Performance Study of Block ACK and Reverse Direction in IEEE n using a Markov Chain Model

Transcription

1 Perormance Study o Block ACK and Reverse Direction in IEEE n using a Markov Chain Model Md. Akbar Hossain, Nurul I Sarkar, Jairo Gutierrez, William Liu School o Computer and Mathematical Sciences Auckland University o Technology Auckland 1010, New Zealand Abstract IEEE n networks are widely used in home and corporate network environments because they oer high-speed wireless Internet access at relatively low-cost. The n standard introduced several key eatures including Block acknowledgement (ACK) and reverse direction (RD) data transmission or enhanced system perormance. An in-depth study o n system capacity or Block ACK mechanisms (both protected and unprotected) and RD data lows is required to assist optimum planning and design o such systems in view o the limited wireless channel capacity. In this paper we study the interdependencies o Block ACK and RD mechanisms using a discrete bi-directional Markov chain model under non-saturated traic loads. We present a mathematical model to derive throughput, delay, and packet loss probability or both protected and unprotected Block ACKs under varying loads. We validate the model using MATLAB based numerical studies. Results obtained show that the combined eect o protected Block ACK and RD lows has a positive impact on system perormance. However, unprotected Block ACK wastes transmission opportunity (TXOP) especially in collisions and thereore degrades the system perormance. Our indings reported in this paper provide some insights into the perormance o n with respect to Block ACK and RD methods. This study may help network researchers and engineers in their contribution to the development o next generation wireless LANs such as IEEE ac.

2 Keywords: Medium Access Control; Block ACK; Markov Chain; Reverse Direction; Distributed Coordination Function 1. Introduction IEEE based wireless local area networks (WLANs) are widely adopted in home and corporate networking environments due to their simplicity in operation, robustness, low cost, well-deined standards (e.g a/b/g/n) and the user mobility oered by the technology. In the standard, the distributed coordination unction (DCF) is deined as a mandatory medium access control (MAC) protocol and the point coordination unction(pcf) is optional [1]. The perormance o DCF has been analyzed extensively using mathematical modeling and simulation [2][3][4]. In [2], Bianchi proposed a Markov chain model or a backo mechanism to evaluate the throughput under saturated traic and error ree channel condition. Bianchi s work assume that packets will eventually transmitted regardless o the no. o retransmissions. However, a station (STA) will increase its contention window size ater each ailed transmission until it reaches the maximum backo stage. Since the maximum backo stage and retry limit are not equal, the contention window size remains the same and STA will continue retransmitting until it reaches a retry limit. I the subsequent transmission is not successul, the packet is discarded. The authors in [5], developed a Markov model which considers a inite retry limit or the transmission control protocol (TCP) over WLANs. They considered saturated traic loads under ideal channel conditions. The extension o Bianchi s model was reported in [6] or inite load analysis. However, the maximum capacity o a wireless node is bounded by queue delays [7]. A inite load Markov model is presented in [7] by integrating a queue model as a new state with a Bianchi model assuming the STA queue is empty ater successul transmission. All o these models are well studied or (a/b/g) networks. The undamental goal o these models is to study the DCF protocol behavior under dierent channel and load conditions. The common thread o these studies is that the system perormance can be 2

3 enhanced by reducing MAC overheads. The e standard [1] published in 2005, proposed a new MAC method called hybrid access method(hcf). A new ACK scheme is being introduced in the e standard known as BA. Unlike the traditional ACK scheme, an ACK is transmitted to reply to multiple data rames rather than per rame as in BA. Hence, the Markov model that has been developed or the traditional DCF protocol does not it well with the BA scheme used to investigate the system throughput perormance. Authors in [8] developed a Markov model or the BA and showed that a block with multiple rames can oers higher throughput than the traditional ACK based two-way or our-way transmission under saturated load and ininite retransmission conditions. But, when the rame consists o only one data rame it suers rom severe throughput degradation due to a couple o additional rames (e.g.ba request and BA). Moreover, it is assumed that data rames received with errors are considered a successul transmission, thus the contention window is reset. Unortunately, according to the standard, receivers will not acknowledge the error data rame. Consequently, the sender has to retransmit the rame and increase the contention window i it does not reach a maximum contention value. Further enhancement o [8] is reported in [4] by introducing a protected BA mechanism. The work reported in [4] inspired by urther extensions o inite load conditions and integrating the RD eatures o n. Beside the BA scheme, rame aggregation mechanism is widely studied in recent literature to enhance the perormance o n networks. In [9] discrete time Markov chain model is used to analyse the post backo behavior due to rame aggregation under an error ree environment. The perormance study shows that, MAC service data unit (MSDU) outperorms the MAC protocol data unit (MPDU) as rame aggregation size becomes larger. An empirical study perorms in [10] also conirms that a signiicant perormance enhancement can be achieved when the rame aggregation and BA schemes are utilized. However, under an error prone channel rame aggregation mechanism experience severe throughput degradation and higher access delay due subrames size [11]. So ar, we only consider the unidirectional data transmission. A bi-dimensional 3

