enor are aumed to perform independent reading, and therefore independent packet generation. The packet generation proce i aumed to be a Poion proce with rate λ = 1 packet per hour, where we aume a continuou monitoring application. Neverthele, here a periodic proce could alo be choen where the enor are polled with a predefined frequency Demontrative Example for the BSL Problem In thi problem, we are given a enor network. We try to locate three ink node accordingly to reach the maximum operation time. The network i hown in Figure 6.2. In thi figure, a olution for three ink i alo preented, where the location of the ink node are marked with mall triangle ( ). The location of the ink node are found uing the well known k-mean clutering algorithm [55, 56]. After the deployment phae, we tried to etimate the network lifetime. For thi, we contructed the routing tree, where the minimum energy tree approach i ued, with the energy metric given in Equation 2.6. Then, we monitored the energy map and the diconnected region map of the network. The energy map indicate the region, where an energy hortage occur, uing io-energy contour. The darker the contour are, the le energy reource i preent in than region. After a period, ome node tart to become exhauted, and therefore all the node in the branch et of thi node will be diconnected

105 88 (ee Definition 3.10 for the definition of branch et). The diconnected region map how thee diconnected node due to energy failure. Figure 6.2. Sample enor network with 200 enor and three ink In Figure 6.4, we how a erie of energy and diconnected region map, where we have taken naphot of the enor network once every 10 day. The map on the left ide are the energy map, and the one on the right ide are correponding diconnected region map. In the energy map, the darkne of the region repreent the energy hortage at thoe node. In the diconnected region map, haded region repreent unreachable region in the network. We oberve here, that the diconnected region increae, a time goe by. Thi behavior i expected, ince the energy reerve of the enor decreae during operation. Energy hortage occur at node, who erve a large branch a a relay node. None of the leaf node encounter an energy problem, however, ome of them cannot reach the ink node a they become diconnected becaue of failure in the relay node. We oberve early failure at enor that are cloe to the ink node, ince they erve a larger branch et.

106 89 (a) Energy map, after day 10 (b) Dic. region map, after day 10 (c) Energy map, after day 20 (d) Dic. region map, after day 20 (e) Energy map, after day 30 (f) Dic. region map, after day 30 Figure 6.3. Energy and diconnected region map, until the 60 th day

107 90 (g) Energy map, after day 40 (h) Dic. region map, after day 40 (i) Energy map, after day 50 () Dic. region map, after day 50 (k) Energy map, after day 60 (l) Dic. region map, after day 60 Figure 6.4. Energy and diconnected region map, until the 60 th day (continued)

108 91 Figure 6.5. Exhauted node veru time Figure 6.6. Unreachable node veru time In Figure 6.5, we how the increae on the number of exhauted node. We oberve the firt failure at the 15 th day. The failed node ha 12 node in it branch et. Therefore, the firt failure caue 11 other functional node to become diconnected. The number of unreachable node can be een in Figure 6.6. Uing thi figure, we can tate that the

109 92 network produce reliable reading only for 24 day, where we pa the threhold for the number of diconnected node, with ρ = Figure 6.7. Unreachable node veru time uing rerouting Figure 6.8. Exhauted node veru time uing rerouting

110 93 In Figure 6.4, we oberve that not every enor node that i cloe to ink node fail, ince thee node may have a very mall number of enor node to erve. Therefore, we can expect that recontructing the minimum energy tree after energy failure could prolong the network lifetime. In order to verify thi expectation, we have modified the monitoring proce. Whenever the reliability threhold i reached, the ink node initiate a new route finding proce, o that exhauted node could be removed from the routing tree, and all other diconnected node have another chance to be connected to the ink node through ome other intermediate node. The reult are hown in Figure 6.7 and Figure 6.8. The number of unreachable node are increaing up to the reliability threhold, with ρ = At that point, a new route recalculation proce i initiated and the network urvive until the next route recalculation phae. Thee recalculation take place with an increaing frequency, ince the remaining battery power on the intermediate enor node decreae with time. Finally, route recalculation cannot build a reliable network anymore, and the network die. The firt recalculation take place at the 24 th day, wherea uing ucceive recalculation, we can utilize the network until the 55 th day, which increae the lifetime more than double Application of the Solution Technique to the MSPOP Problem In thi ection, we perform imulation on multiple, uniformly deployed enor network, and try how the application of the olution technique for the MSPOP problem. We tart with one ink node, and increae the number of ink node by one at every tep, where the location of the ink node are found uing the k-mean clutering algorithm [55, 56]. After each deployment alternative, we tried to etimate the network lifetime. In Figure 6.9, we how the percentage of exhauted node, where the number of ink node i varying from one up to ix. The cluter ize decreae with increaing number of ink node. Therefore, the path from each enor node to the ink node will be horter in the reulting minimum energy tree. A a reult, energy diipation due to packet relay decreae, therefore the percentage of exhauted node decreae. In Figure 6.10, the percentage of unreachable node i hown. When the number of ink node i mall, then the percentage increae very rapidly within the few day. Then,

