Performane Analysis of IEEE 80.11 in Multi-hop Wireless Networks Lan Tien Nguyen 1, Razvan Beuran,1, Yoihi Shinoda 1, 1 Japan Advaned Institute of Siene and Tehnology, 1-1 Asahidai, Nomi, Ishikawa, 93-19 Japan National Institute of Information and Communiation Tehnology Hokuriku Researh Center, -1 Asahidai, Nomi, Ishikawa, 93-111 Japan lannt@jaist.a.jp Abstrat. Multi-hop wireless networks provide a quik and easy way for networking when we need a temporary network or when abling is diffiult. The 80.11 Medium Aess Control (MAC plays an important role in the ahievable system performane. There have been many studies on analyti modeling of single-hop 80.11 wireless networks but only a few on the analysis of multihop wireless networks. Furthermore, the objet of these researhes is an homogeneous ad-ho wireless networks; therefore they are not appropriate for a network with struture suh as wireless mesh networks. This paper introdues an analyti model of throughput performane for the IEEE 80.11 multi-hop networks, whih allows us to ompute the ahievable throughput on a given path in multi-hop wireless networks. The model shows that there is an optimal point at whih throughput is maximized. Using this model and a Markov model for modeling the operation of the IEEE 80.11 DCF we an determine the amount of data that eah node should injet to the network to get the best throughput performane. 1 Introdution Multi-hop wireless networks provide a quik and easy way for networking when we need a temporary network or when abling is diffiult. The 80.11 Distributed Coordination Funtion, Carrier Sense Multiple Aess with Collision Avoidane (CSMA/CA based, is the most popular MAC protool for wireless ommuniation. The analysis in this paper is based on the operation of 80.11 DCF. In wireless networks, the throughput that an be sent through a wireless link depends on various fators suh as the distane between nodes, the transmission power, harateristis of environment like path loss, fading, noise, et. Given the broadast nature in wireless environment, the ahievable throughput on a wireless link not only dependent on the operation data rate on that link, but also depends on number of nodes using the same radio hannel within the two end-points arrier sense area. Considering a traffi flow sent from soure node to destination node through other intermediate nodes, the middle nodes may have to ontend with more nodes than the soure node or the destination node does. Consequently, the soure node an injet more data into the path than the amount that an be forwarded by middle nodes. This
may lead to paket loss and low performane in wireless network sine the ost to resend a paket is high and when injeting the amount of data larger than the one the hannel an aepted makes the ondition even worse and leads to a high paket loss. High paket loss in turn an trigger re-routing and make the network topology instable [1]. To date, there have been a lot of studies on analyti modeling of both single-hop 80.11 wireless networks [], [3], [4], [5], [6] and multi-hop wireless networks [7], [8], [9] [10]. All of these models are assumed to use saturated traffi load (whih mean a node always has a paket ready for transmission exept the model whih is proposed in [10]. Other studies fous on the theoretial upper bound of throughput on an homogeneous ad-ho network [11], [1] or are based on the assumption of global sheduling [13], [14], [15], whih may not be a good assumption in a real wireless networks using IEEE 80.11. In this paper, we introdue an analyti model of throughput performane for 80.11 multi-hop networks allowing us to ompute the ahievable throughput on a given path in multi-hop wireless networks. The model shows that there is an optimal point at that throughput is maximized. Based on this model and Markov model for modeling the operation of the IEEE 80.11 DCF we an determine the amount of data that eah node should injet to the network to get the best throughput performane. Related work Following the analytial methodology introdued for the analysis of ALOHA protool and arrier sense multiple aess [16], [17], a lot of analytial modeling of wireless MAC protools has often foused on single-hop wireless networks. Although some models are proposed for multi-hop wireless networks [18], [19], they an t model the effet of binary exponential bak-off sheme (BEB whih is the key to adjust transmission intervals in IEEE 80.11. Reently there are more researhes on modeling IEEE 80.11 DCF in single-hop wireless networks [],[3], [4], [5], [6]. With a Markov Chain model, the exponential bak-off sheme was aurately modeled. However, these models an t be diretly applied to multi-hop wireless networks due to the hidden node problem. One of the first analytial models of IEEE 80.11 DCF for multi-hop wireless networks is proposed in [7]. The hidden node problem is taken into aount, but transmission of all the nodes is assumed to follow a Poisson proess whih doesn t math the behavior of IEEE 80.11 binary exponential bak-off sheme. In the model whih is proposed by Wang and Garia-Luna-Aeves in [8] the BEB sheme an t be aptured effetively either beause only a simple model for exponential bak-off sheme is used. Some reent works have solved the problem to model behavior of binary exponential bak-off sheme [9], [10]. Carvalho and Garia-Luna-Aeves introdued an analytial model to study operation of 80.11 DCF in multi-hop wireless networks [9]. The model takes into aount the impat of both physial layer and network topology. However, the impat of hidden nodes is not onsidered. David Malone et al. proposed a model whih is effetive in apturing the binary exponential bak-off sheme of
