AN ANALYSIS OF COORDINATED AND NON-COORDINATED MEDIUM ACCESS CONTROL PROTOCOLS UNDER CHANNEL NOISE

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1 AN ANALYSIS OF COORDINATED AND NON-COORDINATED MEDIUM ACCESS CONTROL PROTOCOLS UNDER CHANNEL NOISE Tolga Numanoglu, Bulent Tavli, and Wendi Heinzelman Depatment of Electical and Compute Engineeing Univesity of Rocheste, Rocheste, NY 1467 USA {numanogl, tavli, ABSTRACT In this pape, we pesent an analysis of the effects of channel noise on the pefomance of coodinated and noncoodinated MAC potocols. In ode to obseve the degadation in the pefomance of a coodinated MAC potocol (MH-TRACE) with inceasing BER level, we ceated an analytical model to estimate MH-TRACE s pefomance. This analytical model is validated though simulation expeiments. Ou esults show that despite its highe level of vulneability, the coodinated MAC potocol s pefomance loss is compaable to the pefomance loss of the noncoodinated MAC potocol (IEEE 8.11) fo low to mid BER levels (i.e., BER < 1 4 ). On the othe hand, fo extemely high BER levels (i.e., BER 1 4 ) the pefomance loss of the coodinated MAC potocol is compaatively highe than the pefomance loss of the non-coodinated MAC potocol due to its dependence on contol taffic, which is also affected by the BER level. INTRODUCTION Medium Access Contol (MAC) potocols ae employed to contol access to the channel in ode to egulate tansmissions to avoid o minimize collisions [1]. Futhemoe, the MAC potocol is the key element in detemining many featues of a wieless netwok, such as thoughput, Quality of Sevice (QoS), enegy dissipation, fainess, stability, and obustness [], [3], [4]. In othe wods, the pefomance of a paticula netwok highly depends on the choice of the MAC potocol. MAC potocols can be classified into two categoies based on the collaboation level of the netwok in egulating the channel access: coodinated and non-coodinated. A coodinated MAC potocol opeates with explicit coodination among the nodes and is geneally associated with coodinatos, channel access schedules and clustes. A noncoodinated MAC potocol, on the othe hand, opeates without any explicit coodination among the nodes in the netwok. Fo example, IEEE 8.11 is a non-coodinated Abstact ID: 589. This wok was suppoted in pat by the Univesity of Rocheste Cente fo Electonic Imaging Systems and in pat by Hais Copoation, RF Communications Division. N 1 N 3 N Schedule N 3 N N N 1 N 3 N N 1 N 3 N Collision N N 1 N 3 N 1 Fig. 1. Illustation of coodinated and non-coodinated MAC potocols. The uppe left and ight panels show the node distibutions fo nodes N -. The lowe left panel shows the medium access fo the coodinated scheme, whee node N is the coodinato and the channel access is egulated though a schedule tansmitted by N. The lowe ight panel shows the channel access fo the non-coodinated scheme (e.g., CSMA). Ovelapping data tansmissions of N 1 and N 3 lead to a collision. MAC potocol when opeating in the boadcast mode (i.e., in boadcasting mode, IEEE 8.11 becomes plain CSMA without any handshaking) [5]. Figue 1 illustates the channel access mechanism fo geneic coodinated and non-coodinated MAC potocols. In the coodinated MAC potocol, node N is the clustehead (coodinato) fo the potion of the netwok consisting of five nodes. Channel access is egulated though a schedule that is boadcast by the coodinato. Upon eception of the schedule, nodes tansmit thei data at thei allocated time, and thus collisions among nodes within the same cluste ae eliminated. Time is oganized into cyclic time fames, and the tansmission schedule is dynamically updated at the beginning of each time fame. IEEE is a ecent example of such a coodinated MAC potocol [5]. In the non-coodinated MAC potocol, each node detemines its own tansmission time based on feedback obtained though caie sensing on the channel. Thus, conflicts in data tansmission attempts (i.e., collisions, captue) ae unavoidable in the non-coodinated scheme. IEEE 8.11 is a well-known example of a noncoodinated MAC potocol when it is used fo boadcasting. MH-TRACE (Multi-Hop Time Resevation Using Adaptive

