Performance Evaluation of Deadline Monotonic Policy over protocol

Transcription

1 Performance Evaluation of Deadline Monotonic Policy over 80. protocol Ines El Korbi and Leila Azouz Saidane National School of Computer Science University of Manouba, 00 Tunisia s: ABSTRACT Real time applications are characterized by their delay bounds. To satisfy the Quality of Service (QoS) requirements of such flows over wireless communications, we enhance the 80. protocol to support the Deadline Monotonic (DM) scheduling policy. Then, we propose to evaluate the performance of DM in terms of throughput, average medium access delay and medium access delay distrbution. To evaluate the performance of the DM policy, we develop a Markov chain based analytical model and derive expressions of the throughput, the average MAC layer service time and the service time distribution. Therefore, we validate the mathematical model and extend analytial results to a multi-hop network by simulation using the ns- network simulator. Keywords: Deadline Monotonic, 80., Performance evaluation, Average medium access delay, Throughput, Probabilistic medium access delay bounds. INTRODUCTION Supporting applications with QoS requirements has become an important challenge for all communications networks. In wireless LANs, the IEEE 80. protocol [5] has been enhanced and the IEEE 80.e protocol [6] was proposed to support quality of service over wireless communications. In the absence of a coordination point, the IEEE 80. defines the Distributed Coordination Function (DCF) based on the Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) protocol. The IEEE 80.e proposes the Enhanced Distributed Channel Access (EDCA) as an extension for DCF. With EDCA, each station maintains four priorities called Access Categories (ACs). The quality of service offered to each flow depends on the AC to which it belongs. Nevertheless, the granularity of service offered by 80.e (4 priorities at most) can not satisfy the real time flows requirements (where each flow is characterized by its own delay bound). Therefore, we propose in this paper a new medium access mechanism based on the Deadline Monotonic (DM) policy [9] to schedule real time flows over 80.. Indeed DM is a real time scheduling policy that assigns static priorities to flow packets according to their deadlines; the packet with the shortest deadline being assigned the highest priority. To support the DM policy over 80., we use a distributed scheduling and introduce a new medium access backoff policy. Therefore, we focus on performance evaluation of the DM policy in terms of achievable throughput, average MAC layer service time and MAC layer service time distribution. Hence, we follow these steps: First, we propose a Markov Chain framework modeling the backoff process of n contending stations within the same broadcast region []. Due to the complexity of the mathematical model, we restrict the analysis to n contending stations belonging to two traffic categories (each traffic category is characterized by its own delay bound). From the analytical model, we derive the throughput achieved by each traffic category. Then, we use the generalized Z-transforms [3] to derive expressions of the average MAC layer service time and the service time distribution. As the analytical model was restricted to two traffic categories, analytical results are extended by simulation to different traffic categories. Finally, we consider a simple multi-hop scenario to deduce the behavior of the DM policy in a multi hop environment. Volume 3 Number 4 Page 7

