DAG based In-Network Aggregation for Sensor Network Monitoring

DAG based In-Network Aggregation for Sensor Network Monitoring Shinji Motegi, Kiyohito Yoshihara and Hiroki Horiuchi KDDI R&D Laboratories Inc. {motegi, yosshy, hr-horiuchi}@kddilabs.jp Abstract Wireless sensor network monitoring is important for network maintenance, since it keeps the observer aware of node failures, resource depletion etc. Since communication overheads increase if the sink collects data individually from all sensor nodes, in-network data aggregation methods have been proposed which reduce the overheads. They form a routing tree and data follows up from the edge of the tree to the sink. However, in the event of heavy packet loss, the error margin of the collected data received by the sink grows. Furthermore, when the assumed hop count of the edge of the tree is smaller than the actual count, data can not be followed up from the edge. For the reasons mentioned above, observers find it problematic to assess the state of the network, since the error margin increases as the accuracy of the collected data falls. In this paper, we propose a new in-network aggregation method for sensor network monitoring. The method provides fault tolerance for packet loss by forming a Directed Acyclic Graph (DAG), which allows a node to have multiple parent nodes. In addition, the method can ensure correct data transmission timing, according to the actual hop count of the edge of the DAG. Furthermore, we evaluated the proposed method in comparison with the existing methods, from the perspective of the error margin of the collected data. 1. Introduction The availability of micro-sensors and low-power wireless communications will enable the deployment of sensor networks for a wide range of new services to support user activities [1]. These networks are likely to be composed of many distributed sensor nodes, using unreliable wireless links by default, equipping sensors (e.g. light, sound and motion), functioning self-configurable, and in many cases, without access to renewable energy resources. Thus energy saving is one of the relevant issues for achieving long-lived networks [2]. There is another major issue, which is the improvement in the accuracy of the collected data [3], since obtaining accurate data is the primary objective of the observer. This represents a challenge for sensor networks: to improve their ability to match the actual value of the quantity being collected. A monitoring function will be a crucial component of a deployed sensor network [4]. Such a function indicates node failures, resource depletion, and other abnormalities. Instead of extracting individual node data, aggregations such as average, minimum, maximum, and sum are useful for a statistical understanding of the network status. Hence in-network aggregation methods have been proposed [5][6][7]. They target data reduction through in-network processing, whereby data correlations are exploited to reduce the overall size of the data, and also communication costs at the same time. The methods form a routing tree, of which the root node is a sink (a node placed in a sensor network for data collection). Data follows up from the edge sensor nodes of the tree to the sink. Data transmission timing is set up based on the assumed hop count of the edge. By overhearing messages, nodes learn of potential parent that is one hop smaller than own hop count to the sink. They also learn of children, whose hop count is one hop larger than own count. To specify the in-network aggregation in more detail, a node computes statistical data (e.g. the minimum value) using data received from its children as well as its own, and sends this to its parent. However, since actual wireless links are weak, some of the transmitted packets are lost [9], and such packet loss results in loss of aggregated data of multiple sensor nodes. Consequently, the error margin of the data that the sink receives also increases. When this occurs and adversely affects the accuracy of the collected data, the observer actually monitoring the sensor network finds it difficult to assess the accurate state. Furthermore, when the assumed hop count of the edge (this hop count is termed here to be the maximum hop count) is smaller than the actual count, the error margin also grows, since it is difficult to tune the data transmission timing for nodes (with a hop count exceeding the assumed hop count).

