Performance of A Burst-Frame-Based. CSMA/CA Protocol for High Data Rate Ad. Hoc Networks: Unsaturated Throughput. Analysis

Transcription

1 Performance of A Burst-Frame-Based CSMA/CA Protocol for High Data Rate Ad Hoc Networks: Unsaturated Throughput Analysis Kejie Lu, Jianfeng Wang, Dapeng Wu, and Yuguang Fang Abstract In high data rate wireless ad hoc networks, the throughput of MAC protocols is significantly limited by the overhead such as control messages. To improve the throughput in high data rate networks, we recently proposed [] a general framework for MAC protocols based on the well-known CSMA/CA. The key idea of this framework is to aggregate multiple upper-layer packets into a larger burst frame at the MAC layer, thus the overhead can be substantially reduced. In this paper, we develop an analytical model to evaluate the unsaturated throughput performance of a burst-frame-based CSMA/CA protocol, which is within the framework. The uniqueness of our analytical model is that we consider both the unsaturated traffic condition and a queueing system with bulk service, in which the burst service time depends on the number of packets in the burst and depends on the channel access condition. The This work was supported in part by the US National Science Foundation under Faculty Early Career Development Award ANI The authors are with the department of Electrical and Computer Engineering, University of Florida, Gainesville, FL-326, USA. lukejie@ieee.org, jfwang@ufl.edu, {wu, fang}@ece.ufl.edu. Please direct all correspondence to Prof. Dapeng Wu. Tel. (352) , Fax (352) , URL: wu@ece.ufl.edu.

2 2 proposed analytical method is general and hence applicable to unsaturated performance analysis for other MAC protocols, such as classic IEEE Our numerical results from the analytical method give excellent agreement with the simulation results, indicating the accuracy of our analytical method. Extensive simulation and analysis results also show that, the proposed MAC protocol can significantly improve the throughput performance. Index Terms Ad hoc networks, high data rate, MAC, CSMA/CA, burst frame, analytical model, unsaturated throughput I. INTRODUCTION In the past decade, wireless ad hoc networks have been studied extensively in both academia and industry. With the advances in wireless communication technologies such as multi-input multi-output (MIMO) [2] and ultra-wide Band (UWB) [3], the next generation wireless ad hoc networks are able to provide high data rate (> 00 Mb/s) in the physical layer [4], [5]. To efficiently utilize these high data rate, medium access control (MAC) protocols must be carefully designed. In this paper, we will focus on MAC protocols that are based on carrier sense multiple access with collision avoidance (CSMA/CA), since CSMA/CA is the most popular MAC scheme and has been standardized in IEEE In high data rate wireless ad hoc networks, the throughput of MAC protocols is significantly limited by the overhead, which becomes more serious with the increase of the physical layer data rate. In CSMA/CA, the overhead includes collision, control messages, backoff, and various interframe-spacing. To reduce these overheads, a common solution is to transmit multiple packets in a burst, instead of transmitting them one by one [], [6] [8]. In [], we provided a general framework to address the overhead issue. In this paper, we will elaborate on the performance analysis for a burst-frame-based MAC protocol within the proposed framework. Performance of CSMA/CA protocols, particularly IEEE 802., has been studied extensively

3 3 in the literature [9] [8]. Most of these works are focused on saturation performance analysis, e.g., [9], [0]); here by saturation, we mean a node in the network always has packets ready to be transmitted, thereby saturating the wireless channel. On the other hand, a few works [] [5] address the performance under the unsaturated case. In [], [2], the authors evaluate the unsaturated performance by directly extending the saturation model in [9]; in [3] [5], the authors extend the linear feedback model proposed in [9] to analyze the unsaturated performance. These approaches, however, assume that the size of the queue is zero, which may not be realistic since typically the size of the queue is non-zero. The non-zero-queue case for IEEE 802. has recently been studied in [6], [7], the model of which is based on a G/G/ queue. However, due to computational complexity, the model uses several approximated parameters, such as the probability that a node has no packet to transmit. Consequently, the analysis results in a large deviation from the simulation results. Moreover, the model is not suitable for high traffic load condition since the queue size is assumed to be infinite, which may not be valid in practice. In [8], the system under study is decomposed into a queueing subsystem and a service subsystem. In this model, the MAC layer queue is modelled as M/G//K; the service time is characterized by a transfer function. However, this model is not directly applicable to the unsaturated performance analysis of our burst-frame-based MAC protocol due to the complicated queueing behavior caused by burst frames. Besides the analysis for IEEE 802., queueing systems with batch/bulk service have been studied in [20] [23]. However, all these analyses assume that the service time distribution does not depend on the size of the batch. This assumption, however, is not valid in our study, in which the service time of a burst frame depends on the length of the burst, the number of packets in the burst, and the method of accessing the channel. The packet in service is not part of the queue.

