Delay Analysis and Study of IEEE 802.11p based DSRC Safety Communication in a Highway Environment
Delay Analysis and Study of IEEE802.11p based DSRC Safety Communication in a Highway
Environment
Yuan Yao??,Lei Rao?,Xue Liu?and Xingshe Zhou?
?School of Computer Science,Northwestern Polytechnical University,China
?General Motors Research Lab,USA
?School of Computer Science,McGill University,Canada
Abstract—As a key enabling technology for the next generation inter-vehicle safety communications,The IEEE802.11p protocol is currently attracting much attention.Many inter-vehicle safety communications have stringent real-time requirements on broad-cast messages to ensure drivers have enough reaction time toward emergencies.Most existing studies only focus on the average delay performance of IEEE802.11p,which only contains very limited information of the real capacity for inter-vehicle communication. In this paper,we propose an analytical model,showing the performance of broadcast under IEEE802.11p in terms of the mean,deviation and probability distribution of the MAC access https://www.wendangku.net/doc/5f2296398.html,parison with the NS-2simulations validates the accuracy of the proposed analytical model.In addition,we show that the exponential distribution is a good approximation to the MAC access delay distribution.Numerical analysis indicates that the QoS support in IEEE802.11p can provide relatively good performance guarantee for higher priority messages while fails to meet the real-time requirements of the lower priority messages.
I.I NTRODUCTION
Communication-based safety technology is considered as a more ef?cient approach than the traditional active safety technology in terms of detection range,?eld of view and cost.As a vital part of Intelligent Transportation System(IT-S)Program conducted by USDOT,vehicle-to-vehicle(V2V) communication can provide many safety-related applications such as cooperative forward collision warning,emergency electronic brake lights,lane change assistance,blind spot warning,intersection movement assist and hazardous location noti?cation,etc[1].The IEEE802.11p protocol is now approved to better support V2V communications.Statistics show that V2V systems can deal with79%potential vehicle crashes which can signi?cantly improve road safety[2].This kind of applications has the additional demand on low latency and direct transmission.Once an emergency situation occurs, it’s necessary to inform all surrounding vehicles with safety messages in time.Therefore,most V2V safety applications commonly adopt the broadcast mode for real-time data trans-mission[3].
One of the most important points in a real-time wireless communication is the MAC protocol,hence,the new standard IEEE802.11p for V ANET is currently attracting much atten-tion.For V2V safety applications,a safety-related message needs to be delivered before the deadline.Thus,it’s important to get the MAC access delay of802.11p to analyze if the standard protocol meets the requirements of real-time wireless communications.The MAC access delay,namely the MAC service time,is the time interval from the time instant when a packet becomes the head of the MAC queue to the time instant that either the packet is successfully transmitted or dropped.So far,many researchers have studied the performance of IEEE 802.11p.Most of them only consider the mean MAC access delay in V ANET environment[4]–[6],however,the mean value cannot re?ect the practical situation of V ANET.Even if the mean delay is less than the deadline,large latency may still take place because of the stochasticity of the IEEE802.11p MAC scheme.Therefore,the distribution of the MAC access delay has been more practical for designers to understand the characteristic of the IEEE802.11p MAC protocol.Meanwhile, the distribution of the MAC access delay can be used for further analysis of the queuing delay.[7]and[8]established theoretical models and obtained the MAC access delay dis-tribution of WLANs by constructing probability generating function(PGF)and probability mass function respectively.But these models only take a single type of message into account.
[9]and[10]proposed analytical models for the IEEE802.11e EDCA to evaluate the performance of multi-traf?cs with different QoS supports.However,these models are conducted under saturated conditions which are not suitable for the V2V safety communication.Moreover,all above models[7]–[10] are based on the unicast mode that cannot be used in the broadcast mode.Until recently,there have been some works that studied the MAC delay distribution of IEEE802.11p safety messages broadcast via simulation[11]–[13],but they didn’t obtain explicit expressions.
In this paper,we aim at constructing a complete analytical model to evaluate the capacity of the standard IEEE802.11p when applied to V2V safety applications.We establish two Markov Chains for different priority ACs to analyze the delay distribution in the broadcast mode.Moreover,our model can cover both the non-saturated and saturated conditions. Simulation results show that our analytical model for the mean, deviation and probability distribution is very accurate.In addition,we observe that the MAC access delay distribution is close to a shifting exponential distribution.Numerical analysis indicates that802.11p with QoS support can provide relatively
S
Fig.1:WA VE protocol stack
good performance for the higher priority messages while fails to guarantee the real-time demand of the lower priority messages.