4 Markovian model presented in [12] shows that, bidirectional data transmission signiicantly enhance the overall network perormance. Most o the previous studies on perormance enhancement o n have ocused on rame aggregation mechanisms. Very limited studies have actually analyzed the throughput perormance o n under non-ideal channel conditions using Markov chains. The main contribution o this paper is three old. First, we present a simple Markov model to study the perormance o n standard under nonsaturated traic load. A detailed Markov chain model is developed by considering all possible constrains including load conditions, retry limits and channel state inormation. Second, we derived both Throughput and Packet delay or both the protected BA and non-protected BA schemes. Third, the eect o load conditions is analyzed in terms o packet loss probability. Moreover, an extensive MATLAB based numerical studies is presented to validate analytical model. The rest o the paper is organized as ollows: We describe the BA and RD mechanisms in Section 2. Section 3 presents a detailed discrete Markov model or n with a protected BA mechanism ollowed by three dierent subsections throughput, packet delay probability and mean delay (including MAC delay and Queue delay in consecutive subsections) analysis. A detailed numerical study including a comparative study o various mechanisms is presented in Section 4. A brie discussion in Section 5 ends the paper. 2. Preliminaries 2.1. Block ACK Mechanism The Block ACK mechanism was irst introduced in [1] to reduce the MAC overhead o e and later in n. The basic idea o the BA mechanism is to aggregate several ACK rames into a single rame. There are two dierent types o Block ACK mechanisms: Immediate (Im) and Delayed (D) Block ACK. A urther extension o n or High Throughput(HT) operations classiies each o these Block ACK schemes in two subclasses: Protected 4

5 and non-protected Block ACKs. The scope o this paper is limited to the Im- Block ACK scheme or both protected and non-protected modes. In the Im- Block ACK scheme, transmitters and receivers are known as originators and recipients, respectively. To initialize the new acknowledgement policy, the originator and the recipient will exchange Add Block Acknowledgement(ADDBA) Request/Response rames. Aterwards, a data block with multiple data rames is transmitted rom the originator to the recipient with Block ACK Request(BAR) at the end. The number o data rames in one data block is bounded by the receiver buer size. The recipient sends a Block Acknowledgement (BA) rame or the the entire data block. Figure1(a) shows the protected Block ACK channel access mechanism. In protected Block ACK, beore transmitting an entire data burst, the originator will transmit a single data rame and wait or an ACK rom the recipient. Ater the successul reception o an ACK rame, the originator initiates the transmission opportunity (TXOP) period to transmit the data burst. Thereore, i there is an error or channel collision,this problem would only be experienced by the irst data rame or ACK rame. This concept is most likely an RTS/CTS based our-way handshake (shown in Fig. 1(c)) mechanism except when using a special RTS/CTS rame where as the non-protected Block ACK mechanism is based on a two-way handshake mechanism. The time diagram o the non-protected Block ACK mechanism is depicted in Fig.1. In terms o throughput as a perormance metric, protected Block ACK should outperorm the non-protected Block ACK scheme by reducing the wasted time due to collision or channel errors Reverse Direction We propose an eicient reverse direction (RD) data exchange protocol to improve QoS support and overall eiciency o the IEEE n standard or high rate physical layer. The RD protocol provides mechanisms that signiicantly reduce the MAC-overhead while retaining ull compatibility with legacy systems. Figure 1(c) illustrates the RD scheme with a block ACK mechanism. In this speciied transmission, the receiver may request a reverse data transmission in 5

6 Figure 1: Various Block ACK mechanisms with Reverse Direction the CTS control rame. This allows the transportation o data rames and also aggregates rames, in both directions, in one Transmission Opportunity (TXOP) period. Until now, when the sender STA is allocated with a TXOP, it inorms surrounding STAs about how long the wireless medium will be engaged. Hence, RD achieves better results by supporting on-demand bi-directional data lows using the existing handshake protocol without any additional control rames. Furthermore, it reduces block transmission overhead by eliminating the short interrame space(sifs) or transmission in both directions and relies on a single block acknowledgement rame. Previously, or each uni-directional data transer, the initiating station needed to contend or the channel in a contention-based wireless medium. With RD, the other stations are essentially allowed to send inormation back once the transmitting station has attained a TXOP. Thereore, two roles need to be identiied: RD initiator and RD responder. The RD initiator sends its permission to the RD responder due to a Reverse Direction 6

7 Grant (RDG) in the RDG/More physical layer convergence protocol (PLCP) protocol data unit (PPDU) ield o the high throughput (HT) control ield. The RD mechanism acilitates the data transmission rom both sides (sender and receiver) without urther contending or the medium and reducing the number o contentions by a actor o 1.5 to 2 [13]. Moreover, the proposed RD mechanism reduces the overall MAC overhead associated with collision detection and medium protection. A similar concept or a RD mechanism was presented in [14],where receiver data is piggybacked with a Block ACK to the sender. Obviously this modiication increases the throughput or the system but, as ar as we can ascertain, an overall perormance analysis including error and MAC delay analysis are still not ound in the recent literature. 3. Markov Model or IEEE n with Protected BLOCK ACK In this section, an analytical model is proposed to evaluate the perormance o n under non-saturated load conditions. A two dimensional Markov model is developed to derive the channel throughput and end-to-end delay o successul data transmissions. To simpliy the mathematical model we made the ollowing assumptions. (i) Finite number o stations (ii) Unsaturated load i.e. there is a certain probability that the transmission queue is empty (iii) Channel is prone to errors (iv) No hidden terminals (v) Packets are destroyed only through collisions exceeding the retry limit (vi) Packets are o equal length The proposed model also takes into consideration both basic handshake (twoway) and RTS/CTS handshake (our-way)-based channel access schemes. Developing a Markov model to evaluate the DCF perormance o WLANs was irst shown by using the Bianchi Model [2] under saturated loads with ideal channel 7