4 4 In this work, we take the same transfer-function approach used in [8] to analyze the unsaturated performance of our burst-frame-based MAC protocol. The major contribution of our work is that our analytical method can analyze complicated queueing behavior and provide accurate results, which has not been achieved previously. Our numerical results from the analytical method give good agreement with the simulation results, validating the accuracy of our analytical method. The rest of the paper is organized as follows. In Section II, we briefly describe our MAC protocol for high date rate ad hoc networks. In Section III, we analyze the unsaturated performance of the MAC protocol. Simulation and numerical results will be shown in Section IV. Finally, Section V concludes the paper. II. A BURST-FRAME-BASED MAC PROTOCOL In this section, we briefly describe our burst-frame-based MAC protocol proposed in []. The key idea of this protocol is that a transmitting node can aggregate multiple upper-layer packets into a burst at the MAC layer and transmit the burst to a destination node, instead of transmitting each upper-layer packet individually. In this manner, the overhead can be substantially reduced. In this protocol, we consider only one quality-of-service (QoS) class of traffic for each destination, i.e., all packets for the same destination have the same QoS requirements. Incoming packets are first classified based on its destination, and then put into a corresponding packet queue. Suppose there are N nodes in an ad hoc network; then we can implement N packet queues in each node, where the N queues are used for buffering packets destined to other N nodes. For each queue, we use tail-dropping when there is a buffer overflow. A burst frame will be generated if the total number of packets in the queue exceeds a threshold B min and the server is idle (i.e., there is no other burst waiting for transmission). In addition, we assume that the total number of packets in a burst must be smaller than or equal to a preset value B max. In this protocol, we require that all the packets in a burst frame have the same destination so that most existing functions of IEEE 802. can be re-used. To achieve the fairness among

5 5 destinations, a simple round-robin scheme will be employed for the N queues in a node. When a burst assembly is finished, the burst frame will be stored in a buffer and waiting for transmission. If a burst frame is correctly received, the receiver will send one ACK frame to the transmitter. III. UNSATURATED PERFORMANCE ANALYSIS In this section, we present an analytical model for evaluating our burst-frame-based MAC protocol under different incoming traffic load. Similar to [8], we also decompose the system into a queueing subsystem and a service subsystem. For the queueing subsystem, we extend the model for general bulk service queues [23]. Particularly, we consider that a burst can be assembled only when the total number of packets in the queueing subsystem is greater than or equal to B min ; we also consider the fact that the service time depends on the number of packets in the burst, which is not considered in [23]. For the service subsystem, we analyze the impact of burst assembly on the probability that a server is idle, and on the service time distribution. To facilitate our discussion, we make the following assumptions: There are N identical nodes in the network. At each node, packet arrivals are Poisson with rate λ (packets/sec), and the packets have a common destination. The size of each packet is fixed at P (bits). The burst service time is an integer multiple of a preset time unit τ (sec). Here the burst service time is defined as the time interval from the time epoch that a burst is assembled to the time epoch that the burst is removed from the transmission buffer. 2 A transmission buffer is located in the service subsystem. Packets being stored in a transmission buffer means that the packets are in service. 2 A burst will be removed from the transmission buffer if the burst is successfully received by the destination, or if the number of burst transmission failures exceeds a pre-defined retry limit.