2 Contol fo Enegy Efficiency) is a ecent example of a coodinated MAC potocol that elies on contol packet exchanges fo its opeation. A compaative evaluation of IEEE 8.11 and MH-TRACE fo eal-time data boadcasting using a pefect channel showed that the pefomance of MH-TRACE is bette than IEEE 8.11 in tems of thoughput and enegy efficiency unde vaious netwok conditions [6]. Howeve, due to the elatively complicated design of MH-TRACE, which elies on obust contol packet exchange, the advantages of MH-TRACE ove IEEE 8.11 ae questionable unde a ealistic channel eo model. In ou pevious wok we pesented a compaative pefomance evaluation of IEEE 8.11 and MH-TRACE when they ae utilized fo single hop data boadcasting. The oveall pefomance (e.g., QoS, enegy dissipation) of these potocols is diectly detemined by the pefomance of the MAC potocol fo a elatively low bit eo ate (BER) level (i.e., BER = 1 4 ) though ns- simulations [7]. We used a single-hop boadcasting scenaio to clealy assess the pefomance of the MAC laye without being affected by the uppe layes. Ou analysis evealed that the pefomance of MH-TRACE is still bette than the pefomance of IEEE 8.11 in tems of thoughput and enegy efficiency fo a channel BER of 1 4. In this study we pesent an analysis of the effects of channel noise fo IEEE 8.11 and MH-TRACE fo a wide ange of BER levels though mathematical models suppoted by ns- simulations. BACKGROUND In this section we pesent an oveview of IEEE 8.11 and MH-TRACE when they ae used fo single-hop data boadcasting. IEEE 8.11 In boadcasting mode, IEEE 8.11 uses p-pesistent CSMA with a constant defe window length (i.e., the default minimum defe peiod) [5]. When a node has a packet to boadcast, it picks a andom defe time and stats to sense the channel. When the channel is sensed idle, the defe time counts down fom the initially selected defe time at the end of each time slot. When the channel is sensed busy, the defe time is not decemented. Upon the expiation of the defe time, the packet is boadcast. MH-TRACE Multi-Hop Time Resevation Using Adaptive Contol fo Enegy Efficiency (MH-TRACE) is a MAC potocol designed fo enegy-efficient eal-time data boadcasting [6]. C C 1 C 3 Fame 1 Fame Fame 3 Fame 4 Fame 5 Fame 6 Fame 7 Supefame N - 1 Supefame N Supefame N + 1 C 4 C 5 C 7 C 6 Fig.. A snapshot of MH-TRACE clusteing and medium access fo a potion of an actual distibution of mobile nodes. Nodes C 1 - C 7 ae clustehead nodes. Figue shows a snapshot of MH-TRACE clusteing and medium access. In MH-TRACE, the netwok is patitioned into ovelapping clustes though a distibuted algoithm. Time is oganized into cyclic constant duation supefames consisting of seveal fames. Each clustehead chooses the least noisy fame to opeate within and dynamically changes its fame accoding to the intefeence level of the dynamic netwok. Nodes gain channel access though a dynamically updated and monitoed tansmission schedule ceated by the clusteheads. Each fame consists of a contol sub-fame fo tansmission of contol packets and a contention-fee data sub-fame fo data tansmission (see Figue 3). Beacon packets ae used fo the announcement of the stat of a new fame; Clustehead Announcement (CA) packets ae used fo educing co-fame cluste intefeence; contention slots ae used fo initial channel access equests; the heade packet is used fo announcing the data tansmission schedule fo the cuent fame; and Infomation Summaization (IS) packets ae used fo announcing the upcoming data packets. IS packets ae cucial in enegy saving. Each scheduled node tansmits its data at the eseved data slot. Fig. 3. CA Slot Beacon Contol sub-fame sub-fame Contention Slot Heade IS Slot Slots - MH-TRACE fame stuctue.