In this paper, we propose a new in-network aggregation method for sensor network monitoring. The proposed method forms a Directed Acyclic Graph (DAG), that allows a node to have multiple parents, and collect data using the DAG. Tolerance to packet loss is targeted by using multiple parents as intermediate nodes. Although this method uses multiple parents, it avoids aggregation from the same. When nodes compute a sum of certain data as the in-network aggregation, the avoidance is important, because if multiple parents aggregated the same data, it would be added repeatedly: meaning the computed sum would exceed the actual sum. In addition, the data transmission timing adapts itself to the actual hop count of the edge of the DAG. Through simulation studies, we evaluate the proposed method from the perspective of the error margin of the collected data. The paper is organized as follows. In Section 2, we discuss the existing methods and their problems. In Section 3, we propose a new in-network aggregation method. In Section 4, we evaluate the proposed method using simulation studies. Finally, we present conclusions in Section 5. 2. Existing methods and their problems In this section, we review existing methods concerning in-network aggregation and the data transmission timing control. 2.1 In-network aggregation Existing methods concerning in-network aggregation focus on composable computations, i.e., if W1 and W2 are two disjoint sets of values, then the computation f satisfies the property f(w1,w2) = g(f(w1), f(w2)) for some known function g. Average, sum, minimum and maximum are all examples of composable computations. The sum computation is not only used to calculate the average but also for monitoring the number of sensor nodes. When the number of nodes decreases, the observer is then aware of the failure and can start implementing maintenance activity (e.g. changing the failed nodes). When computing sums, we have to focus on avoiding multiple additions of the same data. Using Figure 1 (a), we show an example. In Figure 1 (a), node A broadcasts V A that is the same as its own data v A (Fig. 1(a) (2)). Node B aggregates the receiving of V A and its own data v B, namely, it calculates the sum of V A and v B (Fig. 1(a) (3)). Node B sends the sum V B (= V A + v B ) toward its parent D (Fig. 1(a) (4)). Node C also aggregates the receiving of V A and its own data v C, and sends V C (= V A + v C ) toward its parent D. As a result, the parent D adds the same data V A twice over (Fig. 1(a) (7)). In this way, when multiple parents treat the data of a child, it results in multiple additions. Thus, Data transmission Wireless link (6)V C C D (7)V D = v D +V B +V C = v D +v B + v C +2 v A (4)V B Aggregated Data (2)V A (5)V C = v C +V A (3)V B = v B +V A Network property of (1)V A = v A A node B Sensor node (6)V C with reference to [5], each node broadcasts data specifying one of the parents. For example, in Figure 1(b), node A broadcasts data which includes the ID C of specifying one parent. Node C aggregates the data from node A, but node B discards it. Therefore, this method can avoid the problem of multiple additions. However, when the node C is unable to receive V A due to a failure of wireless transmission, node D receives data that has not had V A added. As a result, the method involves a problematic increase in the error margin of the data received by the sink. Although the number of nodes is small in the example, even if node A has child nodes (the number of child nodes is M), and each child node has further child nodes (the number of child nodes is N), then the sum of missed V A is sum of (M x N + 1) nodes. Therefore, one of the issues in in-network aggregation is collecting accurate data by targeting tolerance of wireless transmission failure (termed as Issue I). With reference to [7], a node sends half the value of its own data to two parents. Although the ability of at least one parent to receive guarantees that at least half the value is retained, this method encounters the same problem. In this paper, we describe the sum computation and omit other computations, because other computations can be processed easily. B (a) Example of duplicate aggregation problem. C (5)V C = v C +V A D (2)(C,V A ) A (7)V D = v D +V B +V C = v D +v B + v C + v A (4)V B B (3)V B = v B (1)V A = v A (b) The example of solution by specification of one parent node. Fig. 1 Example process of the existing method for in-network aggregation.