6 6 There is no transmission failure due to bit errors. The probability that a burst transmission attempt fails, denoted as p, does not depend on the backoff stage of the node. The propagation delay is negligible. A. The Bulk Service Queueing System Based on the assumptions above, we can model the queueing system in any node as an M/G [B min,b max] //K queue, where K is the capacity of the queue and the superscription [B min,b max ] means that the total number of packets in a burst is an integer in the range of [B min,b max ]. Note that here K is the total number of packets that can be stored in the queue, which does not include packets in the transmission buffer. To analyze this queueing system, we first define the state space of the queueing system according to the status of server and the number of packets in the queue. Particularly, state I k means that the server is idle and there are k customers waiting in the queue; while state A k means that the server is busy and there are k customers waiting in the queue. With the packet assembly policy described in the previous section, we note that if the server is idle, then the maximum number of packets in the queue must be smaller than B min. Therefore, the state space is S = {I 0,I,,I Bmin,A 0,A,,A K }. Let ξ(t) (t 0) be the state of the queueing system at time t; let δ n be the epoch of the n-th burst departure. We now consider the embedded Markov process ξ n, where ξ n is the state of the queueing system just before δ n, which is ξ n = ξ(δ n ). An embedded Markov chain can then be formulated, where the state space is {A 0,A,,A K }. Let p d k (0 k K) be the steady-state probability that ξ n = A k ; let p ij be the steady-state

7 7 transition probability from state A i to state A j for all i, j, where 0 i K and 0 j K: p ij = lim n Pr[ξ n+ = A j ξ n = A i ]. Consequently, p d k can be obtained by solving the embedded Markov chain with all p ij. To calculate p ij, we define α(k, b) as the probability that k packets arrive during one burst service time, given that the burst contains b packets. Let B(t) be the number of packets in the first burst after t. Define B k = B(δ n ) given that ξ n = k. Here we note that B k depends only on the assembly policy, B k = B min k 0 k B min B min <k B max () B max B max k K. Since B k packets will be assembled into the first burst after δ n if ξ n = k, we can see that the number of packets remaining in the queue immediately after the burst is created, denoted by K k,is K k =max(0,k B k ). (2) Therefore, we can calculate all p ij through 0 0 j<k i p ij = α(j K i,b i ) K i j<k. (3) K α(k K i,b i ) k=k i j = K Let q bi be the steady state probability that the burst service time is iτ, given that there are b packets in the burst. Since the packet arrival is a Poisson process with rate λ, α(k, b) can be calculated by α(k, b) = i q bi (λiτ)k e λiτ k!. (4) In summary, we note that p d k can be calculated if all q bi are known.

8 8 M p t = b m,0 = m=0 2( 2p)( p M+ ) ( 2p)( p M+ )+W ( p)( (2p) M+ ) 2( 2p)( p M+ ) ( 2p)( p M+ )+W ( p)( (2p) K+ )+W 2 M p K+ ( 2p)( p M K ) m M m>m (7) B. Exponential Backoff Scheme Using the Markov modelling technique introduced in [9], we can analyze the exponential backoff scheme for the MAC protocol. Specifically, we can partition the continuous time axis into slots, where two consecutive slots are delimited by the event of a value change in the backoff counter. We can then formulate a two-dimensional discrete time embedded Markov chain, shown in Fig., with state {s n,b n }, where n is the index of a slot, b n is the value of the backoff counter in slot n, and s n is the index of the backoff stage in slot n. In Fig., M denotes the maximum index of backoff stages; or equivalently, the maximum number of retries for a packet [0]. Let W and 2 M W denote the minimum and maximum backoff window size, respectively. Then the backoff window size at stage m can be defined as 2 m W m M W m = (5) 2 M W m > M. Define the steady state probability of state {s n = m, b n = i} as b m,i = lim n Pr[s n = m, b n = i]. (6) With the Markov chain in Fig., a closed-form solution for all b m,i can be derived. Let p t be the probability that a node will transmit a burst given that the node is busy. Since a transmission is initiated if and only if b n =0, we can obtain the relationship between p t and p, characterized by Eq. (7).

9 9 Since a successful packet delivery means that there is no collision, we can calculate p through p = [ ( p I )p t ] N (8) where p I denotes the probability that a node is idle (no burst pending for transmission) in slot n. With 0 <p< and 0 <p t <, we can calculate p and p t numerically through Eq. (7) and Eq. (8). To calculate p I,weletd k (t) (0 k K) be the total number of burst departures in time (0,t) such that the number of packets in the queue is k just before the departure; let D(t) = k d k (t) be the total number of burst departures in (0,t). Note that if there are k (k <B min ) packets in the queue just before a departure, then the average time from the departure of the old burst to the epoch that a new burst if formed is (B min k), since packet arrivals are Poisson with λ rate λ. We can then estimate p I as the fraction of time that the server is idle, which is p I = lim B min t ( λ) d k (t) (B min k) d k (t) Similar to [23], lim t t lim t t = B min λ k=0 k=0 [ can be calculated by d k (t) D(t) lim D(t) t t d k (t) (B min k) lim t t [ = p d k lim t t Since D(t) is the total number of served bursts in t, lim t D(t) interval. Therefore, we have lim t B t min D(t) = T s + k=0 p d k ]. (9) ] t. (0) D(t) [ (B min k) ] λ is the average burst departure where T s denotes the average burst service time, which is [ ] K T s = q Bk i (iτ). (2) Finally, p I can be calculated through p I = p d k k=0 B min λt s + i k=0 B min (B min k)p d k k=0 (B min k)p d k (). (3)