The rest of this paper is organized as follows.Section II gives a brief overview of IEEE 802.11p protocol and V2V safety communication in a highway environment.Section III presents the analytical model and derives the mean,deviation and probability distribution of the MAC access delay from a certain tagged node’s view.Section IV validates our model via NS-2simulations.Section V analyzes the numerical results.Finally,Section VI draws the conclusion.
II.IEEE 802.11P FOR V EHICULAR C OMMUNICATION A.An Overview of IEEE 802.11p Protocol
IEEE drafts the Wireless Access in Vehicular Environments (WA VE)protocol to better support vehicular communication.The WA VE protocol stack is shown in Figure 1.It’s composed of IEEE 802.11p and a standard family IEEE 1609.
IEEE 802.11p extends the IEEE 802.11standard for a high-speed vehicular environment based on dedicated short-range communication (DSRC)spectrum.It covers the data link layer and the physical layer of the WA VE stack,while IEEE 1609has been developed to de?ne the upper layers.The MAC layer adopts Enhanced Distributed Channel Access (EDCA)for Quality of Service (QoS)support inheriting from IEEE 802.11e,while the physical layer uses an Orthogonal Frequency Division Multiplex (OFDM)modulation scheme to multiplex data which is similar to the IEEE 802.11a standard (with the transmission rates from 3to 27Mb/s which is half of the bandwidth in the IEEE 802.11a).IEEE 802.11p provides multi-channel control mechanism to operate seven 10-MHz wide channels de?ned in DSRC spectrum.One is the control channel (CCH)for common safety communications only and the remaining six are known as the Service Channel (SCH)for other non-safety applications.
B.EDCA Differentiation Parameters and Backoff Procedure EDCA is designed to enhance the Distributed Coordination Function (DCF)to provide QoS support.It allows four access categories (ACs)with different priorities in a station.Each AC behaves as an enhanced DCF with an independent MAC queue
TABLE I:802.11p EDCA Access Parameters for CCH
AC CWmin CWmax AIFSN TXOP Limit 3aCWmin aCWmax 902aCWmin
aCWmax 601(aCWmin+1)/2-1aCWmin
300
(aCWmin+1)/4-1
(aCWmin+1)/2-1
2
entity that can be differentiated by channel access parameters including Contention Window (CW),Arbitration Inter-Frame Space (AIFS)and Transmission Opportunity (TXOP).The speci?c de?nitions of the 802.11p EDCA are shown in Table I,where AC3corresponds to the lowest priority and AC0corresponds to the highest priority.
Let the W i,j denote the maximum CW size of AC i in the j -backoff stage after the j th unsuccessful transmission,thus,W i,0=CW i,min +1.Let M i be the maximum times that the CW of AC i can be doubled,hence,
M i =log 2
CW i,max +1
CW i,min +1
.
(1)
Then we have
W i,j =
2j W i,0,j ≤M i
2M i W i,0,M i , (2) where L i is the retry limit of the AC i backoff.Without loss of generality,we de?ne L i as L in this paper.One important difference between the DCF and the EDCA is the defer time when the channel is sensed idle.The DCF allows a node to transmit packets when the channel keeps idle for a constant Distributed Inter-Frame Space (DIFS)while the EDCA de?nes different time intervals called AIFS for the priority-based QoS support.The Arbitration Inter-Frame Space Number (AIFSN)is used to determine the AIFS according to AIF S [i ]=SIF S +AIF SN [i ]×σ, (3) where AIFSN [i ]≥2corresponds to the DIFS of 802.11and σdenotes the slot time.In this paper,we de?ne A i as the AIFS differentiation A i =AIF SN [i ]?AIF SN [0]. (4) The TXOP limit allows the consecutive transmissions of several packets when an AC entity occupies the channel.However,TXOP has not been de?ned by IEEE 802.11p yet.The operation of the EDCA backoff procedure is described in [14]shown in Figure 2.The frames from the higher layer arrive at the MAC layer with different priorities,and then enter different queues.The backoff instances in a node can be considered as being independent of each other without virtual collisions.For each AC,if the channel is idle for a period time equal to an AIFS,it transmits.Otherwise,if the channel is sensed busy,the AC will persist to monitor the channel until the idle duration up to the AIFS.At this point,the AC generates a random interval according to its CW value slot time (?) Busy Medium Busy Medium packet ACK? New backoff