3 TABLE I SIMULATION PARAMETERS Aconym Desciption Value T SF Supefame duation 5.17 ms N F Numbe of fames 7 N DS Numbe of data slots pe fame 7 N C Numbe of cont. slots pe fame 6 T H Heade slot duation 9 s T B,CA,C,IS Beacon, CA, Cont., IS slot du. 3 s T D slot duation 43 s N/A packet size 14 B N/A Heade packet size 4-18 B N/A All othe contol packet size 4 B T dop Packet dop theshold 5 ms T V F Voice packet geneation peiod 5.17 ms D T Tansmission ange 5 m D CS Caie Sense ange 57 m # of Packets Numbe of Dopped Packets pe Single Contol Packet Loss Lost Contol Packet Dopped Packets Beacon Heade Contention Fig. 4. MH-TRACE pefomance degadation in tems of dopped data packets fo beacon, heade, and contention packet losses..19 In MH-TRACE, nodes switch to sleep mode wheneve they ae not involved in data tansmission o eception, which saves the enegy that would be wasted in idle mode o in caie sensing. Instead of fequency division o code division, MH-TRACE clustes use the same speading code o fequency, and inte-cluste intefeence is avoided by using time division among the clustes to enable each node in the netwok to eceive all the desied data packets in its eceive ange, not just those fom nodes in the same cluste. Thus, MH-TRACE clusteing does not ceate had clustesthe clustes themselves ae only used fo assigning time slots fo nodes to tansmit thei data. Fo a moe complete desciption of MH-TRACE, the eade is efeed to [6]. ANALYTICAL MODEL In this section we develop an analytical model to estimate the pefomance of MH-TRACE as a function of BER. In ou analysis we do not conside any eo coection scheme, thus, if thee is at least one bit eo within a packet, then that packet is discaded. Random packet eos ae independently intoduced at the eceives. BASIC MODEL To minimize the numbe of paametes in the model, fist we conside a fully-connected netwok with a small numbe of static nodes. The numbe of data slots in one supefame is high enough to suppot all of the nodes in the netwok (see Table I). When thee ae no channel eos, all nodes should be able to tansmit and eceive without any packet dops o collisions. Thee will be only one clustehead in the netwok due to the fact that thee cannot be two clusteheads that can hea each othe diectly. The numbe of data packets geneated pe node pe second, (DP node ), is equal to the packet ate (R packet ) of MH-TRACE (i.e., one packet pe supefame time (1/ )). DP node = R packet = 1 (1) DP node epesents the numbe of data packets geneated by a single node in the netwok and can be egaded as the maximum numbe of packets a node can tansmit given that it has full access to a pefect channel wheneve it needs. Howeve a lossy channel will cause packet dops and theefoe the thoughput of the netwok will dop accodingly. In Figue 4, the coesponding thoughput losses due to coupted beacon, heade and contention packets ae given to illustate the impact of the paticula contol packet on oveall potocol pefomance. In these esults only the specified contol packets ae lost due to channel eos and all the othe packets ae not affected [7]. As can be seen fom the figue, heade packets ae vital to MH-TRACE and ae the packets whose loss has the most impact on the pefomance of MH-TRACE. Loss of contention packets cause 1 times less loss in data packets than loss of heade packets (.19). Finally, fo each beacon packet dopped, only.15 data packets ae dopped. Like beacon packet losses, losses of othe contol packets (e.g., IS, CA) do not significantly affect the thoughput of the netwok. Thus, the heade and contention packets ae the only contol packets whose loss due to channel noise significantly affect the netwok pefomance. Theefoe, we can wite the equation fo the tansmit thoughput of a single node (i.e., tansmit thoughput pe node pe second T node ) in tems of the data packets dopped befoe tansmission due to lost heade packets (DP L H ) and contention (DP L C ) packets: T node = DP node DP L H DP L C ()

