Non-saturated and Saturated Throughput Analysis for IEEE e EDCA Multi-hop Networks

Non-saturated and Saturated Throughput Analysis for IEEE 80.e EDCA Multi-hop Networks Yuta Shimoyamada, Kosuke Sanada, and Hiroo Sekiya Graduate School of Advanced Integration Science, Chiba University, Chiba, 63-85 Japan Email: shimoyamada@chiba-u.jp Abstract This paper presents first-step analytical expressions of non-saturated and saturated throughput for IEEE 80.e Enhanced Distributed Channel Access (EDCA) multi-hop string-topology networks. Internal collisions in each node, concurrent transmission collisions among nodes, differences of CW min and CW max among access categories (ACs), and effects of contention zone are considered. By comparisons with simulation results, the validities of analytical expressions are confirmed. Keywords IEEE 80.e multi-hop networks, throughput analysis, non-saturated throughput, saturated throughput, internal collision, contention zone. I. Introduction The IEEE 80. has become ubiquitous and gains widespread popularity for wireless multi-hop networks. The basic Medium Access Control (MAC) protocol of the IEEE 80. standard is Distributed Coordination Function (DCF) [], which provide no support of Quality of Service (QoS). However, due to a growth of multi-media applications, such as video streaming and voice, importance of supporting QoS is rapidly increasing. For supporting QoS, IEEE 80.e Enhanced Distributed Channel Access (EDCA) is extended from IEEE 80. DCF, which has been standardized in IEEE 80.e []. The EDCA node has four access categories (ACs), which contend channel access independently. It is possible to realize the channel-access-priority differentiations according to ACs by setting the proper EDCA parameters which are CW min, CW max, and arbitration inter frame space number (AIFS N). It is important to obtain analytical expressions of throughput, transmission probability, collision probability, and transmission delay for wireless networks. The analytical expressions provide network performance predictions with very short time and low computation cost compared with network simulators. In addition, it is easy to comprehend the relationships between protocol parameters and network performance when the analytical expressions can be obtained. Therefore, throughput analyses have been carried out for Wireless Local Area Networks (WLANs) with DCF [3]-[5], and EDCA [6]-[0] and for multi-hop networks with DCF []-[3]. There are, however, no theoretical analyses for wireless multi-hop networks with EDCA. Actually, QoS support for wireless multi-hop networks is more difficult and complicated than that for WLANs. Therefore, it is necessary and valuable to establish theoretical analysis procedure for wireless multi-hop networks with EDCA, which provides intuit comprehensions of the network dynamics and design strategies of QoS-aware protocol for multi-hop networks. This paper presents first-step analytical expressions of non-saturated and saturated throughput for wireless multi-hop string-topology networks. Internal collisions in each node, concurrent-transmission collisions among nodes, differences of CW min, and CW max among ACs, and AIFS-differentiation effects are considered and expressed in this analysis. The obtained analytical expressions are verified from comparisons with simulation results. II. Related work A. IEEE 80.e Enhanced Distributed Channel Access (EDCA) IEEE 80.e EDCA is a MAC protocol supporting QoS, which is not considered in IEEE 80. DCF. The node with EDCA has four ACs, which are voice, video, best effort, and background. Each AC of nodes virtually tries to access the channel based on Carrier Sense Multiple Access with Collision Avoidance(CSMA/CA). Figure shows the EDCA diagram with two-class priorities. In Fig., AC is higher priority than AC and AIFS duration of AC k is expressed as d AIFS k. The AIFS duration of AC k is determined by d AIFS k = d S IFS + AIFS N k σ, () where d S IFS is the duration of SIFS, AIFS N k is the AIFS-slot number of AC k, and σ is a system slot time. Table I gives the EDCA parameters standardized in IEEE 80.e []. In Table I, CW min and CW max are the initial and maximum contention window (CW) values, respectively. In IEEE 80.e, voice and video streaming are categorized into high priority ACs, which are expressed as AC[VO] and AC[VI], respectively. Therefore, CW min, CW max and AIFSN of AC[VO] and AC[VI] are smaller than those of other ACs. By applying the EDCA parameters, the frame-transmission-priority differentiation according to ACs can be achieved. In the EDCA, AC k senses a channel state for d AIFS k from a instant when the AC has a transmission frame. After sensing the channel state for d AIFS k, the AC k further senses the channel state during the backoff timer () countdown. The initial value of of AC k in Node i is determined from the range of 0 and CW i,k, where CW i,k is CW of AC k in Node i. At the instant of (a) in Fig., AC in Node can transmit a frame because its is zero. The countdown of Node is stopped at the instant of (a) in Fig. because Node senses channel busy. When the channel becomes idle again, the AC in Node and restart the countdown after waiting for the d AIFS at the instant of (b) in Fig.. There are two types of frame collisions in EDCA. One is