10 0 To summarize this subsection, we note that p and p t can be calculated if all p d k are known. C. Service Time Distribution Let Q b (z) be the probability-generating function (PGF) of q bi, which is Q b (z) = i z i q bi. (4) Due to the simplicity of calculation in the z-transform domain and the one-to-one correspondence between q bi and Q b (z), we compute Q b (z) instead of q bi. This approach is known as the transferfunction approach [8]. To calculate Q b (z), weletx n be the length of slot n and let X n be the length of a period (within slot n), during which the server is busy. Note that for saturated condition, X n X n. However, for unsaturated cases, X n X n. We can then apply the technique used in [8]. In this model, the packet transmission process is characterized by a linear system, shown in Fig. 2, where H(z) is the PGF of X n given that the current node is active but not transmitting; C b (z) is the PGF of X n given that a collision occurs and the current node has transmitted a burst that has b packets; and S b (z) is the PGF of X n given that the current node has successfully transmitted a burst with b packets. Consequently, the transfer function of the linear system is equal to Q b (z). To simplify the notation, we define H m (z) as follows H m (z) = W m [ +H(z)+H 2 (z)+ + H Wm (z) ]. (5) Then Q b (z) can then be calculated through [ M Q b (z) = ( p)s b (z) (pc b (z)) m m ] H i (z) m=0 i=0 +(pc b (z)) M+ M H i (z). i=0 We now consider the calculation of S b (z), C b (z), and H(z). Due to limited space, here we only discuss the calculation for the RTS/CTS access scheme. Since the packet size is fixed, S b (z) (6)

11 and C b (z) can be directly derived as S b (z) = z (Tso+ bp R ) τ C b (z) = z Tco τ (7) where R is the data rate, T so is the time overhead for a successful transmission, and T co is the time overhead for collision. According to IEEE 802. protocol, we have T so = 4T sync +3T SIFS + T DIFS + R (4L PH + L RT S + L CTS + L ACK + L MH ) T co = 2T sync + T SIFS + T DIFS + R (2L PH + L RT S + L CTS ) (8) where T sync denotes the synchronization time, T SIFS denotes the time duration of SIFS, T DIFS denotes the time duration of DIFS, L PH denotes the length of physical frame header in bits (excluding the synchronization preamble), L MH denotes the length of MAC frame header in bits, L RT S denotes the length of ACK frame in bits, L CTS denotes the length of ACK frame in bits, and L ACK denotes the length of ACK frame in bits. To calculate H(z), we define the following parameters: q t denotes the probability that there is at least one packet transmission in N nodes in slot n, which is q t = [ ( p I )p t ] N (9) q s denotes the probability that there is only one packet transmission in N nodes in slot n, which is q s =(N )( p I )p t [ ( p I )p t ] N 2 (20) σ denotes the length of a preset fixed time duration for backoff. When there is no packet transmission, we have X n = σ. In 802.b direct sequence spread spectrum mode, σ = 20µs.

12 2 With these parameters, we have H(z) =( q t )z σ τ + q s S(z)+(q t q s )C(z) (2) where C(z) =C b (z) and B max S(z) = p b S b (z), (22) b=b min p b = p d k, (23) k:b k =b where p b is the probability mass function of the number of packets in a burst. To summarize this subsection, we note that the service time distribution q bi can be calculated if p, p t, and all p d k are known. D. Throughput Analysis Let S(t) be the total number of successfully transmitted packets in [0,t]. Then we have [ K ] S(t) = d k (t) B k + B(0) B(t) ( p M+). (24) k=0 Now define throughput S as the total amount of data (in bits) of MAC payload successfully received in a given time (in sec). Based on Eqs. (24), (0), and (), we have S(t) S = lim P t t P E[B] ( p M+ ) = T s + B min λ (B min k)p d k where E[B] is the average number of packets in a burst E[B] = B max b=b min [b p b ]. k=0 (25) E. Summary of the Algorithm In this analytical model, since p I and p b are unknown initially, we need to use a recursive algorithm to get a good estimate of p I and p b ; once we obtain an accurate estimate of p I and p b, we can calculate the throughput accurately. The recursive algorithm can be summarized as follows.