2 The rest of this paper is organized as follows. In section, we review the state of the art of the IEEE 80. DCF, QoS support over 80. mainly the IEEE 80.e EDCA and real time scheduling over 80.. In section 3, we present the distributed scheduling and introduce the new medium access backoff policy to support DM over 80.. In section 4, we present our mathematical model based on Markov chain analysis. Section 5 and 6 present respectively throughput and the service time analysis. Analytical results are validated by simulation using the ns- network simulator [6]. In section 7, we extend our study by simulation, first to take into consideration different traffic categories, second, to study the behavior of the DM algorithm in a multi-hop environment where factors like interferences or routing protocols exist. Finally, we conclude the paper in section 8. LITTERATURE REVIEWS. The 80. protocol.. Description of the IEEE 80. DCF Using DCF, a station shall ensure that the channel is idle when it attempts to transmit. Then it selects a random backoff in the contention window [0,CW ], where CW is the current window size and varies between the minimum and the maximum contention window sizes. If the channel is sensed busy, the station suspends its backoff until the channel becomes idle for a Distributed Inter Frame Space (DIFS) after a successful transmission or an Extended Inter Frame Space (EIFS) after a collision. The packet is transmitted when the backoff reaches zero. A packet is dropped if it collides after maximum retransmission attempts. The above described two way handshaking packet transmission procedure is called basic access mechanism. DCF defines a four way handshaking technique called Request To Send/Clear To Send (RTS/CTS) to prevent the hidden station problem. A maximum achievable throughput. The native model is also extended in [0] to a non saturated environment. In [], the authors derive the average packet service time at a 80. node. A new generalized Z-transform based framework has been proposed in [3] to derive probabilistic bounds on MAC layer service time. Therefore, it would be possible to provide probabilistic end to end delay bounds in a wireless network.. Supporting QoS over Differentiation mechanisms over 80. Emerging applications like audio and video applications require quality of service guarantees in terms of throughput delay, jitter, loss rate, etc. Transmitting such flows over wireless communications require supporting service differentiation mechanisms over such networks. Many medium access schemes have been proposed to provide some QoS enhancements over the IEEE 80. WLAN. Indeed, [4] assigns different priorities to the incoming flows. Priority classes are differentiated according to one of three 80. parameters: the backoff increase function, the Inter Frame Spacing (IFS) and the maximum frame length. Experiments show that all the three differentiation schemes offer better guarantees for the highest priority flow. But the backoff increase function mechanism doesn t perform well with TCP flows because ACKs affect the differentiation mechanism. In [7], an algorithm is proposed to provide service differentiation using two parameters of IEEE 80., the backoff interval and the IFS. With this scheme high priority stations are more likely to access the medium than low priority ones. The above described researches led to the standardization of a new protocol that supports QoS over 80., the IEEE 80.e protocol [6]. station S j is said to be hidden from S i if S j is.. The IEEE 80.e EDCA The IEEE 80.e proposes a new medium within the transmission range of the receiver of S i and out of the transmission range of S i... Performance evaluation of the 80. DCF Different works have been proposed to evaluate the performance of the 80. protocol based on Bianchi s work []. Indeed, Bianchi proposed a Markov chain based analytical model to evaluate the saturation throughput of the 80. protocol. By saturation conditions, it s meant that contending stations have always packets to transmit. Several works extended the Bianchi model either to suit more realistic scenarios or to evaluate other performance parameters. Indeed, the authors of [] incorporate the frame retry limits in the Bianchi s model and show that Bianchi overestimates the access mechanism called the Enhanced Distributed Channel Access (EDCA), that enhances the IEEE 80. DCF. With EDCA, each station maintains four priorities called Access Categories (ACs). Each access category is characterized by a minimum and a maximum contention window sizes and an Arbitration Inter Frame Spacing (AIFS). Different analytical models have been proposed to evaluate the performance of 80.e EDCA. In [7], Xiao extends Bianchi s model to the prioritized schemes provided by 80.e by introducing multiple ACs with distinct minimum and maximum contention window sizes. But the AIFS differentiation parameter is lacking in Xiao s model. Recently Osterbo and Al. have proposed Volume 3 Number 4 Page 8