stage with double CW N Higher Fig.2:EDCA backoff procedure and starts a backoff procedure.The backoff counter decreases again only when then channel keeps idle for an AIFS time.The destination node sends back an ACK frame to the source node as soon as it receives the delivery,and the source node may transmit a next frame or go to an idle state.If the source node does not receive the ACK within a prede?ned ACK Timeout,another backoff procedure with doubled CW is invoked for transmission failure caused by external collisions.After each unsuccessful transmission,the CW will be doubled until it reaches CW max or the retransmission number is up to the retry limit.In this paper,we are only interested in the delay of packets that are successfully received at the MAC layer.However,different backoff instances in a station cannot ac-cess the channel completely independently because of internal virtual collisions.We will discuss this issue in detail in next Section. C.V2V Safety Communication in a Highway Environment V2V communications for safety is the dynamic wireless ex-change of data between nearby vehicles that offers the oppor-tunity for signi?cant safety improvements.Safety applications usually demand one vehicle interacts with other vehicles near-by directly.Considering the dynamic topology and low delay constraint,single-hop broadcast on CCH is seen as an effective approach to inform neighboring vehicles with safety messages.In V ANET,there are two main types of broadcast messages for safety applications.One is emergent safety messages (or event-driven messages)which are sent when detecting dangers or abnormal situations.This type of messages is closely related to the speci?c safety applications.The other one is routine safety messages (or time-triggered messages).This type of messages basically contains vehicle’s location,velocity,direction and other detail attributions like vehicle size,vehicle length and acceleration control,etc.Due to highly dynamic network topology,routine safety messages have to be sent with high frequency (2Hz ～10Hz)to ensure up-to-date information.An example of these two types messages is Decentralized Environment Noti?cation Messages (DENM)and Cooperative Awareness Messages (CAM)de?ned by https://www.wendangku.net/doc/5f2296398.html,monly,emergent safety messages are generated occasionally but need a fast and guaranteed transmission.Therefore,this type of messages has a higher priority than routine messages. In this paper,we leverage a one-dimensional V ANET model of a typical highway scenario like the Figure 3shows.From the statistic analysis of empirical data,[15]proves that an exponential distribution is a good ?t for highway vehicle traf?c in terms of inter-vehicle distance.That means the vehicles Fig.3:One-dimensional V ANET model are dispersed in a line following Poisson point process with intensity β,namely,the traf?c density (in vehicles per meter).The transmission range (denoted by R )is de?ned as the dis-tance of successfully sending/receiving one packet.It depends on the transmission power and channel fading.The carrier sensing range (denoted by L cs )is de?ned as the distance of detecting a signal and it is the key parameter in the CSMA/CA scheme.The interference range (denoted by L int )is larger than the transmission range and less than the carrier sensing range,because the signal not reaching the receiving threshold may still have impacts on the normal receiving.With density β,we can derive the average number of vehicles in different areas respectively. ????? N tr =2βR N cs =2βR N ht =2β(R +L int ?L cs ) .(5)III.A NALYTICAL M ODEL A.Scenario description We assume the following scenarios for the IEEE 802.11p broadcast on the CCH. ?We only consider two types of messages in a vehicle which are set priorities with AC0(emergent safety mes-sages)and AC1(routine safety messages)respectively.?The safety-critical messages are usually very short so that they can be encapsulated in a single packet.We assume the average packet size E [P ]is the same for all ACs.?The routine safety message is generated periodically with rate λ0.Like some previous studies on safety communica-tion in V ANET [16]–[18],we assume the packet arrival rate λ1(in terms of packets per second)for emergent safety message is satis?ed Poisson process. ?We