111 94 only the node that are cloe to the ink node urvive. Moreover, ince thee node have a relatively le relaying load, their batterie are exhauting rather low. Figure 6.9. Percentage of exhauted node veru time, with different number of ink Figure Percentage of unreachable node veru time, with different number of ink

112 95 Table 6.2. Expected network lifetime, with ρ = Number of ink node Lifetime (day) > 60 A the olution of our problem with ρ = 0. 25, we have to be given a minimum deired network lifetime. If thi period i required to be one month, then it i clear that we have to utilize four ink node. When thi period i required to be at leat two month, then the number of required ink node increae to ix. Table 6.2 ummarize the expected network lifetime for each number of ink node. Figure Comparion of random placement with k-mean algorithm, with three ink

113 96 With a further tet, hown in Figure 6.11, we have checked the quality of the reult of k-mean clutering algorithm. For the network where we have three ink node, we have randomly located thee node, and compared the percentage of the unreachable node with repect to time. We have een a crucial decline in the reult. The network lifetime, with ρ = 0.25, decreae to 13 day, compared to 24 day for k-mean clutering. Therefore, we can conclude that a mart ink location and clutering algorithm ignificantly improve the network lifetime. Although k-mean algorithm ue the imple Euclidean ditance metric to form the cluter, it generate high quality reult compared to random ink location. When we can introduce energy-aware cot metric into our clutering algorithm, we hould expect reult that are more powerful. Figure Change in the number of ink for different network lifetime requirement In Figure 6.12, we have analyzed the change in the neceary number of ink node where we have increaed the number of deployed enor node and the area of the monitored region, while keeping the enor denity contant. We have computed the neceary number of ink node for three different network lifetime requirement with 10, 20 and 30 day. A we alo learned from previou experiment, we have een that higher network lifetime requirement force more ink node to be deployed. Moreover, we ee

114 97 that when we have a larger area, then we have to deploy more ink mode in order to keep the network alive. The mot intereting reult i that, independent of the required network lifetime, the relation between the number of enor node and the number of neceary ink node i found to be linear, where the lope of the line i related with the underlying application deign criteria like the network lifetime requirement, data generation rate and model, network reliability threhold ρ, etc Concluion for the Computational Experiment In order to maximize the lifetime of a enor network, energy reource of each individual enor node mut be conumed effectively. In large-cale enor network, the network mut be divided into maller ub-network, not only to increae manageability of the network, but alo to increae the network lifetime. We have introduced the multiple ink network deign problem, where the bet place for the ink node hould be calculated depending on everal different deign criteria. We have lited thee deign iue together with their formulation. We have dicued everal routing alternative, redeployment cenario, and ink location problem. We have demontrated a ample ink location cae, where the number of ink node wa known before the deployment phae. We have implemented the olution for thi BSL problem, and preented the correponding energy and diconnected region map on a ample enor network for different naphot in time. We have oberved how the diconnected region increae with time. We have encountered with failure at the enor node that are cloe to the ink node, becaue thee node have erved a larger branch et. However, not every enor node that i cloe to ink node fail early, ince thee node might coincidentally have a very mall number of enor node to erve. We have een that recontruction of the minimum energy tree after energy failure occur prolong the network lifetime ignificantly. We have alo propoed a olution technique for the MSPOP problem, and imulated it implementation on random enor network. We have analyzed the effect of adding new ink to the network lifetime. We have preented method to deploy economically feaible amount of ink node while prolonging the network lifetime. We have hown that

115 98 k-mean clutering algorithm provide good ink location. In addition, we have een that the relation between the number of enor node and the number of ink node i linear.