8 conditions. Unortunately Markov Models developed or a/b/g are not substantial enough to explain the n behavior which has distinct eatures such as Protected Block ACK and Reverse Direction Data lows. In our model, we derive both the throughput and end-to-end delays by taking into account protected Block ACKs and Reverse Direction data lows in non-saturated load conditions. The undamental access method o is called distributed coordination unction (DCF) which is based on carrier sense multiple access with collision avoidance (CSMA/CA). For a STA to transmit, it senses the medium to determine i another STA is in transmission. According to DCF distributed protocol there must be a minimum time gap to identiy contiguous rame sequences. Thereore, a transmitting STA must ensure that the medium is idle or this period beore attempting to transmit. I the medium continues to be busy, the STA deers until the end o the current transmission. Ater deerral, or prior to attempting to transmit again immediately ater a successul transmission, the STA selects a random backo interval and decrements the backo interval counter while the medium is idle. A transmission is successul i an acknowledgement (ACK) rame is received rom the targeted STA (unicast) or when a multicast rame is sent completely. A reinement method may be used to urther reduce collisions: the transmitting and receiving STAs exchange short control rames, request to send (RTS) and clear to send (CTS). Let n be the number o stations (STAs)in a WLAN contending or channel access. Let b(t) and s(t) be the stochastic processes representing the backo counter and backo stages at time t respectively. Hence according to DCF, the b(t) value is decremented at the start o every idle slot and a contending station wins the channel when it reaches to zero. Ater successul transmissions i the STA has more data to send a new value would be set or b(t). As the counter value o k = b(t) is chosen to be uniormly distributed over k [0, CW i ], where CW i stands or the contention window size, there is a chance that two STAs end up with the same b(t) values and transmit data simultaneously. This is called a collision. In order to avoid urther collisions, the collided STAs will generate new b(t) values 8

9 determined by: 2 i CW min ; i m, CW i = (1) 2 m CW min = CW m ; i > m 200 Where CW i is an initial size or the contention window and m is a maximum number by which the contention window can be doubled. In this model, m is used to resemble the maximum backo stage. According to the IEEE standard, the value m could be larger than m, while the CW will hold ater that. Thereore, every STA is modeled by a pair o integers (i, k). At the very irst time, the backo stage i = s(t) starts at 0 and is increased by 1 everytime transmissions collide. Once the CW reaches CW m,it will remain at this value until it is reset. That means STA will keep transmitting the packet till it reaches the retry limit. I the transmission is still unsuccessul the packet will be dropped. The two-dimensional process (s(t), b(t)) will be analyzed with an embedded Markov chain (in steady state) at time instants at which the channel state changes. Let (i,k) denote the state o this process. At each stage the STA is described by i, k where i stands or the backo stage and k stands or the backo delay which takes any value in the range o [0, CW i 1]. Let, p denote the rame ailure transition probability rom one stage to another (e.g. rom row i 1 to row i in Fig.2). It is also the probability o an unsuccessul (re)transmission attempt seen by a STA as its rame is being transmitted on the channel. The unsuccessul (re)transmission attempt can happen due to the collision o this station with at least one o the n 1 remaining stations, occurring with probability p coll, where p coll is p coll = 1 (1 τ) n 1 (2) and/or by having a rame with errors, occurring with probability p err (due to channel ading and/or noise). Since both events are independent, the probability p can be expressed as: p = 1 (1 p coll )(1 p err ) = p coll + p err p coll p err (3) 9

10 Figure 2: Two Dimensional Markov Chain Model or n backo In case o an unsuccessul transmission attempt, ater the backo timer expires in state (i, 0), the station moves to any state on row i(i, k) with probability p /CW i. Following a successul transmission (occurring with conditional probability p ) while the observed station is in stage i (0, m), a new packet is admitted in the queue, the station returns to backo stage 0, and its backo timer uniormly selects any integer value in the range (0, CW 0 1) with probability (1 p )/W 0. I the station reaches backo stage m, and once its backo timer reaches 0, its rame can be successully or unsuccessully transmitted. In both cases, a new rame is admitted in the queue and the station returns to backo stage 0,and its backo timer is uniormly chosen in the range (0, CW 0 1) with probability 1/CW 0. Ater a successul transmission or ater m th ailed retransmissions, it is assumed that the buer o the transmitting station is not empty with probability q and empty with probability 1 q. 10