13 3 ) Initialize p I and p b to saturated condition, i.e., let p I =0, p Bmax =, and p b =0for b B max. 2) Calculate p and p t through Eq. (7) and Eq. (8). 3) Calculate service time distribution q bi, using the transfer-function approach. 4) Calculate p d k by using the bulk service queueing model. 5) Calculate p I through Eq. (3). 6) Calculate p b through Eq. (23). 7) Calculate S through Eq. (25) and stop if the result converges, i.e., the difference between the results of two consecutive iterations is less than a preset value (denoted by ε S ); otherwise go to Step 2. Although the convergence of the recursive algorithm has not been proved, the algorithm always achieves convergence in our numerical calculations. IV. SIMULATION AND NUMERICAL RESULTS In this section, we evaluate the performance of the burst-frame-based MAC protocol and compare the numerical results of the proposed analytical method in Section III, to the simulation results. Table II lists the values of the control parameters used in the simulations and numerical analysis. Experiments are conducted with the following setting: All nodes are located in a 4 m 4 m area. Unless otherwise specified, we assume that the number of nodes in the network is N =0. All messages are transmitted with channel data rate R. The size of each packet is fixed at 000 Bytes. Packet arrivals to any node i are modelled by a Poisson process with the same rate λ (packets/s). Consequently, the incoming traffic data rate is R i = NPλ (bits/s). We assume that T sync is identical for all messages.

14 4 We assume that no packet transmission failure occurs due to bit errors. We assume that the RTS/CTS scheme is used. For the analytical model, we let time unit τ = σ, let ε S =0 3, and let the maximum service time be time units. To see how the analytical result evolves with the number of iterations, we plot Figure 3, which shows the throughput obtained from our analytical formulae vs. the number of iterations, where we let B min =, B max =0, and R i =90Mb/s. We can observe that, if the number of iterations is larger than 5, the analytical result converges, and is very close to the simulation result. Figure 4 compares the throughput performance versus incoming traffic rate for three burst assembly policies: ) [B min,b max ]=[, ] (benchmark), 2) [B min,b max ]=[, 0],3)[B min,b max ]= [0, 0], where we assume that R = 00 Mb/s and that T sync = 0µs, which is a typical assumption in [5]. We can see that, compared to the benchmark case, the proposed MAC protocol can significantly improve the throughput performance. Particularly, if R i = R, the benchmark throughput is only about 52.4 Mb/s; while policy 2 and 3 can achieve as high as 88.3 Mb/s and 90.6 Mb/s, respectively. We also note that policy 3 performs slightly better than policy 2 when the traffic load is high. From Fig. 4, we can observe that our analytical model is highly accurate under different incoming traffic rates. The configuration for Fig. 5 is the same as that for Fig. 4, except the synchronization time T sync, which is 00µs. We observe that, as the overhead becomes larger, the throughput performance of the benchmark scheme is significantly lower than the channel data rate. Specifically, the saturated throughput of policy is only about 3.2 Mb/s. In comparison, we can see that the proposed MAC can still achieve rather high throughput. Particularly, if R i = R, policy 2 and 3 can achieve as high as 58.8 Mb/s and 60.3 Mb/s, respectively. Figure 6 illustrates the throughput performance vs. incoming date rate, where we let N =50,