116 99 7. CONCLUSION AND FUTURE WORK 7.1. Concluion One of the mot important deign criterion in wirele enor network i the energy contraint in enor node. In order to maximize the network lifetime, energy reource of each individual enor node mut be managed effectively. In thi thei, we try to develop technique for controlling the total network lifetime. Firt, we have derived new formulation for the multiple ink enor network deign problem. Important characteritic of the enor network infratructure have been analyzed and the neceary definition have been introduced. Thee definition and formulation can be ued in any enor network reearch ince it provide a framework that i independent of the underlying routing algorithm. We have hown that uing multi-hop path that conit of horter link intead of one long link might reult in coniderable energy gain. When the enor node are equipped with tranmitter circuitry that can adut it output level, the enor lifetime can eaily be doubled on the average. We have derived technique, where multi-hop link are more advantageou. We have een that the degree of hopping hould decreae whenever higher overhead energy value are under conideration. We have tudied different multi-hop communication cenario and calculated the energy aving in each cenario. We have alo expanded thee cenario to general cae. The generalization can be applied into any arbitrary triangle and can be ued in energy optimized route calculation. We have analyzed the effect of overhead energy in routing deciion, which i an intrinic component of energy diipation at the enor node. We have een that neglecting thi important factor during routing deciion may reult in wore routing alternative while promoting meaningle multi-hop communication link and cauing a ignificant amount of energy wate. The network lifetime would decreae ignificantly if the routing algorithm doe not conider overhead energy diipation.

117 100 Finally, we have conidered locating multiple ink node to the enor environment and dividing the network into maller ub-network. We have introduced related problem, where the bet place for the ink node hould be calculated depending on everal different deign criteria. We have lited thee deign iue together with their formulation. We have dicued everal routing alternative, redeployment cenario, and ink location problem. Uing a demontrative example, we have hown the olution for the BSL problem, and preented the correponding energy and diconnected region map on a ample enor network for different naphot in time. We have oberved how the diconnected region increae with time. We have alo propoed a olution technique for the MSPOP problem, and imulated it implementation on random enor network. We have analyzed the effect of adding new ink to the network lifetime. We have preented method to deploy economically feaible amount of ink node while prolonging the network lifetime. We have een that the relation between the number of enor node and the number of ink node i linear Future Work There are everal point that might be conidered a a future reearch direction. The enor might have a maximum load limit, which will give the number of enor node that are within their branch et. Uing thi contraint, premature battery exhaution might be prevented. The invetor can chooe ome redeployment during the operation of the enor network. After the redeployment, the routing tree hould be recalculated. The effect of thee redeployment hould be analyzed in term of the network lifetime. The efficiency of the clutering algorithm under different enor deployment hould alo be analyzed. When the enor are deployed non-uniformly rather than being uniform, pecial clutering algorithm might produce better reult.

118 101 APPENDIX A: OPNET IMPLEMENTATION DETAILS Opnet Modeler i a dicrete-event network imulator commercially available ince 1987 [49]. Uing it proce and node modeling capability, and it interface with open C/C++ code library, real-world network cenario can eaily be implemented. In the following ection, wirele enor network implementation detail are preented. A.1. Wirele Senor Network In Figure A.1, a ample cenario i hown. In thi imple network, three different node are ued, enor node, ink node and a configuration node. Senor node are labeled tarting from 1 to 16, ink node are labeled a 91 and 92, finally the configuration node i labeled a conf. Figure A.1. Sample wirele enor network cenario In thi cenario, the node are cattered randomly to a region of ize 1000 m x 1000 m. Although the node placement here i performed manually, the

119 102 configuration tep can catter the node to the area according to a given probability ditribution. A.2. Node Model Both the enor and the ink node are of identical tructure, each with the following node model (ee Figure A.2). The node model contain building block, which repreent individual procee, and connection link, which determine the data flow between the building block. The data flow occur mainly through packet tranfer. Each proce i repreented uing a finite tate machine (FSM), where each tranition between tate occur mainly through interrupt. Figure A.2. Senor node model The model i baed on the ISO OSI 7 layer architecture [50], which conit of an antenna interface, radio tranmitter and receiver, data link layer, network layer, and the

120 103 application layer. The application layer ummarize all the tak of the upper four layer, a their functionality are not a part of thi thei. Senor device are coupled with wirele communication capability through the antenna interface. Thi interface can be modified to preent any directional antenna pattern. However, an iotropic antenna pattern i ued in our imulation. An iotropic pattern radiate (or capture) power equally in all direction. For more detail, the reader can refer to [49]. The antenna interface i connected to the radio tranmitter and radio receiver interface. Thee interface are providing the node with wirele communication link. For each communication, Opnet create a link from the ource node to the detination node. All the node that are in the range of the ource node can receive the data packet imultaneouly. Different imulation parameter can be aigned to the radio interface repreenting the wirele medium, uch a background noie, interference noie, ignal-to-noie ratio, bit error rate, and the radio characteritic, uch a error control code, power model, and modulation type, communication frequency and data rate. Data link layer control the radio interface, and propagate data packet from network layer to the radio interface. In addition, data packet retrieved from the radio receiver are forwarded to the network layer. The network layer control all the routing operation. Data packet that are retrieved from other enor node are forwarded toward a ink node. If a multi-hop connection i etablihed between the enor node and the ink node, then the next-hop enor node i detined. Application layer conit of two part, the ource and the ink. The ource part mimic the behavior of the enor. The enor i aumed to extract information from the environment. Thi information i thereafter encapulated within a data packet and forwarded to the network layer, which i reponible for ucceful delivery of thi packet to a ink node. Senor can create packet with any probability ditribution, which i alo a imulation parameter. The ink part may be configured to receive any application pecific

