Analytical Modeling of IEEE 802.11e Enhanced Distributed Channel Access under a Non-Saturation Condition

: Problem statement: The IEEE 802.11e EDCA protocol with different access Categories (ACs) supporting for Quality-of-Service (QoS). Due to internal or external packet collision, the Contention Window (CW) of the station increases the channel idle time under high Bit Error Rate (BER). Approach: In this study, we propose an analytical model for performance evaluation of IEEE 802.11e EDCA scheme under non-saturation condition and error prone channel. The new markov chain model have decrease the channel idle time in IEEE 802.11 EDCA and considerably increases the throughput for minimum number of station. Results: We develop an expression for the nonsaturation throughput as a function of the number of stations, packet sizes and BER. Conclusion: We validate the accuracy of our analysis with simulation expression. Using this model, the contention factors can be set appropriately to attain particular Quality-of-Service (QoS) requirements.


INTRODUCTION
In recent years, the IEEE 802.11 Wireless Local Area Network (WLAN) has been widely deployed in Indoor wireless Communication and it includes detailed specification of both medium access control and physical layer. The most research area of these two layers is Medium Access Control (MAC) layer in the first sub layer of data link layer. To access the medium from physical layer using MAC layer will be coordinating the random access of the medium. In wireless LAN MAC protocols is to coordinate the access of wireless client station in shared medium using carrier sense multiple Access/Collision Avoidance (CSMA/CA) protocol for MAC layer (IEEE Std. 802.11, 1999).
The IEEE 802.11e MAC layer is to enhancing the quality of services in WLAN which provides a contention-based channel access function and a centrally controlled channel access function called the Hybrid Coordination Function (HCF). The HCF combines a distribution contention-based channel access mechanism, referred to as Enhanced Distributed Channel Access (EDCA) and a centralized pollingbased channel access mechanism referred to as HCF Controlled Channel Access (HCCA). In this article, we concentrate on EDCA protocol which defines multiple Access Categories (AC) services for each station. Different levels of services are provided to each AC includes Contention Window (CW) sizes, Arbitration Interframe Space (AIFS) values and Transmit Opportunity (TXOP) limits for providing QoS to users. In this study we concentrate on the performance analysis of EDCA scheme, in the assumption of non ideal conditions and finite number of terminals.
According to the author's knowledge the first analytical model of DCF was proposed by Bianchi (2000). Bianchi proposed a Markov chain based model to evaluate saturation throughput, the mobile stations always have something to transmit (i.e., the saturation condition), assuming a finite number of stations and ideal channel conditions (no errors).While in (Shyang et al., 2005) the authors extended the Bianchi model in order to consider unsaturated traffic conditions by adding another state (idle) to represent the node with empty queue, not present in the original Bianchi's model, in which the station buffer is empty, after a successful completion of a packet transmission. In the modified model, the packet is discarded after m th backoff stages, while in Bianchi's model, the station keeps iterating in the mth backoff stage until the packet gets successfully transmitted. There are some works on unsaturated traffic condition and post backoff stage for IEEE 802.11b (Malone et al., 2007;Dhanasekaran senthil kumar and Krishnan, 2010;Daneshgaran et al., 2008). However, these models are not based on simplifying assumptions that the IEEE 802.11 standard defines a Station Short Retry Count (SSRC), which is the maximum number of RTS transmission attempts that will be made before a frame is discarded Typically it is set to 5or 7 (IEEE Std. 802.11, 1999;Wu et al., 2002;Chatz imisios et al., 2004;Prakash and Thangaraj, 2010). In (Chatzimisios et al., 2004), the performance of IEEE 802.11 assumes that there is a finite transmission and presence of transmission error. In an adhoc network (Priakanth and Thangaraj, 2009), proposed an efficient packets scheduling and queuing algorithm by achieving better fairness in Medium Access Control (MAC) protocol. In (Murugan and Shanmugam, 2010), proposed a solution to identify the malicious node in both routing and MAC layer in the ahoc network using cumulative frequency based detection technique. Both articles referenced performances of MAC layer without markov model.
The majority of analytical work on the performance of 802.11e EDCA assumes that there is a finite retransmission limit (retry limit) and infinite retry limit under saturation and non-saturation condition using markov chain model (Huang et al., 2007;Wei et al., 2007;Kong et al., 2004;Xiao, 2005;Engelstad and Osterbo, 2005;Inan et al., 2009). The EDCF and provided performance studies via simulation. In (Huang et al., 2007), the performance of IEEE 802.11e has investigated in the error prone channel under saturation condition. Based on the Markov chain model for unsaturated condition (Wei et al., 2007), an analytical approach is proposed for throughput and delay of 802.11e EDCA. (Xiao, 2005;Kong et al., 2004) extended the bianchi markov model to analyze the CW and AIFS differentiation under saturation condition. In (Kong et al., 2004) Kong's model considered the difference of AIFS in back-off procedures, but neglected AIFS while the back-off procedure reminded one timeslot. In (Hui and Devtsilitios, 2005) the authors proposed a new unified performance model to saturation throughput and delay performance of the network. These models were not provided real network condition. A few studies proposed real network condition which is on non-saturation analysis but not considered channel error. Englestad (2005c) presented an analytical model for IEEE 802.11e with Virtual collision handler (VCH) and post-backoff under non saturation condition. Inan et al. (2009) proposed 3dimensional DTMCs under unsaturated traffic which provide accurate treatment of AIFS, CW differentiation and EDCA TXOP. In (Pan and Wu, 2009) throughput of the EDCA is investigated under heterogeneous traffic. In this study, we propose a new markov chain model (proposed model) for analyzing EDCA protocol under non-saturation condition with error-prone channel. Due to internal (virtual) collision occurs within the station, the contention window size of the station is need not to be doubled for packet transmission. In case of transmission error due to fading or packet collision from other stations experiences external collision, the contention window size is doubled for every transmission. Based on this previous work of Xiao 's model (2005), Senthilkumar and Krishnan (2010), we developed a Markov chain model for the EDCA analysis. The study is organized as follows. In this study, we present the new Markov chain model by extending the model proposed initially by Bianchi. Performance of the proposal scheme is analyzed after markov chain model explanation. We discuss numerical results and then finally we present conclusion of this study.