neglect the mobility of vehicles since nodes remain almost stationary within a message transmission time.According to the results of article [19],the vehicles with the speed of 120mi/h only move around 0.053m during a period of a packet transmission,hence the estimated link breaking probability is 0.0052.B.Virtual Collision Model Within one node,each MAC queue of AC i behaves like a virtual station.If two or more ACs of a station try to access the channel in the same time slot,the virtual collision occurs.In this case,the frame with the highest priority will be transmitted and the lower priority frames enter another backoff stage with doubled CWs immediately.If the number Backoff AC 0 - ?0 (higher priority) ?0?1 ?1 AC 1 - ?1 (lower priority) Fig.4:Virtual collision of failed retransmissions reaches the retry limit,the packet will be discarded.Figure 4gives an overview of a node with the virtual collision handling. We use internal/external transmission probability to describe the virtual collision [20].As shown in Figure 4,let i denote the internal transmission probability that the backoff instance of AC i attempts to send a packet in a time slot and p vi denote the virtual collision probability of AC i .Then we have p v 0=0 p v 1= 0.(6) The external transmission probability τi observed by other nodes outside of the station can be calculated as τ0= 0 τ1= 1(1?p v 1)= 1(1? 0).(7) The total transmission probability of a station is given as τ=τ0+τ1. (8) The external collision probability p c can be evaluated as p c =1? ∞ k =0(1?τ) N cs ?1(N cs ?1)k k ! e ?(N cs ?1) × ∞ k =0 (1?τ) N ht N k ht k ! e ?N ht T vuln /σ =1?e ?(N cs ?1)τe ?N ht τT vuln /σ ,(9) where T vuln is the hidden terminal vulnerable period [21],which is twice the packet transmission time if all packets have the same size.The average transmission time is given as T tr = P HY H R b +MAC H +E [P ] R d +δ,(10) where P HY H and MAC H is the header length of physical and MAC layer.R b and R d are the basic rate and data rate respectively.δdenotes propagation delay. C.Markov Chain Model for IEEE 802.11p Broadcast Since there is no ACK frame in broadcast mechanism,the source node cannot detect the external collision.This indicates that only virtual collision affects the backoff procedure.Be-cause the highest priority AC0is free from virtual collision,its backoff procedure is simpli?ed as a one-dimensional Markov Chain with constant contention window size W 0,0shown in Figure 5a.Other lower priority ACs may suffer from internal 0, 0 0, k ···IDLE 1-p b0 p b0 p a0/W 0,0 1-?0 1/W 0,0 ?0 (a)One-dimensional Markov chain for higher priority AC0 N :L ???? ,'/( S EL S S EL S EL S S DL :L :L M M N M :L M ???? S EL S EL S EL S EL ???? ???? S YL :L M 0L 0L N 0L :L 0L ???? S EL EL S EL S EL ???? ???? ???? S YL :L 0L /L /L N /L :L 0L ???? S EL S EL S EL &: VL]H 'RXEOH &: VL]H )L[HG ?L ???? ???????? S YL S YL S YL ???? ???? ???? ?L (b)Two-dimensional Markov chain for lower priority AC1 Fig.5:Markov chain model for backoff instance collisions,which can trigger a new backoff stage with doubled CW,so that should be modeled as a two-dimensional Markov Chain given in Figure 5b. Let s i (t )and b i (t )represent the backoff stage and the backoff counter of AC i at time t .Hence,a state of Markov Chain can be expressed as {s i (t ),b i (t )},and the backoff instance state of AC0can be simpli?ed as {b (t )}for s 0(t )≡0.Specially,we de?ne IDLE state as {-1}and {0,-1}in two Markov Chains respectively. Before solving the Markov Chain,some probabilities here need to be explained and calculated. p ai :is the packet arrival probability of AC i .As the packet of the routine safety message (AC0)is periodically generated and the packet arrival rate of the emergent safety message (AC1)follows Poisson distribution,the probability that it has packets arrival at each MAC queue in a slot time can be calculated by ? ??p a 0=λ0σ p a 1=∞ k =1 (λ1σ)k k !e ?λ1σ =1?e ?λ1σ.