11 Based on the above discussion the transition probabilities o the Markov process are determined as ollows: 1. P (i, k i, k + 1) = 1; k [0, CW i 2], i [0, m] The station s backo timer is decremented rom k+1 to k at ixed i backo stages, i.e. the station has detected an idle slot, so the channel is idle. 2. P (0, k i, 0) = q(1 p )/CW 0 ; k [0, CW 0 1], i [0, m] Ater a successul transmission with probability 1 p, it is assumed that there is a new packet in the transmitting STA buer with probability q to start a new transmission at backo stage P (i, k i 1) = p /CW i ; k [0, CW i 1], i [1, m] The station s backo timer is changed rom 0 to k and the backo stage is changed rom i 1 to i. The probability o this event equals: Pr(transmission is unsuccessul and number k was randomly chosen to initiate the backo timer at stage i)= Pr(transmission is unsuccessul) Pr(number k was randomly chosen to initiate the backo timer at stage i). The probability o unsuccessul transmission equals p and the probability that number k was randomly chosen to initiate the backo timer at stage i equals 1/CW i. 4. P (m, k m, 0) = p /CW m ; k [0, CW m 1] The probability o unsuccessul transmission equals p. The probability that number k was randomly chosen to initiate the backo timer at stage m (maximum backo stage) equals 1/CW m till reaching the retry limit. 5. P (I i, 0) = (1 q)(1 p ); i [0, m] This equation represents the practical scenario i.e. unsaturated traic condition where the transmitting STA s buer is empty with probability 1 q ater a successul transmission. Hence the station will not contend or a channel till the new packet has arrived. 6. P (I I) = 1 q This stage is known as the Idle stage, when STA doesn t have any packet in its buer to transmit. 7. P (0, k I) = q/cw 0 ; k [0, CW 0 1] This means a new packet arrives at the buer with probability q and 11

12 starts a new transmission by using a randomly chosen delay k to initiate the backo counter at stage 0 with probability 1/CW 0 8. P (0, k m, 0) = q/cw 0 ; k [0, CW 0 1] The transition probability mentioned in the previous equation could happen when a packet is discarded due to a ailure to transmit within the retry limit. Here it is assumed that there is at least a packet in the buer. 9. P (I m, 0) = 1 q I the buer is empty with probability 1 q ater the retry limit. Let the stationary distribution o the chain be b i,k = lim t P {s(t) = i, b(t) = k}, i (0, m), k (0, CW i 1), denoting the probability o the station to be in state(i, k). The probability o the station to be in state (i, 0) can be expressed as a n stage transition probability as ollows: b i 1,0 p = b i,0 0 < i m (4) b i,0 = p i b 0,0 0 i m (5) Since the chain is regular, or each k [0, CW i 1] b i,k = CW i k CW i q(1 p ) m 1 b i,0 + b m,0 + q b I i = 0 p b i 1,0 0 < i m (6) Now m m b I = (1 q)(1 p ) b i,0 + (1 q) b I b I (1 q)b I = (1 q)(1 p ) b I = (1 q)(1 p ) q b i,0 m b i,0 (7) 12

13 Now rom equations 6 and 7 m 1 q(1 p ) b i,0 + q b I + b m,0 m 1 = q(1 p ) b i,0 + q b I + b m,0 m 1 = (1 p )[q b i,0 + (1 q) m b i,0 ] + b m,0 Utilizing the relation established in Eq.(4) and make use o Eq.(6) can be written as Now by using the normalization condition or stationary distribution equation: m (8) b i,0 = b0,0 1 p, b i,k = CW i k CW i b i,0 i (0, m), k (0, CW i 1) (9) 1 = = m m m 1 m 1 b i,0 b i,0 b i,k + b I b i,0 b i,k CW i k CW i + b I m = p i CW i k b 0,0 + b I 2 = b m 0,0 p i (2 i CW + 1) + b I 2 ( = b m ) m 0,0 (2p ) i + p i + b I 2 Now or m m (i.e the retry limit is within the range o the maximum backo stage) = b 0,0 2 = b 0,0 2 1 = b 0,0 2 = b 0,0 2 ( (CW (1 (2p ) m+1 )) + 1 ) pm+1 + (1 q)(1 p ) m 1 2p 1 p q + 1 ) pm+1 (1 q)(1 pm+1 ) + 1 2p 1 p q + 1 ) pm+1 2(1 q)(1 pm+1 ) + 1 2p 1 p q ) ( (CW (1 (2p ) m+1 )) ( (CW (1 (2p ) m+1 )) ( A q(1 2p )(1 p ) 13 b i,0 b 0,0

14 where A = q(1 p )CW (1 (2p ) m+1 ) + q(1 2p )(1 p m+1 ) + 2(1 2p )(1 p )(1 q)(1 p m+1 ) b 0,0 = 2q(1 2p )(1 p ) A (10) Now the probability o transmission at any random slot can be written as τ = m b i,0 = 1 pm+1 b 0,0 1 p τ = 2q(1 2p )(1 p m+1 ) ; m m A For m m (i.e retry limit is greater than maximum backo stage) (11) = b m 0,0 2 ( CW i + = b 0,0 2 m i=m +1 p i CW i + m p i ) + b I (1 +1 2pm )(1 p ) + (1 2p )(1 p m+1 (CW (1 q)(1 pm+1 ) + q b 0,0 = 2q(1 p )(1 2p ) B b 0,0 B = q[cw (1 (2p ) mprime +1 )(1 p ) + (1 2p )(1 p m+1 )+ ) + 2 m CW p m +1 (1 2p )(1 p m m ) )+ (1 2p )(1 p ) (12) + 2 m CW p m +1 (1 2p )(1 p m m )] + 2(1 q)(1 p m+1 )(1 2p )(1 p ) Thus τ = m b i,0 = 1 pm+1 b 0,0 1 p (13) τ = 2q(1 2p )(1 p m+1 ) ; m m B So ar, p is still unknown but can be solved by using Eq.(3), where p coll = 1 (1 τ) n 1. p err in Eq.(3), stands or the rame error probability(fer)o a 14