121 104 etup parameter, uch a ening behavior or battery control trategy, it can alo generate a repone for querie initiated by the control center. In thi implementation, the ink part only collect the neceary imulation tatitic. A.3. Network Layer Proce Model The network layer i the interface between the application layer and the data link layer. Thi layer ha the following maor tak: (i) Forwarding data packet generated by the enor unit to the network (ii) Accepting the etup packet from the network, and delivering it to the internal proceor (ink). (iii) Control all the routing operation, forwarding data packet that are retrieved from other enor node toward a ink node. Figure A.3. Proce diagram for the network layer The FSM for thi operation i hown in Figure A.3. The FSM tart with the big arrow, pointing the wait tate. Thi tate perform a delay until the other procee in the imulation are initialized. Thereafter, the initialization tep follow with the init tate, where the control variable are loaded. Then the proce enter the idle tate and wait here

122 105 until a pecific interrupt arrive. The packet interrupt are SRC_ARRVL and DLL_ARRVL, which repreent the packet arrival from the ource and the data link layer repectively. A third interrupt i RT_DISC, which repreent a route dicovery requet, mainly generated by a ink node in the network. Senor node, however, have alo the ability to initiate route dicovery proce, in order to initiate incremental route update. Depending on the interrupt type, the FSM enter into three different tate: (i) xmt tate: When a packet from the ource proce arrive to the network layer, then the SRC_ARRVL interrupt i triggered. Then the FSM enter to the xmt tate, where the packet i forwarded to the data link layer. During thi tranaction, the packet header i filled with the neceary information, uch a the next-hop id to reach to the ink node. (ii) route tate: When a packet from the data link layer arrive, the proce enter to the route tate, after having received the DLL_ARRVL interrupt. Here, mainly another enor node packet i forwarded toward the ink node, by uing the next-hop enor node. When the packet i found to be detined to itelf, then the packet i ent to the ink proce. Here, the neceary etup parameter may be extracted or any query order may be obeyed. (iii) dicover tate: Route dicovery requet arrive through the interrupt RT_DISC. Then, the dicovery packet are forwarded to neighboring enor node depending on the routing algorithm. The FSM can alo enter into thi tate, when another route dicovery requet arrive to the enor node from a different node in the network. Any other interrupt that i arriving to the FSM while it i in the idle tate i ignored, and the FSM tay in the ame tate until an expected interrupt come. Having proceed thee interrupt, the FSM return back to the idle tate, where wait for a further interrupt. A.4. Data Link Layer Proce Model Data link layer connect the network layer with the phyical layer where the radio tranmitter and receiver are located. Correponding FSM i hown in Figure A.4. The actual functionality of the data link layer together with the MAC layer i not implemented here, becaue the reult that the imulation are examining were independent of thi

123 106 functionality. Anyone, who eek for a detailed data link layer or MAC layer functionality, however, can eaily replace thi layer with a detailed implementation. Figure A.4. Proce diagram for the data link layer After the two delay tate wait_0 and wait_1, where the FSM wait until other procee to be initialized, the config tate follow. Here, again the initial configuration parameter are loaded that are neceary for the imulation. Then the FSM enter the idle tate, where it wait until a pecific interrupt arrive. Here, only new packet arrival create an interrupt for thi proce. Therefore, any other interrupt i ignored and the FSM tay in the idle tate, when an unexpected interrupt arrive. The packet interrupt are NWL_ARRVL and RX_ARRVL, which repreent the packet arrival from the network layer and the radio receiver repectively. Depending on the interrupt type, the FSM enter into two different tate: (i) xmt tate: When a packet from the network layer arrive to the data link layer, then the NWL_ARRVL interrupt i triggered. Then the FSM enter to the xmt tate, where the packet i forwarded to the radio tranmitter. (ii) up tate: When a packet from the radio receiver arrive, the proce enter to the route tate, after having received the RX_ARRVL interrupt. The packet i then forwarded to the network layer, where a deciion on the next-hop detination of thi