(11)ρi :represents the probability that there is at least one packet waiting in the queue of AC[i ].In other words,it’s the utilization of the server for the MAC queue of AC i de?ned as ρi = λi μi ,i =0,1,(12) Busy Medium SIFS slot time (?) AC [0] Fig.6:AIFS differentiation of ACs where μi is the average service rate of the queue (in packets per second).Note that,if ρi =0is satis?ed,it’s the extreme non-saturated case that there is no packet preparing to send.On the other hand,when ρi is equal to 1,the IDLE state will be eliminated from the Markov Chain.So,our model covers extreme non-saturated,intermediate non-saturated and saturated conditions by changing ρi from 0to 1.As an important role played in our model,the estimation of ρi will be elaborated later. p bi :is the backoff blocking probability.For a given backoff instance of AC i in a node,p bi is equal to the probability that the node senses other nodes occupy the channel or there is transmission attempted by other ACs in the node.As shown in Figure 6,it’s obviously that the lower priority ACs are deferred for a longer time than higher ones since the bigger AIFSN,thus,the backoff blocking probability is calculated by p bi =1?? ? ?P (k )1 j =0 j =i (1? j )?? ? A i +1 ,i =0,1 P (k )= ∞ k =0 (1?τ) N cs ?1(N cs ?1)k k ! e ?(N cs ?1) . (13) The stationary distributions of two chains are de?ned as ? ??b 0,k =lim t →∞ P {b (t )=k }k ∈(0,W 0,0?1) b 1,j,k =lim t →∞ P {s 1(t )=j,b 1(t )=k }j ∈(0,L ) k ∈(0,W 1,j,0?1). (14) As the fact that the sum of the stationary probabilities of all states in the Markov Chain equals to one,the limiting probability of state b 0,0and b 1,0,0is obtained as (15). The internal transmission probability can be expressed by ???????????ω0=b 0,0= (W 0,0+1)2(1?p b 0)+1?ρ0p a 0 ?1ω1=L j =0 b 1,j,0=1?p L +1v 11?p v 1 b 1,0,0.(16)D.MAC Access Delay Analysis The MAC access delay,namely the MAC service time,is the time interval from the time instant when a packet becomes the head of the MAC queue to the time instant that either the packet is successfully transmitted or dropped.The MAC delay of AC i is a non-negative random variable of which the distribution can be seen as a discrete time sequence ts i,k with probability q i,k when the time is slotted by a very small unit (q i,k is the steady state probability that the delay equals to ts i,k times slottime).Hence,the probability generating function (PGF)of the access delay (T s i )is given by P T s i (z )= ∞ k =0 q i,k z ts i,k . (17) We can use the transfer-function approach to evaluate the PGF because the whole process can be seen as a Z-transform domain linear system shown in Figure 7.The access delay is composed of the backoff time and the transmission time.The backoff time is a random variable according to the backoff blocking probability while the transmission time is deterministic.Since packet size is assumed same for all ACs,the transmission time of one packet is a constant,thus,the PGF of transmission time (T tr )is expressed as T R (z )=z T tr . (18) In the EDCA backoff procedure,the backoff counter of AC i decreases one slot time (σ)when the channel is sensed idle,while it is frozen for a time period of T tr +AIF S [i ]once a successful transmission is detected.Considering the backoff blocking probability mentioned above,the PGF of the average time that backoff counter decreases by one of AC i is given as H i (z )=(1?p bi )z σ+p bi z T tr +AIF S [i ],i =0,1. (19) B 0,0(z ) TR (z ) 1 1 P Ts0(z ) (a)System block diagram for packet processing of AC0 TR (z ) ··· ··· (b)System block diagram for packet processing of AC1 (c)System block diagram for backoff instance of AC i (i=0,1) Fig.7:Z-transform linear system From Figure 7,we can obtain the transfer functions,i.e.the PGF B i,j (z )and P T si (z )through mason formula.?????????????????B 0,0(z )=1W 0,0W 0,0?1 k =0[H 0(z )]k B 1,j (z )=?????????1W 1,j W 1,j ?1 k =0[H 1(z )]k ,j ∈(1,M 1)1W 1,M 1 W 1,M 1?1 k =0 [H 1(z )]k ,j ∈(M 1,L ). (20) ? ????? ?????b0,0= (W0,0+1) 2(1?p b0) + 1?ρ0 a0 ?1 b1,0,0= 1?p L+1 v1 1?p v1 +W1,0 ?1 2(1?p b1) +W1,0p v1 [1?(2p v1)M1] (1?p b1)(1?2p v1) + 2M1?1W1,0p M1+1 v1 (1?p L?M1 v1 ) (1?p b1)(1?p v1) + 1?ρ1 p a1 ?1 .(15) ? ???????? ????????P T s0(z)=T R(z)B0(z)=T R(z) W0,0 W0,0?1 k=0 [H0(z)]k P T s1(z)=(1?p v1)T R(z) L n=0 p n v1 n j=0 B1,j(z) +p L+1 v1 L j=0 B1,j(z) . (21) The mean of the MAC access delay can be calculated by T Si=1 μi =dP T si (z) dz |z=1=P T si (1),i=0,1.(22) And the deviation of the MAC access delay is given as D Si=P T si (1)+P T si (1)? P T si (1) 2 ,i=0,1.