4 Both (DP L H ) and (DP L C ) can be expanded as the poduct of thee pats. Numbe of data packets dopped pe heade/contention packet loss (DP L peh /DP L pec ). Numbe of heade/contention packets sent to a node/clustehead pe second (HP node /CP node ). Pobability of dopping a heade/contention packet (P H /P C ). As contention packets ae elatively shot (4 bytes), they ae less likely to be dopped than heade packets (16 bytes fo 6 boadcasting nodes). Futhemoe, since the souces ae continuous bit ate and MH-TRACE utilizes automatic channel access enewal, once a node gets channel access, it will not loose it and thus will not need to tansmit contention packets fo the est of the simulation time. Moeove, the numbe of dopped data packets pe lost heade packet is 1 times lage than the numbe of dopped data packets pe lost contention packet, as shown in Figue 4. Theefoe it is easonable to assume that the effect of losing contention packets can be neglected. Based on this assumption, the tansmit thoughput pe node pe second becomes: T node = DP node DP L H (3) T node = 1 DP L peh HP node P H. (4) In Equation (4), DP L peh is a constant (1.99) and HP node is equal to DP node since each node eceives one heade pe supe fame fom its clustehead. Finally P H depends on the length of the heade packet L H and is calculated fom the Bit Eo Rate (BER) of the channel. Theefoe, P H = {1 (1 BER) L H }. (5) T node = {1 (1 BER) LH } (6) T node = 1 [ {1 (1 BER) L H }]. (7) In ode to get the numbe of eceived packets pe second in the netwok we need to multiply the tansmit thoughput pe node pe second with the numbe of neighboing nodes N 1 (note that all the nodes can hea each othe in this netwok). Moeove, each data packet is eceived with a pobability P D, which is the pobability that a data packet (with length L D = 14 bytes) goes though the channel with no eo at a given BER. Accodingly, the eceive thoughput pe node pe second (T ) becomes: T = (N 1) T node (1 BER) LD. (8) Note that the eceive thoughput pe node pe second of IEEE 8.11 is simply equal to N 1 (1 BER) L D since in CSMA-type potocols such IEEE 8.11 in boadcasting Aveage Numbe of Received Packets MH TRACE MH TRACE Model IEEE 8.11 IEEE 8.11 Model Bit Eo Rate Fig. 5. Aveage numbe of eceived packets pe node pe second vesus bit eo ate (BER). mode, only data packets ae sent though the lossy channel and the thoughput is detemined by the BER of the channel and length of a data packet. We used the ns- simulato to validate the analytical model. The channel ate is set to Mbps, and all nodes have a CBR (Constant Bit Rate) data souce with 3 Kbps data ate, which coesponds to one voice packet pe supefame. The simulations ae un fo 1 s and epeated with the same paametes five times. In Figue 5 the analytical model fo MH-TRACE and IEEE 8.11 ae plotted against inceasing BER. Also the simulation esults ae included fo both potocols to demonstate the accuacy of the models. The thoughput of MH-TRACE dops by almost 5% at a BER aound On the othe hand, IEEE 8.11 etains almost 55% of its initial thoughput at the same BER (note that the initial thoughputs of both potocols ae the same). This diffeence can be tanslated into the fact that IEEE 8.11 pefoms 1% bette than MH-TRACE, which expeiences a wose pefomance degadation due to lost coodination packets [7]. These esults show that the analytical model poposed to estimate the thoughput of MH-TRACE is quite accuate. The model captues the fact that coodinated MAC potocols ae moe vulneable than non-coodinated MAC potocols to channel noise due to thei dependence on the obustness of the contol taffic. Howeve, in ou model, we teated the clustehead as a egula node inside the netwok, but in eality, a clustehead would not dop any data packets due to lost heade packets since the clustehead is the one geneating the heade packets. Theefoe, ou model slightly undeestimates the thoughput of MH-TRACE by teating the clustehead as an odinay node.

5 H n 1 L L- n 3 H- H- H Region 1 Region 3 Region y Assumptions: * Coodinates of the location of node n i is the oigin fo calculation. * x is distance between theoigin and the edge of the field. Theefoe; * x anges fom zeo to. * The coveage does not depend on vetical displacement of the node. (Povided that node stays inside egion.) Fig. 6. n L- Region 1 Region Region 3 L Rectangula field patitioned into thee diffeent egions. n i x x Can be calculated by a simple integal A(x ) = π 1 Aveage Coveage= A(x )dx GENERAL MODEL In this section, we conside a ectangula field (L H) in which a cetain numbe of nodes (N), which have a communication adius (), ae andomly deployed. We use a statistical voice souce model that classifies speech into sputs and gaps (i.e., gaps ae the silent moments duing a convesation). Duing gaps, no data packets ae geneated, and duing sputs, data packets ae geneated at 3 Kbps data ate. Both sputs and gaps ae exponentially distibuted statistically