Node AC AC daifs d AIFS countdown Carrier sensing Carrier sensing d SIFS Collision d AIFS daifs Select in [0, CW - ] countdown Internal Collision Frame SIFS ACK Time Node AC AC daifs daifs countdown dframe Frame SIFS dack ACK daifs Collision daifs daifs countdown Time Select in [0, CW - ] Select in [0, CW - ] state No Zone No No Zone Channel busy Zone Channel busy Zone Zone Channel busy L[slot] system slot time (a) (b) (c) (d) (e) (f) Fig.. IEEE 80.e EDCA diagram with two-class priorites the frame collisions with other node frames. A frame from AC in Node collides with a frame from AC in Node as shown in the instant of (c) in Fig.. The other is the internal (virtual) collision, which occurs among ACs in the same node. The internal collision occurs when s of multiple ACs in the same node become zero simultaneously as shown in the instant of (f) in Fig.. In Fig., the AC- frame, which is in higher priority, can be transmitted from Node. Many transmission opportunities are obtained in AC compared with AC because d AIFS is smaller than d AIFS. During d AIFS, only AC can transmit a frame. In this paper, the interval when only AC can transmit a frame is expressed as Zone, which is expressed as interval between (d) and (e) in Fig. The slot number of Zone is expressed as L = AIFS N AIFS N. Obviously, internal collisions never occur in Zone. On the other hands, there is possibility that two types of collision occurs after Zone, as shown in Fig. of interval between (e), (f). We call this interval as Zone. Generally, Zones and are also said contention zones [7]-[8], [0]. If a frame transmitted by a certain AC is collided, the AC doubles the CW and resets the. CW value of AC k in Node i is determined by CW i,k ( j) = j (CW mink + ) 0 < j m k, m k (CW mink + ) = CW maxk m k < j R k, where j is the retry transmission number, R k is retry limit, CW maxk + and m k = log CW mink +. When a node can receive a frame, the node returns an ACK frame to the transmitter. The frame transmission is in success when the transmitter receives the ACK frame. B. Analytical Expression Derivations There are many throughput analyses for IEEE 80. DCF [3]-[5]. Bianchi presented the Markov-chain model DCF for WLANs in the saturated condition [3]. A simple transmission-probability expression compared with the Bianchi model was presented in [4]. In the next step, the analyses for non-saturated condition were carried out by combining () the queuing theory and the saturated-condition analysis techniques. Namely, the non-saturated transmission probability can be obtained from saturated transmission probability and non-empty-buffer probability, which is derived from the queuing theory [5]. Additionally, throughput analyses for WLAN with IEEE 80.e EDCA were also carried out [6]-[0]. In [6], Markov-chain model for the countdown with the EDCA was proposed. This model considers the differences of CW min and CW max among ACs. The contention zones were, however, not considered in [6]. In [7] and [8], the strategy for expressing the contention-zone effects was introduced. When all nodes are in the same carrier sensing range, the nodes start the countdown simultaneously. Namely, it can be stated that the collision probability depends on the contention zones. The effects of contention zones can be expressed by considering the collision probabilities of each AC. In [9]-[0], the non-saturated throughput analysis for WLAN with EDCA was carried out, which also applied the queuing theory to the saturated-condition analyses. Recently, throughput analyses for multi-hop networks with DCF were carried out. Throughput analyses in [] and [] were based on the assumption of saturated environment and hidden node existence. Non-saturated throughput analysis in multi-hop networks with DCF appeared with no hidden-node condition [3]. As described above, there are many analytical expressions of throughput for multi-hop networks with different environments. There is, however, no throughput analysis for multi-hop networks with EDCA until now. Due to growth of multi-media applications, it becomes important to support MAC-level QoS control in multi-hop networks. Supporting QoS in multi-hop networks is more difficult and complicated than that in WLANs. The analytical expressions of throughput for multi-hop networks with the EDCA are helpful in comprehensions of the network performance and valuable for the QoS-aware MAC protocol.