15 MAC data rame or an ACK rame or the given STA which can be expressed as an independent events as ollows: p err = 1 (1 F ER data )(1 F ER ack ) = F ER data + F ER ack F ER data F ER ack (14) We can rewrite FER with respect to STA s mobility, receiver ading margin, transmission carrier requency, and rame duration [15]. F ER = 1 exp( ρ d 2πρTp ) Where ρ is the ading margin decided by the receiver structure, d is the maximum doppler requency calculated rom the STA speed and the carrier requency,and T p represents rame duration. Hence, Eq.(3) becomes: p = 1 (1 τ) n 1 (1 F ER data )(1 F ER ack ) (15) In this analysis, the unsaturated traic behavior is characterized by deining a MAC queue(q) in equations 11 and 13. q can be deined as the probability that there is at least one packet to be transmitted in the STA queue. Assume, the packet arrival rate at each STA buer rom upper layer is λ pkt/sec and µ represent the packet processing rate assuming that the queue has a length o K. By using a M/M/1/K queueing model[15], the probability q, that there is at least one packet in the queue is: q = 1 1 λ µ 1 ( λ µ )K+1 (16) Here µ = τs(1 τs)n 1 σ s. τ s and σ s are packet transmission probabilities at any random slot and average slot times at saturated load conditions. Equations 15,11, and 13 represent a non-linear system with two unknown parameters τ and p having single solution which can be solved numerically Throughput Analysis Let P tr be the probability that at least one station transmits a packet in a randomly selected slot time with probability τ and P s is the conditional probability that an occurring packet transmission is successul. For a WLAN with n 15

16 contending stations, the probabilities P tr and P s can be written as P tr = 1 (1 τ) n ; P s = nτ(1 τ)n 1 1 (1 τ) n (17) Considering that a random slot is empty with probability (1 P tr ) and that it contains a successul transmission with probability P tr P s, a collision with probability P tr (1 P s ) and P err in 14 is the probability o a channel access ailure due to channel error. According to [3], the throughput S is deined as a ratio o successully transmitted payload size over a randomly chosen slot duration: S = P tr P s (1 P err )E[P T ] (1 p tr )σ + P tr P s (1 P err )T s + P tr (1 P s )T c + P tr P s P err T e (18) where σ is the backo slot duration, T s is the average time that the channel is captured with successul transmission, T c is the average time that the channel is captured by stations which collide and T e is the average wasted time due to a channel access ailure caused by channel error due to mobility and ading eects. Hence the duration o a channel slot is the period o time the channel stays in one state:idle, ail including collision and error and inally success. Let T data,t ack,t rts,t cts,t bar, T ba, T hob and T hack be the transmission times (measured in microseconds) o an MPDU, an ACK rame, a RTS rame, a CTS rame, a BlockAckReq (BAR) rame, a BlockAck (BA), a Head o Brust(HOB) and a Head o ACK(HACK) rame, respectively. As in [4] it is also assumed that the rame could be corrupted due to either collision or channel error that leads to retransmission and increment o the backo stage. When using the protected block ack mechanism, a data burst transmission cannot be initiated at TXOP i there is an error or collision in the HOB or HACK rames [1]. Hence, a data 16

17 burst duration T s,t e,t c is given by T ack + T sis + (T data + T sis ) B + T bar + T sis + T ba + T RD ; Protected Block ACK Scheme T data + T Tsis ) B + T bar + T sis + T ba + T RD + T dis ; T s = Unprotected Block ACK Scheme T rts + T cts + 2T sis + (T data + T sis ) B + T bar + T sis + T ba + T RD + T dis ; RTS/CTS scheme (19) T hob + T eis + (T sis + T hack ) Protected Block ACK Scheme 1 F ER hob F ER hob +F ER hack F ER hob F ER hack (T data + T Tsis ) B + T bar + T sis + T ba + T RD + +T dis T e = Unprotected Block ACK Scheme T rts + T eis + (T sis + T cts ) RTS/CTS scheme 1 F ER rts F ER rts+f ER cts F ER rtsf ER cts (20) T hob + T eis Protected Block ACK Scheme (T data + T Tsis ) B + T bar + T sis + T ba + T RD + +T dis T c = Unprotected Block ACK Scheme (21) T rts + T eis RTS/CTS scheme T RD = T sis +(T data +T sis ) B RD +T bar +T sis +T ba (ReverseDirection) (22) All o the above mentioned time equations consider RD transmissions which can easily be unplugged to calculate the throughput without RD. According to [4], 17

18 it is also assumed that the HOB rame is always successul to gain the TXOP. Thus E[P T ] is given by L (E[B] 1)(1 F ER data ) + L (E[B RD ])(1 F ER data ) + L; Protected Block ACK with RD, L (E[B] 1)(1 F ER data ) + L; E[P T ] = Protected Block ACK without RD, L (E[B])(1 F ER data ); RTS/CTS Method and Unprotected Block ACK. (23) 3.2. Packet Drop Probability The packet drop probability is the probability that a packet is dropped when the retry limit is reached. Moreover, a packet may be dropped when the sending queue is ull. Hence the total packet drop probability is the sum o both o these events Packet Drop Due to Retry Limit A packet is ound in the last backo stage m i it encounters m collisions in the previous stages and it is eventually discarded or dropped. Thus, the packet drop probability due to reaching the retry limit can be written as a unction o the last backo stage: P drop = b m,0 b 0,0 p = p m.p = p m+1 = [1 (1 p )(1 τ) n 1 ] m+1 (24) Packet Drop Due to Queue Let us consider the M/M/1/K queue system, where there are K rames in the system shown in Fig. 3. Now, by using one o the balanced equations, the steady state probability can be written as 18