2.2 Data transmission timing control In-network aggregation begins following up from the edge of the tree to the sink, since parent nodes need to aggregate the data of their child nodes before they send data. Therefore, the data transmission timing of child nodes is earlier than their parent nodes. For example, the data transmission timing of node C in figure 1 (b) becomes namely, the point after it has received data from the child node A. Consequently, the timing shifts according to the number of hop counts to the sink, whereby namely, data are transmitted in turn from the largest hop count nodes (at the edge of the tree). To achieve such transmission timing control, various methods have been proposed [6][7]. The timing is set up when the sink broadcasts a request message (known as REQ) to the entire network which orders the start of the data collection. The data collection frequency T, the data transmission delay between nodes, etc are specified in the REQ. A node, with a hop count of n, waits for T(n) wait (given by the following formula) after receiving the REQ. Subsequently, it transmits an REP message including aggregated data. Following the transmission, the node transmits the REP at intervals of T. T (n) wait = 2T - 2 ( n) For example, node A (with a hop count of one) receives an REQ after progress from the time at which the sink transmitted the REQ. The node waits for T (1) wait = (2T - 2 ) and then sends an REP. The REP transmitting time is after ( + 2T - 2 ) from the time at which the sink transmitted the REQ. When the hop count is two, node B receives the REQ after 2 progress: from the time at which the sink transmitted the REQ. The node waits for T (2) wait = (2T - 4 ) and then sends an REP. The REP transmission time is after (2 + 2T - 4 ). Thus, data transmission timing of the node B is faster than its parent node A for (= (2 + 2T - 4 ) - ( + 2T - 2 )). In this method, the maximum hop count has to be assumed as T/, that is a maximum hop count in T (n) wait > 0. However, when the assumed hop count T/ is smaller than the actual count, it is difficult to tune the data transmission timing for nodes (with a hop count exceeding T/ ). As a result, the error margin of the data received by the sink grows, because it will receive data which does not reflect their data. Therefore, the ability of each node to tune oneself to the timing correctly remains an issue, even if the assumed hop count differs from the actual count (termed as Issue II). [8] is another method that does not use the waiting time. However, the drawback of the method is that a number of additional REP messages are transmitted to extract the first data collection. Sink Sensor node B C D A Wireless communication area of node A Packet loss rate from node A to parent nodes B, C and D:p=0.2 Success rate at least one of parent nodes can receive:(1-0.2 3 )=0.99 Success rate of specifying one parent node:(1-0.2 1 )=0.80 Fig. 2 Example of increased success rate when two or more parent nodes are used. 3. Proposal of a DAG-based in-network aggregation method We propose a new in-network aggregation method, which solves Issues I and II, for sensor network monitoring. Specifically, the proposed method works on the basis of the following primary design principles: (1) The formation of a Directed Acyclic Graph (DAG), which allows a node to have multiple parents, for data collection. The multiple parents provide tolerance to wireless transmission failure as intermediate nodes. (Solution for the Issue I ) (2) Extending data transmission timing control for tuning correctly according to the actual hop count on the edge of the DAG.(Solution for the Issue II ) 3.1 In-network aggregation using multiple parents Based on the design principle (1), the proposed method forms DAG and collects data using multiple parents. The multiple parents aggregate data from a child node, although they do not process in the case of the existing method [5]. Thus a success rate, represented by one of the parent nodes successfully receiving data from a child node, is set to (1-p n ): n is the number of parents and p is the packet loss rate of the wireless links. The success rate exceeds (1-p 1 ), which is that of the existing method. Comparing another method, the success rate is the same in the case where a node retransmits the data (n-1) times to a single parent. The proposed method achieves the rate without the power consumption actual retransmission would require, and provides tolerance for wireless transmission failure. Figure 2 shows an example of the multiple parents. In order to use multiple parents, we have to avoid the problem of multiple additions of the same data (described in section 2.1). Subsequently, we describe below the details of the processing procedure