TABLE I. IEEE 80.e parameters setting AC CWmin CWmax AIFSN BK 5 03 7 BE 5 03 3 VI 7 5 VO 3 7 0 3 N- N -q 0 q -q Zone Zone -q q q q L- L q Fig.. Network topology used for analysis and simulation -q III. Analytical model The purpose of the analysis in this paper is to obtain end-to-end throughput for each AC in wireless multi-hop networks with IEEE 80.e EDCA as a function of offered load. Figure shows N-hop string topology with one-way flow, which is considered in this paper. In Fig., frames generated at source node 0 are forwarded to the destination node N through the relay nodes. The analysis in this paper based on the following assumptions.. A node can sense frame transmissions of all the other nodes and there is no hidden node for all the nodes. Therefore, only concurrent-frame-transmission collisions occur among nodes. This type of collision occurs in case that two and more nodes start frame transmissions simultaneously.. The channel condition is ideal. Therefore, transmission failures occur due to only the collisions. 3. Each node has two ACs as shown in Fig.. AC has higher priority than AC. The frame size of AC is the same as that of AC. 4. The value of TXOPlimit is zero. 5. ACs in all nodes have a individual and infinite buffer. 6. Only the source node generates a frame. The frames of AC k in the source node is generated according to offered load of AC k, which is expressed as o f f eredload k. The following analysis considers the differences of AIFS N, CW min and, CW max according to ACs, internal collisions due to the EDCA mechanism, and concurrent-transmission collisions among nodes. A. Transmission and collision probabilities The transmission probability for AC k in Node i is expressed as τ i,k = τ i,k p i,k, (3) where τ i,k is the transmission probability of AC k in Node i under the condition that the AC has frames and p i,k is the non-empty buffer probability. Now γ i,k expresses collision probability of frames transmitted from AC k in Node i. By using γ i,k, the transmission probability under the condition that Fig. 3. Markov chain of the system elapsed time (unit: slot) AC k in Node i has frames is expressed as [0] τ i,k = + γ i,k + γ i,k + + γr k i,k b a,0 + b k, γ i,k + b k, γ i,k + + b k,k k γ R k i,k, (4) where b k, j = CW i,k( j)+. Applying the result in [8], γ i,k is given by γ i, = π γ i,, + π γ i,, N = π ( τ j, ) j=0, j i N + π ( τ j, )( τ j, ), (5) j=0, j i N γ i, = ( τ j, ) j=0 N j=0, j i ( τ j, ), (6) where π, and π are the state existing probabilities of Zone and, respectively. Additionally, γ i,,l is the collision probability of Zone l for AC in Node i. Figure 3 shows the Markov-chain model for the elapsed time since d AIFS is ended. From Fig. 3, the state existing probabilities of Zone and are obtained as π = π = + q + q + + ql + q + q + + ql + ql q L q, (7), (8) ( q )( + q + q + + ql + ql q ) where q l is the probability that the channel is idle in Zone l, which are equal to the probability that all nodes transmit no frame, namely, q = q = N ( τ i, ), (9) N ( τ i, )( τ i, ). (0) B. Non-empty buffer probability and frame arrival rate In this paper, the queuing theory is used for obtaining the non-empty buffer probability in each AC, which follows the

analysis strategy in [5]. From Assumption 5, each AC can be expressed by using the G/G/ queue model. From the queuing theory and frame arrival rate in [5], the non-empty buffer probability in (3) is given by p i,k = min(, λ i,k y i,k ), () where λ i,k is frame arrival rate of AC k in Node i, y i,k is average MAC service time of AC k in Node i, and the min function prevents p i,k from exceeding. Under the condition that p i,k is lower than, AC k in Node i is in non-saturated state. Conversely, under the condition that p i,k =, AC k in Node i is in saturated state. By using (), it is possible to express both the non-saturated