15 5 T sync =0µs, and R = 200 Mb/s. We compare two burst policies: ) [B min,b max ]=[, ] (benchmark), and 2) [B min,b max ]=[3, 5]. Similar to Fig. 4 and Fig. 5, we observe that policy 2 can significantly outperform the benchmark policy. Interestingly, we can see that the throughput when R i = R is not the maximum throughput. Specifically, we note that the maximum throughput for the benchmark policy is 68.5 Mb/s, achieved when R i =80Mb/s; the maximum throughput for policy 2 is 25.6 Mb/s, achieved when R i = 40 Mb/s. These results will be useful for designing admission control schemes, which can adjust incoming traffic date rates in order to optimize the overall throughput. Figure 7 shows the normalized throughput, defined as S/R, vs. channel date rate, where we let N =0, T sync =0µs, and R i /R =0.9. In this case, we compare two burst assembly policies: ) [B min,b max ]=[, ] (benchmark), and 2) [B min,b max ]=[2, 0]. We can observe that, for both policies, the normalized throughput decrease with the increase of channel date rate, which implies that the overhead is more significant when the date rate is higher. Similar to previous results, we see that the proposed MAC protocol significantly outperforms the benchmark protocol. In addition, we can observe that, for policy 2, the decrease of normalized throughput is less than that for the benchmark case. Specifically, when the channel data rate increases from 50 Mb/s to 500 Mb/s, the normalized throughput of the benchmark policy decreases from 64% to 20%; while the normalized throughput of policy 2 decreases from 87% to 67%. In summary, our analytical model is quite accurate under different conditions. Such accuracy has not been achieved by the previous analysis. V. CONCLUSIONS In this paper, we develop an analytical model to evaluate the unsaturated throughput performance of a burst-frame-based CSMA/CA protocol, in which multiple upper layer packets can be assembled into a large burst frame at the MAC layer. The proposed analytical model is unique in that we consider both the unsaturated traffic condition and a queueing system with bulk service,

16 6 in which the burst service time depends on the number of packets in the burst and the method of channel access. Moreover, the proposed analytical method is general and hence applicable to unsaturated performance analysis for other CSMA/CA protocols, for example, IEEE Extensive simulation and analytical results also show that, the proposed MAC protocol can significantly improve the throughput performance, compared to the conventional protocol where upper layer packets are transmitted individually. More importantly, our numerical results from the analytical method give excellent agreement with the simulation results; such accuracy has not been achieved by the previous analysis; hence our analysis represents a major contribution. REFERENCES [] K. Lu, D. Wu, and Y. Fang, A novel framework for medium access control in ultra-wideband ad hoc networks, Dynamics of Continuous, Discrete and Impulsive Systems (Series B) Special Issue on Ultra-Wideband (UWB) Wireless Communications for Short Range Communications, (to appear), [Online]. Available: camera.pdf [2] D. Gesbert, M. Shafi, D. shan Shiu, P. J. Smith, and A. Naguib, From theory to practice: an overview of MIMO space-time coded wireless systems, IEEE J. Select. Areas Commun., vol. 2, no. 3, pp , Apr [3] S. Roy, J. R. Foerster, V. S. Somayazulu, and D. G. Leeper, Ultrawideband radio design: The promise of high-speed, short-range wireless connectivity, Proc. IEEE, vol. 92, no. 2, pp , Feb [4] Airgo Networks (Web Page). [Online]. Available: [5] IEEE P /037r, DS-UWB physical layer submission to Task Group 3a, Mar. 2004, Project: IEEE P802.5 Working Group for Wireless Personal Area Networks (WPANs). [6] Y. Xiao, MAC performance analysis and enhancement over 00 Mbps data rates for IEEE 802., in Proc. IEEE VTC Fall, Oct. 2003, pp [7], Concatenation and piggyback mechanisms for the IEEE 802. MAC, in Proc. IEEE WCNC, Mar. 2004, pp [8] Y. Yuan, D. Gu, W. Arbaugh, and J. Zhang, High-performance MAC for high-capacity wireless LANs, in Proc. IEEE ICCCN, [9] G. Bianchi, Performance analysis of the ieee 802. distributed coordination function, IEEE J. Select. Areas Commun., vol. 8, no. 3, pp , Mar [0] H. Wu, Y. Peng, K. Long, S. Cheng, and J. Ma, Performance of reliable transport protocol over IEEE 802. wireless LAN: analysis and enhancement, in Proc. IEEE INFOCOM, June 2002, pp