80.11 DCF in both saturated and non-saturated environment [10]. This model helps us in studying the relation between input load and output load of a node depending on several parameters of IEEE 80.11 DCF. There are some researh results on the apaity of general ad-ho network [11], [1] and mesh network [13]. It was shown that for stationary networks, the apaity for eah node derease as O(1/ n ; meanwhile for the mobile networks that an tolerate long delay, the apaity may remain onstant. In mesh networks, the authors in [13] laimed that gateways are bottleneks and the available apaity for eah node redues to O(1/n, where n is the number of node assoiated with one gateway. 3 Network model We onsider a multi-hop wireless network in whih eah node uses IEEE 80.11 DCF for medium aess ontrol and has only one radio interfae operating on the same radio hannel. In our model we also assume that only one transmission rate is used although 80.11 a/b/g standards support multiple transmission rates At the MAC layer, the data payload is assumed to be 104 bytes plus 34 bytes from MAC header. Request-to-Send (RTS and Clear-to-Send (CTS are assumed to be sent at the lowest data rate that is supported by physial layer. At the appliation layer, we assume that there is single data flow and our goal is to present an analytial model to ompute ahievable throughput along a path. Beause of having only one flow in the network so the model we use only onsider intra-flow interferene ourring for pakets of the same flow transported over different wireless links. The inter-flow will be taken into aount in our future model. 4 Throughput Analysis The analytial model that we use to ompute ahievable throughput along a wireless multi-hop path is based on the model presented in [] but it takes into aount hidden nodes whih strongly affets ahievable throughput in multi-hop wireless networks. Similar to [11] we define three radio ranges: Transmission range (R t : represents the range in whih a frame an be suessfully reeived if there is no interferene from other nodes. This value is determined by transmission power, reeiver sensitivity and radio propagation properties. A node B is onsidered in transmission range of node A if pakets ome from node A are reeived at node B with power higher than minimum reeption power of node B. Carrier sense range (R s : represents the range in whih a transmission an trigger arrier sense detetion at radio interfae of the node. This value is determined by reeiver s sensitivity and also transmission power, radio propagation properties. A node B is onsidered in arrier sense range of node A if pakets ome from node A are reeived at node B with power higher than minimum detetion power of node B. Interferene range (R i : represents the range in whih the station in reeive mode will be interfered by other transmitter and thus suffers a loss.
Considering a transmission from node A to node B, the hidden nodes in this ase are the nodes that are inside the interferene range of node B (reeiver but outside both transmission range of node B and arrier sense range of node A (transmitter. Let s say C is a node in the hidden node set. Beause C is outside the arrier sense range of node A so it is not aware of transmissions between A and B. Any transmission of C will orrupt the transmission between A and B. The RTS/CTS sheme an t solve hidden node problem, and this reason makes performane of IEEE 80.11 worse in multi-hop wireless networks. Our model will take into aount the impat of the hidden node problem on the throughput of a given path. We onsider n fixed nodes and n - 1 nodes send traffi to the next nodes along that path as illustrated in the Figure 1. The following notations are used to denote subset of n nodes. Carrier sense range of node j Transmission range of node j j - 4 j - 3 j - j - 1 j j + 1 j + j + 3 j + Transmission range of node j + 1 Interferene range of node j + 1 Fig. 1. Illustration of the three different ranges. C j refers to subset of nodes within arrier sense range of node j. C j + refers to the subset C j plus node j itself. I j refers to the subset of nodes within interferene range of node j. T j refers to the subset of node within transmission range of node j. Let S to be normalized system throughput, whih an be ompute as fration of time that hannel is used to suessfully transmit payload data. In a slot time hannel an be idle, busy with a suessful transmission or busy with a ollision. In order to alulate the average length of a slot time we have to onsider what an happen in a slot time or the probability that hannel has one of three different states. Let n be maximum number of nodes in the interferene range of nodes in the path, τ the probability that a node transmits in a random hosen slot time, and P tr the probability that there is at least one transmission in the onsidered slot time. One time slot is denoted as σ. Beause of n different nodes ontent on the hannel, eah node will transmit in a slot time with probability τ. n tr = 1 (1 τ (1 P