19 Figure 3: M/M/1/K Queue Model λ(1 p drop )p 0 = µp 1 Similarly it can be shown that p 1 = λ(1 p drop) p 0 µ p 1 = ρp 0 ; where, ρ = λ(1 p drop) µ p n = ρ n p 0 ; n = 0, 1, 2,...K K 1 λ(1 p drop) µ p n = 1 p 0 = ( λ(1 pdrop ) 1 n=0 µ ) K+1 Note that not all the rames arriving at the queue enter the queue because rames are not allowed into the queue when there are already K rames in the queue. Thereore, the rames are dropped with probability P k = ρ k p 0 ( ) K λ(1 pdrop ) 1 λ(1 p drop) µ (25) = ( ) µ K+1 λ(1 pdrop ) 1 Thus, the total probability o packet loss is µ P loss = P drop + P K ( ) K λ(1 = [1 (1 p )(1 τ) n 1 ] m+1 Pdrop ) 1 λ(1 P drop) µ + ( µ λ(1 Pdrop ) 1 µ ) K+1 (26) 19

20 3.3. Mean Delay The delay D can be deined as the time elapsing rom the instant the rame is inserted in the MAC buer to the time in which it is successully transmitted by receiving an acknowledgement or this rame. From this deinition it is obvious that delay is associated with two actors: a medium access delay due to the number o contending stations and a queueing delay or load conditions and rame processing rates at the queue. So, the average delay is D avg = D MAC + D Q MAC Delay The MAC delay or a successully transmitted packet is deined to be the time interval rom the time the rame is at the head o the MAC queue ready or transmission until an acknowledgement or this packet is received. As per [16], the average MAC delay is given by E[D MAC ] = E[X]E[slot] Here E[X] is the average number o slots spent or a successul transmission. Let STA be in the i backo stage and get the channel access with probability c i. The average number o slots utilized by the STA in the i backo stage is (CW i + 1)/2, i (0, m) and the probability that the rame reaches the backo stage i and it is not discarded is pi pm+1, i (0, m). Hence, 1 p m+1 [ ] m (p i p m+1 )((CW i + 1)/2) E[X] = 1 p m+1 n=0 E[slot] = (1 p tr )σ + P tr P s (1 P err )T s + P tr (1 P s )T c + P tr P s P err T e [ ] m (p i p m+1 )((CW i + 1)/2) E[D] = 1 p m+1 (1 p tr )σ + +P tr P s (1 P err )T s + n=0 + P tr (1 P s )T c + P tr P s P err T e (27) 20

21 Queueing Delay By using Little s ormula [15], the expected time spent (i.e.queuing delay) in the queue can be calculated as D Q = E[N] λ(1 P drop ) (28) Here E[N] is the expected number o packets in the queue given by E[N] = K np n = n=0 = ρp 0 d dρ K nρ n P 0 n=0 ( ) 1 ρ K+1 1 ρ ( 1 ρ K+1 (1 ρ)(k + 1)ρ K ) = ρp 0 (1 ρ) 2 ( ρ(1 ρ K+1 ) (1 ρ)(k + 1)ρ K+1 ) = (1 ρ)(1 ρ K+1 ) ( ρ(1 (K + 1)ρ K + Kρ K+1 ) ) E[N] = (1 ρ)(1 ρ K+1 ) Now using equation 28, D Q becomes ( ρ(1 (K + 1)ρ K + Kρ K+1 ) D Q = (1 ρ)(1 ρ K+1 ) ) 1 λ(1 P drop ) (29) Thereore the mean delay is given by [ ] m (p i p m+1 )((CW i + 1)/2) D = 1 p m+1 ((1 p tr )σ + P tr P s (1 P err )T s + P tr (1 P s )T c + n=0 ( ρ(1 (K + 1)ρ K + Kρ K+1 ) ) 1 +P tr P s P err T e ) + (1 ρ)(1 ρ K+1 ) λ(1 P drop ) (30) 4. Numerical Studies We study the characteristics o various IEEE n Block ACK schemes and to validate analytical model using MATLAB based numerical studies. Table 1 lists the parameters used in the numerical study. The protected Block ACK with and without reverse direction and non-protected Block ACK with and without RD are considered or comparison purposes. 21