(7)V A = v A +V B +V C +V E A (6 )(A,V B,V E (6)(A,V C,V E ) (5 )V B = v B +V D +V H B C (5)V C = v C +V F +V I (4 )(B,V D,V H ) (4 )(A, V E ),(B,V H ),(C,V I ) (4)(C,V F,V I ) (3 )V D = v D +V G D E F (3)V F = v F +V J (2 )(D,V G ) (2 )(B,V H ) (2)(C,V I ) (2 )(F,V J ) G (1 )V G = v G H (1 )V H = v H I (1)V I = v I J (1 )V J = v J Fig. 3 Example of in-network aggregation using two or more parent nodes. when performing in-network aggregation using multiple parents and avoiding the problems mentioned. (1) REQ flooding and obtaining the parent nodes list The sink broadcasts an REQ to the entire network, which then orders the start of the data collection. The REQ has some fields to specify the data collection frequency T, the data transmission delay between nodes, the hop count to the sink (in the case of the sink itself, the hop count is set to zero) etc. Those fields are the same as used in the existing method. In addition to those fields, we add a new field that indicates a parent node list. The list includes node IDs of parent nodes that are learned by receiving multiple REQs. When the node rebroadcasts the received REQ, it includes the parent node list in the REQ. Thus, when a node receives an REQ from a parent, the node can know the parent s parent nodes by reviewing the list. If the node receives an REQ from its children, the node discards the REQ. The node uses information of the parent s parent nodes, which are two hops ahead, for processing procedure of in-network aggregation described below. DAG is formed that each node set its multiple parents as the next hop nodes toward the sink. (2) Processing procedure of in-network aggregation Using figure 3, we describe the processing procedure. In the figure, node A is a sink and the other nodes are sensor nodes. Processing 1) Decision of destination of requiring aggregation. If a node has multiple parents and there is one common parent's parent node, then the parent's parent is designated as a destination requiring aggregation. Information concerning the parent s parent and its number can be viewed by receiving the parent node lists. For example in figure 3, node I receives the parent node list {B, C} of node E and {C} of node F. Since C is common to the lists, node I designates C as a destination for V I. Then node I broadcasts an REP that includes destinations requiring aggregation: C and data V I (Fig. 3(2)). If a node has multiple parents and there are some parent s parent nodes included, then it decides a parent s parent node based on the most common items in the lists. If a node has multiple parents and there are no parent s parent nodes, then it decides one of the parent nodes. If a node has only one parent node (ex. Node J in the figure 3), then it decides the parent as the destination. Processing 2) Data aggregation and forwarding A node receives an REP from a child node, and then it processes Aggregation, Forwarding or Discarding. For example in the figure 3, node F receives an REP, which includes (F, V J ), from node J. Node F aggregates V J because the destination F and its own ID is the same (Fig. 3 (3)). The node F also receives (C, V I ) from node I. The node F treats (C, V I ) as forwarding data, because the destination is its parent node C. Node F designates node C as a destination for V F, since it has only one parent node. Node F then broadcasts an REP, which

Sink (T + 2T) (T+T) T T 3 T 2 1st data collection 2nd data collection Time Sensor node (a) Example of Sensor Network Topology. 1 2 3 4 5 T(2)wait ( 4) T(3)wait T(4)wait T(5)wait T T T :Time of REP transmission ( 4)... :Time of REQ transmission (b) Example of Transmission Time in each Number of Hop Counts. Fig. 4 Example of REP transmission timing control. includes (C, V F, V I ). Similarly, node E broadcasts an REP, which includes (A, V E ), (B, V H ) and (C, V I ). So, node C receives (A, V E ), (B, V H ) and (C, V I ) from node E, and (C, V F, V I ) from node F. Node C treats (A, V E ) as forwarding data, but discards (B, V H ) because the destination is not the same as its own or its parent node ID. The node C aggregates (C, V I ) and (C, V F, V I ). At that time, the node C does not aggregate V I multiple times, since V I is common between the two pair. Therefore, this method can avoid multiple additions of the same data, as described in section 2.1. The node C computes the sum of own data v C,, and V I and V F (Fig. 3(5)). In this way, the V I can move two hops using two routes by way of parent nodes E and F. Each node performs the aforementioned processing steps 1 and 2. The process provides tolerance against packet