3 different works to evaluate the performance of the IEEE 80.e EDCA [3], [4], [5]. They proposed a model that takes into consideration all the differentiation parameters of the EDCA especially the AIFS one. Moreover different parameters of QoS have been evaluated such as throughput, average service time, service time distribution and probabilistic response time bounds for both saturated and non saturated cases. Although the IEEE 80.e EDCA classifies the traffic into four prioritized ACs, there is still no guarantee of real time transmission service. This is due to the lack of a satisfactory scheduling method for various delay-sensitive flows. Hence, we need a scheduling policy dedicated to such delay sensitive flows..3 Real time scheduling over 80. A distributed solution for the support of realtime sources over IEEE 80., called Blackburst, is discussed in [8]. This scheme modifies the MAC protocol to send short transmissions in order to gain priority for real-time service. It is shown that this approach is able to support bounded delays. The main drawback of this scheme is that it requires backoff value is inferred from the deadline information. 3 SUPPORTING DEADLINE MONOTONIC (DM) POLICY OVER 80. With DCF all the stations share the same transmission medium. Then, the HOL (Head of Line) packets of all the stations (highest priority packets) will contend for the channel with the same priority even if they have different deadlines. Introducing DM over 80. allows stations having packets with short deadlines to access the channel with higher priority than those having packets with long deadlines. Providing such a QoS requires distributed scheduling and a new medium access policy. 3. Distributed Scheduling over 80. To realize a distributed scheduling over 80., we introduce a priority broadcast mechanism similar to [8]. Indeed each station maintains a local scheduling table with entries for HOL packets of all other stations. Each entry in the scheduling table of node S i comprises two fields (S j, D j ) where S j is the source node MAC address and D j is the constant intervals for high priority traffic; otherwise deadline of the HOL packet of node S j. To the performance degrades very much. In [8], the authors introduced a distributed broadcast HOL packets deadlines, we propose to use the two way handshake DATA/ACK access mode. priority scheduling over 80. to support a class of When a node S dynamic priority schedulers such as Earliest i transmits a DATA packet, it Deadline First (EDF) or Virtual Clock (VC). Indeed, piggybacks the deadline of its HOL packet. Nodes the EDF policy is used to schedule real time flows hearing the DATA packet add an entry for S i in according to their absolute deadlines, where the their local scheduling tables by filling the absolute deadline is the node arrival time plus the delay bound. To realize a distributed scheduling over 80., corresponding fields. The receiver of the DATA packet copies the priority of the HOL packet in ACK before sending the ACK frame. All the stations that the authors of [8] used a priority broadcast did not hear the DATA packet add an entry for S i mechanism where each station maintains an entry for the highest priority packet of all other stations. Thus, using the information in the ACK packet. stations can adjust their backoff according to other 3. DM medium access backoff policy stations priorities. Let s consider two stations S and S The overhead introduced by the broadcast transmitting two flows with the same deadline D priority mechanism is negligible. This is due to the ( D is expressed as a number of 80. slots). The fact that priorities are exchanged using native DATA and ACK packets. Nevertheless, authors of [8] proposed a generic backoff policy that can be used two stations having the same delay bound can access the channel with the same priority using the native 80. DCF. by a class of dynamic priority schedulers no matter if Now, we suppose that S and S transmit flows this scheduler targets delay sensitive flows or rate sensitive flows. with different delay bounds D and D such as D < D, and generate two packets at time instants In this paper, we focus on delay sensitive flows and propose to support the fixed priority Deadline t and t. If S had the same delay bound as S, Monotonic (DM) policy over 80. to schedule its packet would have been generated at time t such delay sensitive flows. For instance, we use a priority as t = t + D, where D = (D D ). broadcast mechanism similar to [8] and introduce a new medium access backoff policy where the At that time, S and S would have the same Volume 3 Number 4 Page 9

4 priority and transmit their packets according to the Volume 3 Number 4 Page 0

5 80. protocol. following assumptions: Thus, to support DM over 80., each station uses a new backoff policy where the backoff is given Assumption : by: The system under study comprises n contending The random backoff selected in [0,CW ] stations hearing each other transmissions. according to 80. DCF, referred as BAsic Backoff (BAB). Assumption : The DM Shifting Backoff (DMSB): Each station S i transmits a flow F i with a delay corresponds to the additional backoff slots that bound D i. The n stations are divided into two a station with low priority (the HOL packet traffic categories C and C such as: having a large deadline) adds to its BAB to have the same priority as the station with the C represents highest priority (the HOL packet having the shortest deadline). n nodes transmitting flows with delay bound D. C represents n nodes transmitting flows Whenever a station S i sends an ACK or hears with delay bound D, such as D < D, an ACK on the channel its DMSB is revaluated as D = (D D ) and (n + n ) = n. follows: DMSB(S i ) = Deadline(HOL(S i )) DT min (S i ) () Where DT min (S i ) is the minimum of the HOL Assumption 3: We operate in saturation conditions: each station has immediately a packet available for transmission after the service completion of the previous packet []. packet deadlines present in S i scheduling table and Assumption 4: Deadline(HOL(S i )) is the HOL packet deadline of A station selects a BAB in a constant contention node S i. window [0,W ] independently of the transmission attempt. This is a simplifying assumption to limit the Hence, when S i has to transmit its HOL packet complexity of the mathematical model. with a delay bound D i, it selects a BAB in the contention window [0,CW min ] and computes the WHole Backoff (WHB) value as follows: WHB(S i ) = DMSB(S i )+ BAB(S i ) () Assumption 5: We are in stationary conditions, i.e. the n stations have already sent one packet at least. Depending on the traffic category to which it belongs, each station S The station S i decrements its BAB when it i will be modeled by a Markov Chain representing its whole backoff (WHB) senses an idle slot. Now, we suppose that S i senses process. the channel busy. If a successful transmission is heard, then S i revaluates its DMSB when a correct 4. Markov chain modeling a station of category ACK is heard. Then the station S i adds the new C DMSB value to its current BAB as in equation (). Whereas, if a collision is heard, S i reinitializes its DMSB and adds it to its current BAB to allow colliding stations contending with the same priority Figure illustrates the Markov chain modeling a station S of category C. The states of this Markov chain are described by the following quadruplet (R,i,i j, D ) where: as for their first transmission attempt. S i transmits R : takes two values denoted by C and when its WHB reaches 0. If the transmission fails, S i doubles its contention window size and repeats the ~ C. When R =~ C, the n stations of above procedure until the packet is successfully category C are decrementing their shifting transmitted or dropped after maximum backoff (DMSB) during D slots and retransmission attempts. wouldn t contend for the channel. When R = C, the D slots had already been 4 MATHEMATICAL MODEL OF THE DM POLICY OVER 80. elapsed and stations of category C contend for the channel. i : the value of the BAB selected by In this section, we propose a mathematical model to evaluate the performance of the DM policy [0,W ]. using Markov chain analysis []. We consider the Volume 3 Number 4 Page will S in