Consider a transmission between node j and node j+1 and suessful transmission need k time slot. Let P s be the probability that the transmission is suessful, whih is given by probability that there is only the sender transmit at the time in C j and none of nodes in {I j U I j+1 }/{T j U T j+1 } transmit in k time slot. Let h be number of nodes in {I j U I j+1 }/{T j U T j+1 }, these nodes are alled hidden nodes. nτ (1 τ (1 τ Ps = P n 1 hk ( We an express the ahievable throughput S as the following ratio E S = E tr p sl Where E p is average amount of payload information is suessfully transmitted in a slot time, E sl being average length of a slot time. (3 Fig.. Suess time and ollision time with basi aess and RTS/CTS mehanism. Let E(P be average paket payload size. Sine a paket an be transmitted suessfully in a slot time with probability P tr.p s, we may have E p = Ptr Ps E(P (4 The average length of a slot time is obtained onsidering that: a slot time is idle with probability 1-P tr ; ontain a suessful transmission with probability P tr.p s and ontains a ollision with probability P tr (1-P s. Thus equation (3 an be expressed as (1/ n Ptr Ps E[ P] S = (1 P σ + P P T + P (1 P T tr tr s s tr s (5
Where T s is the average time that the hannel is sensed busy by a suessful transmission, T being average time that hannel is sensed busy by a ollision and σ is duration of a slot time. The value of T s and T depends on the aess mehanism used. Firstly, we onsider the system uses the basi aess mehanism. Denoting δ as propagation delay, from Figure we an obtain the value of T bas s and T bas as follows T bas s = Phy _ hdr + MAC _ hdr + E[ P] + SIFS + δ + ACK + DIFS + δ (6 T bas = Phy _ hdr + MAC _ hdr + E[ P] + DIFS + δ (7 where E[P] is the average length of longest paket involve in the ollision. In our model we assume that all pakets have the same payload length so that E[P] = E[P] = P Seondly, onsidering the system in whih eah paket is transmitted by using RTS/CTS mehanism T s and T an be omputed by the following equations: T RTS s = RTS + SIFS + δ + CTS + SIFS + δ + Phy _ hdr (8 + MAC _ hdr + E[ P] + SIFS + δ + ACK + DIFS + δ T RTS = RTS + DIFS + δ (9 In order to see the relation between S and τ we rearrange equation (5 as T where T = σ. S = T s T (1/ n E[ P] σ + tr P P tr s [ P ( T 1 + 1] As T s, T, n, E[P] and σ are onstants and let us all From (1 ( and (11 F( τ 1 P P = tr tr s [ P ( T 1 + 1] 1 T 1 ( = T F τ n n hk 1 hk τ (1 τ τ (1 τ + 1 By analyzing the relation between F and τ we an get the relation between S and τ. Taking the derivative of (1 with respet to τ. ( T = τ df d It is easy to see that 1(1 τ n + T nτ (1 τ τ ( n n+ hk + hk T (10 (11 (1 (13
lim + τ > 0 lim τ > 1 df (14 < 0 dτ df (15 > 0 dτ From (14 and (15 there must be a value of τ in the range [0:1] at that the value of F is minimum and hene it maximizes the value of S. It is possible to assume that τ 1. That assumption omes from the mehanism of the IEEE 80.11 DCF standards [1]. Aording to [1] the minimum value of ontention window (CW 0 is 3 so the value of τ should be smaller than 1/CW 0 (0.031 and our assumption is valid. To find that value of τ under the ondition τ 1 we an approximate df dτ n n( n 1 (16 ( 1 τ 1 nτ + τ Making equation = 0 to be quadrati equation and then we an solve it. Paket Payload MAC header Physial header ACK RTS CTS Channel Bit Rate Propagation delay Slot Time SIFS DIFS Table 1. System Parameters. 104 bytes 7 bits 19 bits 11 bits + Physial header 160 bits + Physial header 11 bits + Physial header 1 Mbit/s 1 μs 0 μs 10 μs 50 μs Figure 6 shows the theoretial maximum throughput that an ahieve with DCF with the RTS/CTS mehanism. The parameters used to ompute numerial results are summarized in Table 1. 5 Simulation and Analysis Results In this setion some results of both analysis and simulation are presented for evaluating the effetiveness of the proposed analytial model. For simulation we use ns-.7 [], with CMU Monarh Projet wireless and mobile ns- extensions [3]. The network topology used inludes 100 nodes, whih are putted in a line. The distane between two nodes is hanged from 00 m to 54 m to vary the number of nodes in the
interferene range. The transmission range and arrier sense range are set to be 50 m and 550 m, respetively. The data rate used in all simulations is 1 Mbps and the other parameters are set aording to the Table 1. The traffi soure for a node will send data at several onstant rates; these rates are set to one of the following rate 0, 30, 40, 50, 70, 90, 10, 150, 00 Kbps for monitoring the hanges of throughput at eah node. The simulation results in Figure 3, 4 and 5 show that when the input traffi load inreases 80.11 multi-hop wireless network will get to saturation status but with higher number of node in the interferene range the throughput will be dereased quikly beause of ollisions. Fig. 3. Single node throughput versus single node traffi load (n = 5; h = 1. In the analytial model, the input traffi load is represented by transmission probability τ, where τ is the probability that a node transmits in a random hosen slot time. The value of τ obviously depends on the node s input traffi load, traffi of other nodes in its arrier sense range and the mehanism is used to aess media (IEEE 80.11 DCF in this ase. By using a Markov model, the relation between τ and input traffi load an be obtain from a researh of K. Duffy et al [10].