22 Table 1: Summary o IEEE n parameters Payload 1500 bytes r 2 Mbps T-PHY 192 r* 1 Mbps T-DATA 192+(224+Payload)/r Data Rate 11 Mbps T-ACK /r* Block Size 5 T-RTS /r* Block Size RD 3 T-CTS /r* Fading Margin 0.05 T-BAR /r Velocity 5m/s T-BA /r Queue Length 50 Figure 4 shows the increasing the number o STAs on channel throughput perormance or a packet arrival rate o 8pkts/sec.One can observe that in all cases throughput initially increases with the number o STAs but urther increments o network size signiicantly reduce the throughput. This is very obvious in traditional WLANs due to collisions as the number o STAs increases in the network. Moreover, it is observed that the slope o the throughput degradation is stier in the case o Block ACK with RD as compared to protected Block ACK RD and in average the protection with the Block ACK mechanism provides 32.54% higher throughput. Collisions and FER rates are the dominating actors that make this dierence in perormance. As discussed in earlier, collisions and errors are only experienced by the initial data rames in the protected Block ACK mode. I the initial data rame is correctly transmitted then the STA will initiate the rest o the data burst where as in an unprotected scenario, (which used the Block ACK mode) there is no such protection mechanism (RTS/CTS is not considered in two way handshake scheme) resulting in a ull data burst experiencing the collisions and errors (resulting in higher collision and error times). Hence, to ully utilize the RD eature o n, it should be integrated with the protected block ACK mechanism to achieve higher throughput. Another special observation is that, the protected block ACK scheme outperorms the RTS/CTS scheme as RTS/CTS has extra overheads. Figure 5 shows the packet delay increases when the network size grows in 22

23 8.5 x Protected Block ACK RD Protected Block ACK Without RD Non protected Block ACK RD Non protected Block ACK without RD Arrival Rate = 8pkts/sec Throughput(bps) No. o STAs Figure 4: Channel throughput o protected Block ACK with and without RD and nonprotected block with and without RD. all cases due to a higher number o collisions. As a large number o stations attempt to access the channel, more collisions occur, the number o retransmission increases and stations suer longer delays. The protected Block ACK results in delays lower than that o the non-protected Block ACK scheme or both RD and without RD cases, since collisions only experienced by the irst data rame in case o the protected Block ACK scheme where as the whole data burst experienced collisions in the non-protected Block ACK. However, the overhead is a little bit higher in the protected Block ACK scheme due to an additional ACK rame or the irst data rame. This additional ACK rame eventually is more important to reduce the wasted time in terms o collisions or channel errors or higher data transmissions. Moreover, Fig.6 shows the variation o packet 23

24 delay with respect to packet arrival rates. The dierence o packet delay mostly remains constant between protected and non-protected Block ACK, since the packet delay contributions come rom packet arrival rates and queue length as shown in Eq.(29). However packet delay is highly impacted by the number o stations given that the MAC delay s contribution become dominant Protected Block ACK RD Protected Block ACK without RD NonP-Block ACK RD NonP-Block ACK without D RD Arrival Rate = 8pkts/sec 1 Packet Delay (Sec) No. o STAs Figure 5: Packet delay versus number o stations. The eiciency o the set o parameters used on the packet loss probability is explored in Fig.7 or protected Block ACK scheme. one can observe that shows that the choice o higher values or the contention window improve the packet loss probability by reducing the number o collisions. When W = 32, m = 6, m = 5 are used, the packet loss probability increases rapidly and is mostly exponential in nature. Now, using the same settings except a retry limit ixed to 7, the packet drop probability decreases about 48%. This is also true or 24

25 Protected Block ACK RD,STA = 10 NonP-Block ACK RD, STA = 10 Protected Block ACK RD, STA = 20 NonP-Block ACK RD,STA = Packet Delay (Sec) Arrival Rate (pkts/sec) Figure 6: Packet delay versus Arrival rate. maximum backo stage. The packet loss probability can urther be reduced by increasing contention window size rom 4 to 5. This is because the station will get more transmission opportunity according to Eq.(24). However, we observe that the packet loss or the exponential backo mechanism is smaller than the packet loss as a result o queueing mechanism (Fig.8). The probability o packet loss is almost zero or the arrival rate o 8pkts/sec in case o the protected Block ACK with 10 stations and dramatically increases due to queue overlows. We observe similar trend or various access schemes despite o their early queue saturation.. Figure 9 shows the probability o packet loss versus the number o stations. We observe that, the transmission probability, τ s decreases with the number o STAs, hence increasing the probability o collisions. However, at the initial stage (or N < 5) τ is increased a bit and starts decreasing. Interestingly the quantity o τ increments at the initial stage can be characterized by the packet arrival rate. It is shown that or lower packet rates (e.g. λ = 10pkts/sec) τ 25

26 0.07 Probability o s Packet Loss w = 32,m=6,m = 5 w = 64,m=7,m =5 w = 64,m=7,m =4 w = 32,m=7,m =5 Arrival Rate = 8pkts/sec No. o STAs Figure 7: Probability o packet loss against the number o stations Probability o s Packet Loss Protected RD, STA = 10 NonP-Block ACK RD, STA = 10 Protected RD, STA = 20 NonP-Block ACK, STA = Arrival Rate (pkts/sec) Figure 8: Probability o packet loss versus arrival rates or N = 10 and 20 stations. Comparison o various access methods. increases by whereas it is only or λ = 30pkts/sec.. Figure 10 illustrates the variation o throughput with τ or both protected and non-protected Block ACK schemes. We observed that non-protected Block 26