Markov model for IEEE 802.11e EDCA:
We consider a WLAN in Unsaturation (Nonsaturation) condition, ie., buffer of the transmitting station is empty, after a successful transmission. To analyze an EDCA protocol, we extend the previous works on following assumption: (1) real channel condition; (2) channel is prone to errors due to fading channel; (3) finite and fixed number N of contending stations. Traffics are categorizing into N different Access categories according to their QoS requirements. For simplicity, we summarize all parameters related with the nth AC have a subscript n. Fig.1 shows that the state of the nth AC by {n, i, k}. Here, i, (i = 0, 1, ….., m n ) represents the backoff stage, where m n denotes the retry limit. k (k = 0,1,2, …, W n,i -1) represents the value of backoff counter, where W n,i is the contention window size in the backoff stage i for the nth AC. The state (n, i, k) represents the i th backoff stage of nth AC with backoff counter value k and the CW size of backoff stage i of nth AC is expressed as: where, W n, o = CW n,min +1, m n is the backoff stage of which CW size is the maximum CW size and m' n is the frame retry limit. Our main aim in this performance study is the effective modification of the EDCA MAC protocol in order to characterize the behavior of MAC in the event of channel errors. In the basic AC, the contention window is doubled after every unsuccessful transmission. Unsuccessful transmission happens in two cases: (i) internal collision or virtual collision of a packet with other packets with in a station, (ii) due to error in the channel and packet collision with other station. Let b(t) be the stochastic process that represents the backoff timer for a specific station and s(t) be the stochastic process representing the backoff stage [0,…..,m] for a given station at time t; where m is the packet retry limit. Our analysis assumes that the network consists of n Contending stations and that each station has not always a packet available for transmission. The key assumption of our model is that the collision-error probability (p col ) and transmission error (p e ) of a transmitted packet is constant and independent of the number of collisions or transmission errors of this packet has suffered in the past. We assume that collisions (internal collision) and transmission error (external collision) events are statistically independent. The three dimensional discrete time Markov chain is depicted in Fig. 1. In this Markov chain, the only nonnull one step transition probabilities are as follows: If there is no packet in a buffer after a successful transmission, the station is waiting in the idle state until a new packet arrives: The first Eq. in (2), beginning of each slot time, backoff time is decremented. The second equation in (2) states that, the initialization of backoff window after successful transmission for a new packet. The new value of the backoff timer is uniformly chosen in the interval (0, W n,0 -2).The third equation represent that the probability of unsuccessful transmission due to internal collision (p n ), but maintenance the same backoff window. The fourth equation accounts that, probability of unsuccessful transmission due to external collision or channel error (p eq ). In Eq. (2) p eq represents the external collsion and channel errors, p n represents that the probability due to internal collision and q represents the probability of atleast one packet awaiting transmission at the start of a counter decrement. The probability of successful transmission is (1-q n ) (1-p eq ). Let b n, i, k = lim t→∞ P[s(n, t) = i, b(n, t) = k] be the stationary distribution of the Markov chain. In steady state, we can derive the following relations through chain regularities. Analysis and Throughput Computation: A transmitted frame collides when two or more stations transmit during slot time, so the probability p n that transmitted frame collides and channel busy probability p b in a slot can be expressed as: The values of P and τ are still unknown in above Eq. 8-9 which can be solved using numerical techniques and represents as nonlinear equations. The probability that no station is transmitting in the slot time is expressed as: Non-Saturation Throughput: Let P n,s be the probability that a successful transmission occurs in a slot time of the nth AC and P s denote the probability that successful transmission occurs in a slot time. We have:

RESULTS AND DISCUSSION
In this study, we present numerical results that show the impact of transmission errors on the system capacity. The network parameters used in these results are shown in Table 1 and we assume every station is able to listen each other and there are no hidden terminals in the systems. The Figure validates our mathematical analysis since an almost exact match is observed between analytical (symbols) and simulation results (lines) from our IEEE 802.11e simulator developed with the NS-2 simulation package. Figure 2 compares number of stations for each AC per station against throughput. In this graph, the highest priority of AC shows that higher throughput for fixed packed length.   Figure 3 shows the throughput versus number of station with probability of error. Here, the channel bit rate is increases and the throughput slightly decreases with increased networks. Figure 4 compares the simulation and analytical results of modified model by plotting the throughput against different packet arrival rate for transmission error channel. In this graph, the low traffic of all AC shows that the modified model Fig. 4: Throughput versus packet arrival rate significantly increases the throughput. From above results, the number of higher priority ACs is AC0 gives an acceptable throughput performance for all situation.

CONCLUSION
In this study, we have presented an analytical model that calculates throughput of the IEEE 802.11e EDCA protocol. We have presented an accurate analytical model to evaluate the performance of EDCA under nonsaturation conditions. Simulation and analysis results show that our analytical model can accurately predict the throughput performance of IEEE 802.11e EDCA under nonsaturation conditions in presence of channel errors. Based on this model we derive a novel and generalized expression for the station's transmission probability, which is more realistic, such as traffic load conditions (different ACs) and non ideal channel conditions. Our study shows that an optimally chosen number of contending stations can significantly improves the network throughput.