and saturated states. In most throughput analyses for WLANs, it is assumed that all nodes can generate frames by themselves. From Assumption 6, however, relay nodes can have frames only by receiving frames from the previous node. Therefore, the frame arrival rate of a relay node is the same as the throughput of the previous node. From the above discussions, the frame arrival rate is expressed as o f f eredload k, i = 0, λ i,k = s F i,k F, i [, N ], () where s i,k is throughput for AC k in Node i, and F is the payload size. C. Average MAC service time The MAC service time can be defined as the time interval between the instant when a frame reaches the head of queue and that when the ACK frame for the frame transmission is received successfully. The average MAC service time for AC k in Node i is y i,k = X i,k ω k, (3) where X i,k is the average -countdown slot number of AC k in Node i for one-frame-transmission success and ω k is the average time for one slot time of AC k, which includes not only system slot time but carrier sensing one. From (4), we have X i,k = b k,0 + b k, γ i,k + b k, γ i,k + + b k,r k γ R k i,k. (4) The carrier sensing time in Zone is different from that in Zone because of the difference of the channel access opportunities between Zone and Zone. Therefore, the one slot time in Zone and should be considered separately. The decreases when the channel is in the idle state and is kept during other s transmissions. Therefore, we have ω = π ω, + π ω, = π (σq + ε ( q )) + π (σq + ε ( q )), (5) ω = (σq + ε ( q )), (6) where ω,l is the average one-slot time of AC in Zone l, and ε k is the freezing interval for each AC k. The freezing interval is the duration from the instant when the countdown is stopped for the carrier sensing to that when the countdown restarts after AIFS duration. Concretely, ε and ε are ε = d FRAME + d S IFS + d ACK + d AIFS σ, (7) ε = d FRAME + d S IFS + d ACK + d AIFS σ + δ, (8) where d FRAME is frame-transmission duration, d ACK is ACK-transmission duration, and δ is average freezing duration added by the transmission in d AIFS. Note that the freezing interval depends on the ACs because of the difference of AIFSN according to ACs. The freezing duration δ in (8) is the average total duration of AC- transmissions in Zone until d AIFS is ended once. Therefore, we have δ = L j= N ( τ i, )) j ( ( τ i, ))d j N ( L j= N (, (9) N ( τ i, )) j ( ( τ i, )) where d j = d AIFS σ + ( j )σ + d FRAME + d S IFS + d ACK. D. Throughput expressions The throughput for AC k in Node i is expressed as s i,k = = E[Payload information in a slot time] E[Length of a slot time] α i,k F, (0) ω k where α i,k is the frame-transmission-success probability, which is the same as the probability that AC k in Node i transmits a frame and the frame transmission is in success. From (7)-(0), we have α i, = τ i, ( π q τ i, + π q ), () ( τ i, )( τ i, ) α i, = τ i, q τ i,. () Obviously, the end-to-end throughput of AC k is the throughput of AC k in Node N, namely, S k = s N,k. (3) From (3), (5), and (6), 4N algebraic equations are obtained as functions of 4N+ unknown variations: τ 0,,, τ N,, τ 0,,, τ N,, γ 0,,, γ N,, γ 0,,, γ N,, o f f eredload, o f f eredload R 4N+. Therefore, when offered loads for each category are given, the other unknown values can be obtained by solving the algebraic equations and the end-to-end throughput of multi-hop network with EDCA can be obtained. IV. Simulation verification For verifying the analytical expressions, ns- simulations are carried out. The network topology for the simulations is the same as that in Fig.. Table II gives the system parameters used in analytical derivations and simulations. The EDCA parameters for ACs and follows the those for AC[VO] and AC[BE], respectively, which are given in Table I. In ns- simulations, the transmission frames are generated randomly in only Node 0, and are forwarded to node N by using static-route