27 Probability o Collision Arrival Rate = 10pkts/sec c Arrival Rate = 30pkts/sec c τ No. o STAs Figure 9: Relationship between probability o collision and τ or varying no. o stations. ACK degrades perormance severely when the no. o STAs is increased as a result o excessive times wasted in the channel contention. Consequently, nonprotected Block ACK scheme also suers rom higher packet delays and packet loss probability as shown in Fig. 11 and Fig. 12, respectively. Throughput(bps ) x 10 6 Protected Block ACK NonP-Block ACK Arrival Rate = 8pkts/sec τ No. o STAs Figure 10: Relationship between Throughput and τ or varying no. o stations. 27

28 Packet Delay (sec) Protected Block ACK NonP-Block ACK Arrival Rate = 8pkts/sec τ No. o STAs Figure 11: Relationship between packet delay and τ or varying no. o stations. Probability o s Packet Loss Protected Block ACK NonP-Block ACK Arrival Rat = 8pkts/sec τ No. o STAs Figure 12: Relationship between probability o packet loss and τ or varying no. o stations. 28

29 5. Conclusion In this paper, we investigated the interdependencies o Block ACK and RD mechanisms or n using a discrete bi-directional Markov chain model under non-saturated traic loads. We developed a mathematical model to derive system throughput, delay, and packet loss probability or both protected and unprotected Block ACK methods under various loading. The model is validated by MATLAB-based numerical studies. Results obtained have shown that the better system perormance (i.e. up to 33% higher throughput and 48% less packet dropping) can be achieved using protected Block ACK in conjunction with RD data transmission. We ound that unprotected Block ACK wastes TXOP especially during collisions and degrades system perormance signiicantly. To ully utilize the system perormance, n stations should employ protected Block ACK mechanism with RD lows. The work reported can help network planners to deploy high-speed based networks and to contribute in the development o next generation wireless local area network ac amendment. Our uture work will report on the design and perormance evaluation o a crosslayer MAC protocol design supporting multimedia applications over ac. Development o an extensive simulation model to validate our numerical results presented here is also our ongoing work. Reerences [1] S. Committee, Wireless lan medium access control (mac) and physical layer (phy) speciications: Amendment 8: Medium access control (mac) quality o service enhancements, IEEE Computer Society, [2] G. Bianchi, Perormance analysis o the ieee distributed coordination unction, IEEE Journal on Selected Areas in Communications,, vol. 18, no. 3, pp , March [3] F. Daneshgaran, M. Laddomada, F. Mesiti, and M. Mondin, Unsaturated throughput analysis o ieee in presence o non ideal transmission 29

30 channel and capture eects, IEEE Transactions on Wireless Communications, vol. 7, no. 4, pp , [4] H. Lee, I. Tinnirello, J. Yu, and S. Choi, Throughput and delay analysis o ieee le block ack with channel errors, in 2nd IEEE International Conerence on Communication Systems Sotware and Middleware. IEEE, 2007, pp [5] H. Wu, Y. Peng, K. Long, S. Cheng, and J. Ma, Perormance o reliable transport protocol over ieee wireless lan: analysis and enhancement, in proc Twenty-First Annual Joint Conerence o the IEEE Computer and Communications Societies,, vol. 2. IEEE, 2002, pp [6] F. Alizadeh-Shabdiz and S. Subramaniam, A Finite Load Analytical Model or the IEEE Distributed Coordination Function MAC, WiOpt 03: Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, p. 2 pages, Mar [Online]. Available: [7] Y. S. Liaw, A. Dadej, and A. Jayasuriya, Perormance analysis o ieee dc under limited load, in proc. IEEE Asia-Paciic Conerence on Communications. IEEE, 2005, pp [8] T. Li, Q. Ni, T. Turletti, and Y. Xiao, Perormance analysis o the ieee e block ack scheme in a noisy channel, in 2nd IEEE International Conerence on Broadband Networks. IEEE, 2005, pp [9] B. S. Kim, H. Hwang, and D. K. Sung, Eect o rame aggregation on the throughput perormance o ieee n, in IEEE Wireless Communications and Networking Conerence, March 2008, pp [10] V. Visoottiviseth, T. Piroonsith, and S. Siwamogsatham, An empirical study on achievable throughputs o ieee n devices, in 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks, WiOPT 2009., June 2009, pp

31 [11] N. Hajlaoui, I. Jabri, and M. Ben Jemaa, Analytical study o rame aggregation in error-prone channels, in 9th International Wireless Communications and Mobile Computing Conerence, July 2013, pp [12] N. Mohammad and S. Muhammad, Modeling and analyzing mac rame aggregation techniques in n using bi-dimensional markovian model, in Networked Digital Technologies. Springer, 2012, pp [13] D. Akhmetov, n: Perormance results o reverse direction data low, in IEEE 17th International Symposium on Personal, Indoor and Mobile Radio Communications,, Sept 2006, pp [14] A. Milad, Z. Bin Muhamad Noh, A. Shibghatullah, and M. Algaet, Design a novel reverse direction transmission using piggyback and piggyback with block ack to improving the perormance o mac layer based on very high speed wireless lans, in proc. IEEE Conerence on Inormation Communication Technologies (ICT), April 2013, pp [15] L. Kleinrock, Queueing systems, volume 1: theory, [16] P. Chatzimisios, A. C. Boucouvalas, and V. Vitsas, IEEE wireless lans: perormance analysis and protocol reinement, EURASIP Journal on Wireless Communications and Networking, vol. 2005, no. 1, pp ,