6 Figure : Markov chain modeling a category C Station (i j ) : corresponds to the current backoff moves to the state (~ C,i j,i j, D ), i =..W j = 0.. min(d,i ). of the station S. D : corresponds to (D D ). We choose the negative notation D for stations of Now, If S is in one of the states C to express the fact that only stations of (C,i,i D, D ), i = (D + )..W and at category C have a positive DMSB equal to least one of the (n ) remaining stations (either a D. category C or a category C station) transmits, Initially S selects a random BAB and is in then S moves to one of the states one of the states (~ C,i,i, D ), i = 0..W. (~ C,i D,i D, D ), i = (D + )..W. During (D ) slots, S decrements its backoff if none of the (n ) remaining stations of category C transmits. Indeed, during these slots, the n stations of category C are decrementing their DMSB and wouldn t contend for the channel. 4. Markov chain modeling a station of category C Figure illustrates the Markov chain modeling a station S of category C. Each state of S Markov chain is represented by the quadruplet (i, k, D j, D ) where: When S is in one of the states i : refers to the BAB value selected by S in (~ C,i,i (D ), D ), i = D..W and [0,W ]. th senses the channel idle, it decrements its D slot. k : refers to the current BAB value of S. But S knows that henceforth the n stations of D j : refers to the current DMSB of S, category C can contend for the channel (the D j [0, D ]. slots had been elapsed). Hence, S moves to one of the states (C,i,i D, D ), i = D..W. D : corresponds to (D D ). When S selects a BAB, its DMSB equals However, when the station S is in one of the D and is in one of the states (i,i, D, D ), states (~ C, i,i j, D ), for i =..W, i = 0..W. During D slots, only the n j = 0.. min(d,i ) and at least one of the stations of category C contend for the channel. (n ) remaining stations of category C transmits, then the stations of category C will If S senses the channel idle during D slots, it reinitialize their DMSB and wouldn t contend for moves to one of the states (i,i,0, D ), i = 0..W, channel during additional D slots. Therefore, S where it ends its shifting backoff. Volume 3 Number 4 Page