End to end throughput of AC-k [Mbps] 4 3.5 3.5.5 0.5 0 TABLE II. System parameters Packer payload(data) 04 bytes MAC header 8 bytes PHY header 4 bytes ACK size 0 bytes Data rate 8 Mbps ACK bit rate Mbps Transmission range 60 m Carrier sensing range 5 m Distance of each node 5 m SIFS time 6 µsec σ (slot time) 9 µsec R k (Retry limit) 7 Simulation for AC Simulation for AC Analysis for AC Analysis for AC (b) (a) 0 0.5.5.5 3 3.5 4 Offered load per AC [Mbps] Maximum End-to-End Throughput [Mbps] Fig. 5. 6 4 0 8 6 4 0 Analysis forac Analysis for AC Simulation for AC Simulation for AC 0 3 4 5 6 7 Number of hops Maximum end-to-end throughputs of ACs as the number of hops each AC in each Node. The obtained analytical expressions are verified from comparison with simulations results. Acknowledgment This research was partially supported by Scholarship Foundation and Grant-in-Aid for scientific research (No. 365649 and No. 336067) of JSPS, Japan. References Fig. 4. End-to-end throughputs of three-hop network for ACs as a function of offered load settings. Additionally, the frame generation probability of AC is the same as that of AC. Figure 4 shows the end-to-end throughputs of three-hop network for both ACs as a function of each offered load. For (a) and (b) in Fig. 4, the end-to-end throughputs of AC and AC are saturated because the AC and AC in the source node are in saturated state. However, the ACs of relay nodes are never in saturated state. Namely, the end-to-end throughputs of ACs depend on the state of ACs of source node in topology of Fig.. Figure 5 shows the maximum end-to-end throughputs of N-hop network for both ACs as a function of hop numbers. It is seen from Fig. 4 and Fig. 5 that the analytical predictions agree with the simulation results well, which show the validity of the analytical expressions in this paper. V. Conclusion This paper has presented first-step analytical expressions for non-saturated and saturated throughput for multi-hop string topology networks with EDCA. In this analysis, the obtained expressions offered transmission and collision probabilities for [] IEEE Standard for Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications, Nov. 997, P80. [] IEEE Std 80.e specific requirements Part : Wireless Lan Medium Access Control (MAC) and Physical Layer (PHY) Specifications, Amendment 8:Medium Access Control (MAC) Quality of Service Enhancements, 005. [3] G. Bianchi, Performance analysis of the IEEE 80. distributed coodination function IEEE J. Sel Commun., vol. 8, no. 3, pp. 535-547, Mar. 000. [4] A. Kumar, E. Altman, D. Miorandi, and M. Goyal, New insights from a fixed point analysis of single cell IEEE 80. Wireless LANs, IEEE/ACM Trans. Netw., vol. 5, no. 3, Jun. 007. [5] Q. Zhao, D. H. K. Tsang, and T. Sakurai, A Simple and Approximate Model for Nonsaturated IEEE 80. DCF, IEEE Transactions on Mobile Computing, vol. 8, no., pp. 539-553, 009. [6] Y. Xiao, Performance Analysis for Priority Schemes for IEEE 80. and IEEE 80.e Wireless LANs, IEEE Trans. Wireless Comm., vol. 4, no. 4, pp. 506-55, 005. [7] J. W. Robinson and T. S. Randhawa, Saturation throughput analysis of IEEE 80.e enhanced distributed coordination function, IEEE J. Sel. Areas Commun., vol., no. 5, pp. 97-98, Jun. 004. [8] V. Ramaiyan, A. Kumar, and E. Altman, Fixed point analysis of single cell IEEE 80.e WLANs: Uniqueness, multistability and throughput differentiation, in Proc. ACM SIGMETRICS 005, Banff, Alberta, Canada, Jun. 005, pp. 09-0. [9] P.E. Engelstad and O.N. Osterbo, Non-Saturation and Saturation Analysis of IEEE 80.e EDCA with Starvation Prediction, Proc. Eighth ACM Int l Symp. Modeling Analysis and Simulation of Wireless and Mobile Systems (MSWiM 05), pp. 4-33, 005.

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