loss by using multiple parents as intermediate nodes, although it can avoid multiple additions of the same data. 3.2 Control of data transmission timing Based on the design principle (2), we extend the data transmission timing control for tuning correctly according to the actual maximum hop count of the edge of the DAG. Using figure 4, we describe details of the extension below. The dotted lines in figure 4 (a) indicate the hop counts, while figure 4 (b) shows the REQ and REP transmission timing. Nodes, where the hop count is n (n T/ ), control their own timing, using the same means as the existing method. For example, a node, with two hop counts, waits for T(2) wait = (2T - 4 ) after receiving the REQ then broadcasts an REP. The time of the first REP broadcasting is T 2 in the figure 4. Following the first REP broadcast, the node broadcasts with the cycle of T interval. Nodes, where the hop count is n (n > T/ ), receive the REQ after the first REP transmission of nodes (their hop counts is n T/ ). For example in figure 4 (b), nodes where the hop count is 4 receive the REQ after the first REP transmission of nodes, and their hop count is 3. Therefore, nodes, where the hop count is n (n > T/ ), can not be in time for the first transmission and hence participate from the next time onwards or later. Firstly, they compute integer k, which satisfies the following formula (1), using T, and its own hop count n. Next, using the value k, they compute T(n) wait given by the following formula (2). 2n/(T/ ) - 1 k < 2n/(T/ ) (1) T(n) wait = T + k T - 2 ( n) (2) The value k is calculated based on the hop count and it shows the times of collection in which a node should participate. For example in the figure 4 (b), nodes with a hop count of 4 compute the value, it becomes 2. They wait for T (4) wait = (3T - 4 ) upon receiving the REQ and then they broadcast an REP. Using the above processing, each node can tune oneself to the data transmission timing correctly even if the assumed maximum hop count T/ differs from the actual count. 4. Evaluation 4.1 Simulation set up In this section, we evaluate the proposed method using simulation studies and compare it with following methods.

(A) A node sends half the value of its own data to two parents [7]. (B) A node sends data specifying one of the parents [5]. We implemented simulation programs within a TinyOS simulator [10]. The simulator can simulate sensor networks, which consist of sensor nodes called MOTE [11]. Nodes use CSMA (Carrier Sense Multiple Access) as a medium access control protocol. The wireless channel capacity is 40 Kbps. Meanwhile, the simulator uses a packet loss model, which is obtained based on experiment results using MOTE. The packet loss rate is about 10% assuming a distance between the two nodes of 0 3 meters. However, the rate increases to 100 % if the distance exceeds 12 meters. In the range 3-12m, the rate increases gradually from 10% to 100 % based on increasing the distance. Thus, a proper distance between nodes is about 3 meter. In the proposed method, an REQ includes the source node ID (2 bytes), the hop count to the sink (1 byte), the collection data type (1 byte), the data collection number: M (2 bytes), the data collection frequency T (4 bytes), the data transmission delay between nodes: and a parent node list. An REP includes a list of (destination IDs requiring aggregation, data, and the source ID of the data). Both of the REQ and REP include the list, so their size is variable based on the list length. In existing methods (A) and (B), an REP is fixed in size, since their methods do not use such a list. We adapt the transmission timing control of the proposed method to the existing methods (A) and (B). We specify the number of nodes in a network as a collection data type. The data collection frequency T is 3 seconds. The number of data collection M is 100 times, while the parameter is 100 msec. As a performance metric, we use the relative root mean square error as follows: 1 t M ( V V ) 2 / M V t 1 where V t is the observed value at time t and V is the actual value. A node is placed into one point in a grid. The sink is placed into one of the corners of the grid, and sensor nodes are placed in other points. 4.2 Simulation results (1) Results of varying packet loss rate We evaluated the proposed method from the perspective of packet loss tolerance. Nodes were placed within a 5 x 5 grid. We varied the distances between nodes, since the packet loss model was mainly dependent on the distance between the nodes. Figure 5 t Error Rate for number of nodes of each number of hop counts. 