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18 8 TABLE I SUMMARY OF PARAMETERS USED IN THE ANALYTICAL MODEL. Parameters for the queueing subsystem I k A k S = {I 0,I,,I Bmin,A 0,A,,A K } ξ(t) δ n Description state of the queueing system when the server is idle and there are k customers waiting in the queue state of the queueing system when the server is busy and there are k customers waiting in the queue state space of the queueing system state of the queueing system at time t the departure time of the n-th burst ξ n ξ(δ n ) p d k p ij α(k, b) p I B(t) B k steady state probability that the system state is A k just before a burst departure steady state transition probability from state A i to A j probability that there are k packet arrivals during a burst service time if the burst has b packets probability that the server is idle number of packets in the first burst after t B(δ n) if ξ n = k K k max(0,k B k ) d k (t) D(t) Parameters for the service time subsystem τ q bi p p t T s Q b (z) number of burst departures in (0,t), just before which there are k packets in the queue total number of burst departures in (0,t) Description the unit of service time steady state probability that the burst service time is iτ, given that there are b packets in the burst probability that a collision occurs in a slot probability that a node will transmit a burst in a slot average service time probability-generating function (PGF) of q bi X n length of slot n (in unit of τ) X n length of a period (within slot n), during which the server is busy (in unit of τ) S b (z) C b (z) H(z) S(z) C(z) PGF of X n if a burst transmission succeeds in a slot and the burst has b packets PGF of X n if a burst transmission fails in a slot and the burst has b packets PGF of X n if the current node backs off PGF of X n if a burst transmission succeeds in a slot and the current node backs off PGF of X n if a collision occurs in a slot and the current node backs off

19 9 TABLE II SETTING OF THE MAC PROTOCOL. Minimum contention window size 8 Maximum contention window size 256 σ 2 µs SIFS µs DIFS 5 µs Retry limit 4 Queue size 50 ( p) p/w /W0 0,0 0, 0,W 2 0,W 0 0 p/wi ( p) i,0 i, i,w 2 i,w i p/wi+ i p/wm ( p) M,0 M, p/wm M,0 M, M,W 2 M M,W M Fig.. State transition diagram for the backoff scheme.

20 20 S (z) b p p p p X(z) /W 0 p C (z) b /W p C (z) b p C (z) b /W M p C (z) b Y(z) H(z) H(z) H(z) /W 0 /W /W M H(z) H(z) H(z) /W 0 /W /W M /W 0 H(z) /W H(z) /W M H(z) Fig. 2. Service system diagram. 90 Analysis Simulation 85 Throughput (Mb/s) Iteration Fig. 3. Analytical results vs. number of iterations (B min =,B max =0,R i =90Mb/s).

21 2 Throughput (Mb/s) [Bmin,Bmax]=[,] (Ana) [Bmin,Bmax]=[,] (Sim) [Bmin,Bmax]=[,0] (Ana) [Bmin,Bmax]=[,0] (Sim) [Bmin,Bmax]=[0,0] (Ana) [Bmin,Bmax]=[0,0] (Sim) Incoming traffic data rate (Mb/s) Fig. 4. Throughput performance vs. incoming traffic data rate with different burst assembly policies (N =0,T sync =0µs, R = 00 Mb/s). Throughput (Mb/s) [Bmin,Bmax]=[,] (Ana) [Bmin,Bmax]=[,] (Sim) [Bmin,Bmax]=[,0] (Ana) [Bmin,Bmax]=[,0] (Sim) [Bmin,Bmax]=[0,0] (Ana) [Bmin,Bmax]=[0,0] (Sim) Incoming traffic data rate (Mb/s) Fig. 5. Throughput performance vs. incoming traffic data rate with different burst assembly policies (N =0,T sync = 00µs, R = 00 Mb/s).

22 [Bmin,Bmax]=[,] (Ana) [Bmin,Bmax]=[,] (Sim) [Bmin,Bmax]=[3,5] (Ana) [Bmin,Bmax]=[3,5] (Sim) Throughput (Mb/s) Incoming traffic data rate (Mb/s) Fig. 6. Throughput performance vs. incoming traffic data rate with different burst assembly policies (N =50,T sync =0µs, R = 200 Mb/s). 0.8 Normalized throughput [Bmin,Bmax]=[,] (Ana) [Bmin,Bmax]=[,] (Sim) [Bmin,Bmax]=[2,0] (Ana) [Bmin,Bmax]=[2,0] (Sim) Channel data rate R (Mb/s) Fig. 7. Throughput performance vs. channel data rate with different burst assembly policies (N = 0,T sync = 0µs, R i/r =0.9).