Fig. 4. Single node throughput versus single node traffi load (n = 11; h = 1. where 1 q W0 τ = η (1 q(1 p(1 (1 q q W0 1 (1 p q qw0 qw0 ( qw0 + 3q η = + W0 W0 1 (1 q (1 q(1 (1 q q( W0 + 1( p(1 q q(1 p + (1 q + (1 q pq W + 0 (1 p (1 q(1 p W0 1 (1 q M 1 W0 (1 p p( p + 1 (1 p Here, p is the probability that a node senses the hannel busy on an attempted transmission, q being the probability that the node s buffer has pakets waiting for transmission, W 0 being the minimum ontention window of the node and being M W 0 the node s maximum ontention window size. M is the maximum bak-off stage. On other hand, based on the nature of wireless environment we have a relation between τ and p 1 (17 n 1 p = (1 τ (18 where n is number of node in the interferene range of the node inluding itself. Based on the assumption that we an ompute the value of q from given input traffi load of the node, by solving equations (17 and (18 we an find the value of p and τ
at that the node operates. Getting the value of τ by doing so is somehow diffiult. However, with the given network topology, the analytial model an predit the maximum throughput of a node or the input traffi load an be used to saturate the network. Fig. 5.. Single node throughput versus single node traffi load (n = 3; h = 1. Fig. 6. Single node throughput versus transmission probability τ, obtained by the analytial model. Figures 3, 4, and 5 present the simulation results with different network onditions while Figure 6 shows the analytial results. It is an be seen that the maximum values of throughput from simulation results are reasonably onsistent with the maximum throughputs from analytial results. The maximum values of throughput in figures 3, 4, and 5 are 114 kbps, 70 kbps, 36 kbps while the analytial model gives us the values
of 106 kbps, 59 kbps, 31 kbps respetively. Thus we an say that the analytial model an be applied to predit the saturation throughput on a given path of 80.11 multihop wireless networks and onsequently the optimum input traffi load is obtained. 6 Conlusions In this paper we propose an analytial model for analyzing the throughput performane of IEEE 80.11 multihop wireless networks. Comparison with simulation results shows that the model is suessful to estimate the saturation throughput on a given path in the multihop wireless network. The model also allows us to understand how the interferene range and hidden node affet to throughput performane or say in other way the impat of physial onditions to MAC performane. By using this model performane of MAC protool in IEEE 80.11 multihop wireless network an be studied more effetively. For the future work, we will study the issue of improving throughput performane in IEEE 80.11 wireless mesh network and in partiular, we will fous on routing protool and admission ontrol mehanism for that network. We will also need a better model whih allows us to predit per hop throughput as well as delay time and jitter with inter-flow interferene and multiple transmission rates will be taken into aount. Aknowledgements. The finanial support from the 1st entury COE program Verifiable and Evolvable e-soiety, Japan Advaned Institute of Siene and Tehnology, is gratefully aknowledged. Referenes 1. P. C. Ng, S. C. Liew, Re-routing Instability in IEEE 80.11 Multi hop Ad ho Networks, IEEE WLN 04, Nov. 004, Tampa, USA. G. Bianhi, Performane analysis of the IEEE 80.11 distributed oordination funtion, IEEE Journal on Seleted Areas in Communiations, vol. 18, no. 3, pp. 535 547, 000 3. Mohammad Hossein Manshaei, Gion Reto Cantieni, Chadi Barakat, Thierry Turletti: Performane Analysis of the IEEE 80.11 MAC and Physial Layer Protool. WOWMOM 005: 88-97 4. Chuan H. Foh, M. Zukerman, Performane Analysis of the IEEE 80.11 MAC Protool, EW00 Proeedings, 00 5. Xiao Y and Rosdahl J, Performane Analysis and Enhanement for the Current and Future IEEE 80.11 MAC Protools, ACM SIGMOBILE Mobile Computing and Communiations Review (MCR, speial issue on Wireless Home Networks, Vol. 7, No., Apr. 003, pp. 6-19 6. F. Cali, M. Conti, and E. Gregori. Dynami tuning of the IEEE 80.11 protool to ahieve a theoretial throughput limit. IEEE/ACM Transations on Networking, 8(6:785 799, Deember 000 7. H. Chhaya and S. Gupta. Performane modeling of asynhronous data transfer methods of IEEE 80.11 MAC protool. Wireless Networks, 3:17 34, 1997
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