(23) We can deriveρi by iterative method elaborated below. Step1:Initializeρi according to the network condition; Step2:Solve the multivariate nonlinear equations which is composed of(6),(7),(13)and(16)with8variables p vi,p bi, i andτi(i=0,1); Step3:Calculate the average MAC access delay T s i according to equations(18)～(22); Step4:ρi=min(λi T s i,1),if allρi≤εare satis?ed, whereεis a prede?ned error bound,the iteration is completed. Otherwise,go to Step2with newρi. Finally,we can derive the probability density function (PDF)of the MAC access delay according to the properties of PGF. p k(t si)=P{t si=k}=P(k) T si (0) k! ,i=0,1.(24) IV.M ODEL V ALIDATION In this section,we compare the theoretical values of our model for the mean,standard deviation,and PDF of the MAC access delay with NS-2simulation results.[12]indicated that packet size of100bytes is just long enough to broadcast basic status of vehicles,but for security consideration,the length should be much longer.In this paper,the packet size E[P]is set to be500bytes.Each vehicle has two active ACs with packet arrival rates of2pkts/s(AC0)and10pkts/s(AC1) respectively.Since the transmission range of IEEE802.11p is up to1000m at data rate of3Mbps and less than200m at data rate of27Mbps,we choose a moderate value500m as TABLE II:Traf?c and network parameter settings Parameter Value Parameter Value Highway length2200m PHY header48bits Density0.01～0.1vhls/m MAC header112bits Average distance100m～10m Date rate3Mbps Transmission range500m Basic rate1Mbps Carrier sensing range700m Slot time13μs Interference range600m SIFS32μs Retry limit4Propagation delay2μs Fig.8:Mean of the MAC access delay the transmission range R at rate6Mbps in simulation.Table II presents the traf?c parameters of a typical highway scenario and the network parameters of the IEEE802.11p MAC layer. Figure8and9show the mean access delay and standard deviation(by taking square root of equation(23))of the IEEE 802.11p MAC layer with varied traf?c density respectively. Meanwhile,min and max delay observed from simulations are listed in Table III.From Figures8and9,there is a good agreement between analytical values and simulation results. We can observe that both the higher and the lower priority ACs have the very low average access delay.However,the standard deviation curve of AC1grows rapidly with the traf?c density increasing.This indicates that the maximum delay deviates from average delay largely so that the mean value cannot re?ect the real network condition at heavy traf?c density.From the table III,we can see that the maximum delay of AC1is over300ms at the traf?c density of0.1vhls/m. Figure10shows the probability distribution of the MAC Fig.9:Standard deviation of the MAC access delay TABLE III:Min/Max MAC access delay Density(vhls/m)Min Delay(ms) AC0/AC1 Max Delay(ms) AC0/AC1 0.01 1.5373/1.5638 3.9954/6.4080 0.02 1.5377/1.5634 5.3343/16.5296 0.03 1.5371/1.56338.6794/32.4688 0.04 1.5376/1.564211.4207/56.8845 0.05 1.5373/1.563825.1149/84.8991 0.06 1.5371/1.563245.4646/124.9323 0.07 1.5372/1.563562.9478/176.2043 0.08 1.5371/1.563575.3410/211.8008 0.09 1.5370/1.563986.0945/268.5323 0.10 1.5371/1.564198.7202/325.5742 access delay with varied traf?c density.Observe that all the analytical results match the simulation results very well,espe-cially,our model has a close tail distribution with simulation. V.N UMERICAL A NALYSIS A.Distribution Analysis We notice that the PDF envelope of the MAC access delay is similar to the exponential distribution.In this section,we compare the cumulative distribution function(CDF)of the exponential distribution with the distributions of two samples. One is derived from simulation,and the other is generated with PDF of our analytical model.Since the minimum delay of an AC is not0,we assume the distribution of the MAC access delay of AC i satis?es a shifting exponential distribution with its minimum delay(denoted by a i).We?rst calculate the minimum delay of each AC. If an AC i detects the channel is idle for AIFS[i]and successfully accesses the channel without any contention,this AC i will get a minimum delay value(noted by a i in our work). With the given packet size and data rate,we can easily obtain the minimum delay as follows a i=AIF S[i]+T tr,i=0,1.(25) With the parameter settings in Section IV,a0and a1are 1.5371ms and1.5631ms,respectively.Then,the PDF of the shifting exponential distribution is de?ned as follows f i(x)= θi e?θi(x?a i),x≥a i