1.0 0.8 0.6 0.4 0.2 0.0 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 100% 80% 60% 40% 20% 0% Fig. 5 Node distance and error. Hop count: 1 Hop count: 2 Hop count: 3 Hop count:4 4 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 4.00 Fig. 6 Rate for number of nodes of each number of hop counts. shows the relation between the distance and error. The error of all methods grows as the distance becomes long, since the packet loss rate increases. Although the error of the proposed method is smaller than that of the existing methods, the degree of improvement in error has also diminished at distances of three meters or more. This is because the number of nodes, which have only one parent node, increases in line with distance. Such nodes process in a manner similar to the existing method (B). However, when the distance is about 2.25 meters, the proposed method achieves about half the error rate of existing methods. We also performed the simulation beyond the distance of Figure 5. But under such conditions, some nodes can not receive REQ or transmit REP to their parents, since the packet loss rate becomes large. This is because it is over the distance between nodes which can perform effective wireless communication assumed by the packet loss model. Figure 6 shows the ratio of the numbers of nodes for each of the hop counts. The hop count for 92% of nodes is one, when the distance is 1 meter. Under such conditions, almost all nodes can receive the REQ directly from the sink and their parent becomes the sink. Since their parent is only a single node, they

Sum of transmitted REP size (Kbytes) Sum of received REP size (Mbytes) 200 150 100 50 0 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 (a) Sum of transmitted REP size. 3.0 2.5 2.0 1.5 1.0 0.5 0.0 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 (b) Sum of received REP size. Fig. 7 Sum of size of all transmitted and received REP during simulation. Battery Life (months) 30 25 20 15 10 5 0 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 Fig. 8 Battery life of sensor node. process in a manner similar to the existing method, which diminishes improvement in the error rate of the proposed method. In figure 5, however, improvement in the error rate becomes significant from about 1.5 meters, where 25% of nodes are two hops. Therefore, when 25% or more of nodes are two or more hops, the ability of the proposed method to reduce the error rate becomes remarkable. Figure 7 shows the sum total of the transmitted and received REP sizes. The sum of the proposed method is larger than that of the existing methods, since the REP of the proposed method includes a list. Using results including the sum total of the transmitted and received message sizes, we estimated the lifetime of sensor nodes. It was assumed that the node would consume 12 ma during transmission, and 8 ma during reception respectively [11]. The initial battery capacity value is assumed to be 2000 ma-hr. Figure 8 shows the estimated lifetime. The proposed method is shorter lifetime than existing methods, since the sum of Error 1.0 0.8 0.6 0.4 0.2 0.0 4 9 16 25 36 49 Number of nodes Fig. 9 Number of nodes and errors. the message size increases. However, there is a tradeoff between the accuracy and the lifetime: since the proposed method achieves improved accuracy. Obtaining accurate data is the primary objective of the observer. (2) Results when the number of nodes is varied The number of sensor nodes will be increased or decreased based on the sensing area. Hence, we evaluate variation of the number of sensor nodes in the area. The distance between nodes in a grid is two meters, with a constant node density maintained. Figure 9 shows the relation between the error and the number of nodes. When the number of nodes is 4 and 9, all nodes communicate with the sink by one hop. Under such conditions, their parent becomes the sink and they process in a manner similar to the existing method. Thus, the error of the proposed method is almost the same as that of the existing methods. As the number of nodes increases, the proposed method reduces errors to a greater degree than existing methods. When the number of nodes is 16 or more, the number of nodes which hop count is more than two hops also increases. For example, when the number of nodes is 49, 25 % of nodes are one hop, 65 % are two hops and 10 % are three hops. Increasing the hop counts means a rise in the number of points where the in-network aggregation processing takes place. However, by reducing the error rate, the proposed method provides more accurate data than the existing methods. At least as far as our experiments are concerned, the proposed method outperforms existing methods from the perspective of the accuracy of collected data.