independent andom vaiables, with means η s = 1.s and η g = 1.35s, espectively [8]. Ou appoach to this moe complex model will be basically the same as befoe. We begin by calculating the tansmit thoughput pe node pe second (T node ) when the channel is pefect. In addition to Equation (7) we need a tem that captues the effect of the voice souce model. This tem can easily be epesented with the atio of sputs to the whole convesation (η). Theefoe, we can wite T node as in Equation (9). T node = 1 [1 1.99{1 (1 BER) L H }][η] = 1 η s [1 1.99{1 (1 BER) LH }][ ] η s + η g (9) Afte obtaining the expession fo the tansmit thoughput pe node pe second, we have to find an expession fo the aveage numbe of nodes within the communication age of a given node (i.e., the aveage numbe of neighbos fo a given node). In Figue 6, the ectangula field is patitioned into thee diffeent egions accoding to the coveage chaacteistic of a node in a paticula egion. Fo example, a node inside egion 1 (e.g., n ) has its full coveage within the boundaies of the field. Theefoe, any node inside egion 1 utilizes 1% of its total coveage. Wheeas nodes inside egions and 3 (e.g., n 1 and n 3 ) Fig. 7. Calculation of the pecentage coveage of a node inside egion. have a pat of thei coveage outside the field of inteest and consequently the aveage pecentage coveage fo these nodes is less than 1%. Finding the pecentage coveage fo each egion will lead us to the aveage numbe of neighbos. We stat the deivation of the pecentage with egion. In Figue 7 the appoach we used fo obtaining the pecentage is given. The aea of the piece of cicle shaded in Figue 7 can be expessed as follows: I = x x dx = π 4 x x acsin(x ). Thus, the aveage coveage fo egion (α ) becomes, α = 1 = 1 A(x )dx = π 3. ( π I(x ) ) dx (1) (11) Afte obtaining the aveage coveage as in Equation (11), we can easily calculate the pecentage coveage of egion (σ ). σ = α π = 1 3π (1) Next we deive the aveage coveage fo egion 3 (σ 3 ). The aea in question is divided into thee pats (see Figue 8). Accoding to this patitioning we have A = π (A 1 + A A 3 ), which is the coveage fo a node inside egion 3. The integals fo A 1 and A ae the same as I given in Equation (1) and can be expessed as I(x ) and I(y ), espectively.

6 y ( ) A 3 = x y x = y y dx + y acsin( ) (13) x x acsin( x ) + y x. Afte obtaining A 3, we can calculate the aveage coveage α 3 by taking the aveage of A. α 3 = 1 = π 9 4. Thus, σ 3 becomes: A (x, y ) dx dy (14) σ 3 = α 3 π = 1 9 (15) 4π This is the last pecentage coveage we needed to calculate the oveall pecentage coveage (σ), o the aveage numbe of nodes within the ange of a given node inside the ectangula field. Below we give the esulting σ in tems of the communication adius, the length of the field L and the height of the field H. σ = σ 1(L )(H ) + σ (H + L 4) + 4σ 3 LH (16) This expession can be used to calculate the aveage numbe of neighboing nodes (N N ) fo a node inside of a ectangula field by multiplying σ with π (i.e., the coveage of a node with communication adius ) and the node density ( (N 1) LH ). Note that thee ae N 1 nodes emaining that can be neighbos. (N 1)σπ N N = (17) LH Now, we can combine Equation (17) with Equation (9) to get the eceive thoughput pe node pe second T. Aveage numbe of eceived packets MHTRACE no eo Numbe of Nodes Fig. 9. Aveage numbe of eceived packets pe node pe second vesus numbe of nodes. T = N N T node (1 BER) L D (18) Accoding to ou model, given that we have a constant simulation aea and the same taffic model, thoughput inceases as the numbe of nodes in the netwok inceases. In othe wods, the model suggests that thoughput inceases linealy with inceasing node density. Howeve, ou pevious wok showed that thoughput pe node pe second goes into satuation as the numbe of nodes in the netwok inceases (see Figue 9). This tend is a esult of packet collisions and dops emeging fom mobility and inceased contention fo channel access [7]. Accoding to this fact, we have to modify ou initial thoughput value (thoughput when thee is a pefect channel) in ode to get a moe accuate model fo thoughput. Since it is extemely challenging to model the dynamical behavio in Figue 9 analytically, the initial thoughput values ae calibated accoding to feedback fom simulation esults. SIMULATIONS In this section we pesent simulations to demonstate the validity of the analytical esults. The simulation paametes ae given in Table II. y TABLE II SIMULATION SETUP y => x A 1 x => A => A 3 Fig. 8. Calculation of the pecentage coveage of a node inside egion 3. PARAMETER SET 1 SET Numbe of Nodes 1 1 Simulation Aea 1m x 1m 1m x 1m Simulation Time s s Potocol MH-TRACE/ MH-TRACE/ IEEE 8.11 IEEE 8.11 Numbe of Repetition 1 1 Node Mobility Stationay Mobile

7 Aveage Numbe of Received Packets MH TRACE MH TRACE Model IEEE 8.11 IEEE 8.11 Model Bit Eo Rate Fig. 1. SET 1 (Stationay nodes): Aveage numbe of eceived packets pe node pe second vesus bit eo ate (BER). The esults of SET 1 simulations ae given in Figue 1, which pesents the eceive thoughput pe node pe second fo MH-TRACE and IEEE 8.11 along with the analytical esluts as a function of the BER. MH-TRACE thoughput is obtained fom the analytical model in Equation (18). The guideline fo IEEE 8.11 is obtained by using the pobability of successful data packet tansmission ((1 BER) L D ) and the initial thoughput value. When we look at Figue 1, we see that the thoughput of MH-TRACE is highe than IEEE 8.11 fo low BER (i.e., BER < 1 4 ). Howeve, as BER inceases, MH-TRACE thoughput deceases below the thoughput of IEEE Although this pefomance loss seems to be a dawback fo any coodinated potocol, we have to keep in mind that the BER value at which the pefomance of MH-TRACE becomes wose than IEEE 8.11 causes almost 3% of the data packets to be dopped. Fo SET simulations, nodes ae mobile and we use a Random Way-Point mobility model with node speeds chosen fom a unifom distibution between. m/s and 5. m/s (the aveage pace of a maathon unne) with zeo pause time. As shown in Figue 11, the aveage thoughputs fo MH-TRACE and IEEE 8.11 ae almost 4% moe than Aveage Numbe of Received Packets MH TRACE MH TRACE Model IEEE 8.11 IEEE 8.11 Model Bit Eo Rate Fig. 11. SET (Mobile nodes): Aveage numbe of eceived packets pe node pe second vesus bit eo ate (BER). the thoughputs with stationay nodes. This is a esult of the mobility model which makes the nodes accumulate in the middle of the field instead of distibuting them unifomly [9], poviding a lage aveage numbe of neighbos (N N ) than in the stationay case. Theefoe the initial thoughput value is calibated. Note that afte adjusting the initial value the fom of the cuve tacks the simulation esults closely. CONCLUSIONS In this pape we poposed an analytical model fo the thoughput of MH-TRACE. Paametes such as netwok aea, numbe of nodes and BER of the channel ae included in the model. Moeove, we deived an expession to detemine the aveage numbe of single-hop neighbos. The impact of channel eos on the pefomance of MH-TRACE and IEEE 8.11, which ae examples of coodinated and non-coodinated MAC potocols, espectively, ae estimated by using this model. We also pesented ns- simulations to demonstate the validity of the model. As expected, the pefomance of MH-TRACE is bette than IEEE 8.11 fo low-mid BER levels. Howeve, fo extemely high BER ates IEEE 8.11 pefomance is bette than MH-TRACE due to the dependence of MH-TRACE on the obustness of the contol packet taffic. Howeve, fo highe data ates o node densities, we expect MH-TRACE to pefom bette than IEEE 8.11 even unde vey high BER levels due to its coodinated channel access mechanism. REFERENCES [1] W. Stallings. Wieless Communications and Netwoks. Pentice-Hall,. [] A. Chanda, V. Gummalla, and J. O. Limb. Wieless medium access contol potocols. IEEE Communications Suveys and Tutoials, 3: 15,. [3] P. Mohapata, J. Li, and C. Gui. QoS in mobile ad hoc netwoks. IEEE Wieless Communications, 1(3):44 5, June 3. [4] D. A. Maltz, J. Boch, and D. B. Johnson. Lessons fom a full-scale multihop wieless ad hoc netwok testbed. IEEE Pesonal Commun. Mag., 8(1):8 15, Feb 1. [5] T. Cooklev. Wieless Communication Standats. IEEE Pess, 4. [6] B. Tavli and W. B. Heinzelman. MH-TRACE: Multi hop time esevation using adaptive contol fo enegy efficiency. IEEE Jounal on Selected Aeas of Communications, (5):94 953, June 4. [7] T. Numanoglu, B. Tavli, and W. B. Heinzelman. The effects of channel eos on coodinated and non-coodinated medium access contol potocols. IEEE Intenational Confeence on Wieless and Mobile Computing, 5 (Available at numanogl/wimob 5.pdf). [8] D. J. Goodman and S. X. Wei. Efficiency of packet esevation multiple access. IEEE Tans. Vehic. Tech., 4(1):17 176, Feb [9] W. Navidi and T. Camp. Stationay distibutions fo the andom waypoint mobility model. Technical Repot MCS-3-4, The Coloado School of Mines, Apil 3.