5. Conclusion In this paper, we proposed a new in-network aggregation method for sensor network monitoring. In order to monitor the sensor network, certain innetwork aggregation methods have been proposed: capable of saving energy by reducing the data size. They form a routing tree and data follows up from the edge of the tree to the sink. However, failure in wireless transmission triggers an increased error margin in the collected data received by the sink. As a result, the observer who monitors the sensor network finds it increasingly difficult to assess the state of the network accurately. Furthermore, when the assumed hop count of the edge is smaller than the actual count, data can not follow up from the edge. The proposed method forms a Directed Acyclic Graph (DAG), that allows a node to have multiple parents, and collects data using the DAG. By using multiple parents as intermediate nodes, the method provides tolerance for the failure in wireless transmission. Although the method uses multiple parents, the method avoids being aggregated by the same. In addition, the method can tune the data transmission timing control correctly according to the actual hop count of edge of the DAG. Furthermore, by performing simulation studies, we evaluated the proposed method and compared it with existing methods. The results show that there is a trade-off between the accuracy of collected data and the lifetime of the sensor nodes. Although the lifetime of the proposed method may be shorter than existing methods, it still outperforms existing methods from the perspective of the accuracy of the collected data. Hence the proposed method is useful because obtaining accurate data is the primary objective of the observer. Acknowledgments The authors would like to thank Mr. Tohru Asami, President, Chief Executive Officer of KDDI R&D Laboratories Inc. for his constant encouragement in this research. This work is the result of network selfconfiguration technology which is the sub project of the ubiquitous networking project in Japan, called the Ubila project. This work is supported by the Ministry of Internal Affairs and Communications (MIC). References [1] A. Hac, "Applications of Wireless Sensor Networks, " in Handbook of WIRELESS SENSOR NETWORK DESIGN, Wiley publisher, pp. 323-362, 2003. [2] D. Culler and D. Estrin, "Overview of Sensor Networks, " IEEE Computer Mag., Vol. 37, No. 8, pp. 41-49, August 2004. [3] S. Tilak, N.B. Abu-Ghazaleh and W. Heinzelman, "A Taxonomy of Wireless Micro-Sensor Network Models," ACM Mobile Computing and Communications Review, Vol. 6, Issue 2, pp. 28-36, April 2002. [4] A. Cerpa, W. Ye, Y. Yu, J. Zhao and D. Estrin, "Networking issues in wireless sensor networks," Journal of Parallel and Distributed Computing (JPDC), Vol. 64, Issue 7, pp. 799-814, July 2004. [5] J. Zhao, R. Govindan and D. Estrin, "Computing Aggregates for Monitoring Wireless Sensor Networks," Proc. of the First IEEE Int. Workshop on Sensor Network Protocols and Applications (SNPA'03), May 2003. [6] I. Solis and K. Obraczka, "The Impact of Timing in Data Aggregation for Sensor Networks," Proc. of the IEEE Int. Conf. on Communications (ICC), Vol. 6, pp. 3640-3645, June 2004. [7] S. Madden, M. J. Franklin, J. M. Hellerstein and W. Hong, "TAG: a Tiny Aggregation Service for Ad-Hoc Sensor Networks," Proc. of the 5th Annual Symposium on Operating Systems Design and Implementation (OSDI), pp. 131-146, December, 2002. [8] S. Madden, R. Szewczyk, M. J. Franklin and D. Culler, Supporting Aggregate Queries Over Ad-Hoc Wireless Sensor Networks, Proc. of the fourth IEEE Workshop on Mobile Computing Systems and Application (WMCSA), pp.49 58, June 2002. [9] J. Zhao and R. Govindan, "Understanding packet delivery performance in dense wireless sensor networks," Proc. of the first ACM Int. Conf. on Embedded networked sensor systems (SenSys), pp. 1-13, Nov. 2003. [10] P. Levis, N. Lee and D. Culler, "TOSSIM: Accurate and Scalable Simulation of Entire TinyOS Applications," Proc. of the First ACM Conference on Embedded Networked Sensor Systems (SenSys), pp. 126 137, Nov. 2003. [11] MICA2 MOTE, Crossbow technology Inc., http://www.xbow.com/