7 Figure : Markov chain modeling a category C Station When S is in one of the states (i,i,0, D ), ξ = {(i,i, D j, D ),i = 0..W, i = 0..W, the (n ) other stations of category j = 0..(D )} C have also decremented their DMSB and can γ : the set of states of S, where stations contend for the channel. Thus, S decrements its of category C contend for the channel BAB and moves to the state (i,i,0, D ), i =..W, only if none of the (n ) remaining stations transmits. (pink states in figure ). γ = {(i,i,0, D ),i = 0..W (i,i,0, D ),i =..W } If S is in one of the states (i,i,0, D ), Therefore, when stations of category C are in i =..W, and at least one of the (n ) one the states of ξ, stations of category C are in remaining stations transmits, the n stations of one of the states of ξ. Similarly, when stations of category C will reinitialize their DMSB and S category C are is in one of the states of γ, moves to the state (i,i, D, D ), stations of category C are in one of the states of i =..W. γ. 4.3 Blocking probabilities in the Markov chains Hence, we derive the expressions of S According to the explanations given in blocking probabilities p and p shown in paragraphs 4. and 4., the states of the Markov figure as follows: chains modeling stations S and S can be divided into the following groups: p : the probability that S is blocked given that S is in one of the states of ξ. p is ξ : the set of states of S where none of the the probability that at least a station S of n stations of category C contends for the the other (n channel (blue states in figure ). ) stations of C transmits ξ = {(~ C,i,i j, D ),i = 0..W, given that S is in one of the states of ξ. j = 0.. min(max(0,i ), D )} p = ( τ ) n (3) γ : the set of states of S where stations of category C can contend for the channel (pink states in figure ). γ = {(C,i,i D, D ),i = D..W } where τ is the probability that a station S of C ξ : the set of states of S where stations of = transmits given that the states of ξ : τ = Pr[S transmits ξ ] (~C π,0,0, D ) S is in one of (4) W min(max(0,i ),D ) (~C,i,i j, D ) category C do not contend for the channel π (blue states in figure ). i =0 j =0 Volume 3 Number 4 Page 3

8 π (R,i,i j, D ) is defined as the probability of p the state (R,i,i j, D ), in the stationary : the probability that S is blocked conditions and Π = {π (R,i,i j, D ) } given that S is the is in one of the states of γ. S 4.4 Transition probability matrices 4.4. Transition probability matrix of a where τ is the probability that a station category C station S of C transmits given that S Let P is in one be the transition probability matrix of the station S of the states of γ. of category C. P {i, j} is the probability to transit from state i to state j. We τ = Pr[S transmits γ ] have: (C π,d,0, D ) = (6) W π (C,i,i D, D ) π i = D probability vector of a category C station. S p = ( τ ) n ( τ ) n (9) The blocking probabilities described above p : the probability that S is blocked allow deducing the transition state probabilities and given that S is in one of the states of γ. having the transition probability matrix P i, for a p is the probability that at least a station station of traffic category C i. S of the other (n ) stations of C transmits given that S is in one of the states of γ or at least a station S of the n stations of C transmits given that one of the states of γ. p = ( τ ) n ( τ ) n (5) Therefore, we can evaluate the state probabilities by solving the following system []: Π P = Π is in π i = and τ the probability that a station S of i =.. min(w, D ) C transmits given that i i i j (0) j P {(~ C,i,i j, D ), (~ C,i,i ( j + ), D )} = p,i =..W, j = 0.. min(i, D ) () P {(~ C,i,, D ), (~ C,0,0, D )} = p, is in one of the () states of γ. P {(~ C,i,i D +, D ), (C,i,i D, D )} = p,i = D..W τ = Pr [S transmits γ ] (3) = W π (0,0,0,D ) P {(~ C, i, i j, D ),(~ C, i j, i j, D )} (4) = p, i =..W, j =.. min(i, D ) W (7) π (i,i,0,d ) + π (i,i,0,d ) i =0 (i,k,d j,d ) i = P {(~ C, i, i, D ), (~ C, i, i, D )} = p, is defined as the probability i =..W of the state (i, k, D j, D ), in the P {(C,i,i D, D ),(~ C,i D,i D, D )} stationary condition. Π = {π (i,k,d j,d ) } = p,i = (D + )..W is the probability vector of a category C station. P {(C,i,i D, D ),(C,(i ),(i D ), D )} In the same way, we evaluate p and p the = p,i = (D + )..W blocking probabilities of station S shown in figure : p : the probability that S is blocked given that S is in one of the states of ξ. i = 0..W p = ( τ ) n (8) P {(~ C,0,0, D ), (~ C, i,i, D )} =, If (D < W ) then: Volume 3 Number 4 Page 4 (5) (6) (7) W (8)

9 P {(C, D,0, D ),(~ C, i, i, D )} = τ, = f (τ,τ,τ ) W (9) τ,τ,τ ) i = 0..W τ = f (τ,τ,τ ) By replacing p and p by their values in under the constraint equations (3) and (5) and by replacing P and Π τ > 0,τ > 0,τ > 0,τ <,τ <,τ < in (0) and solving the resulting system, we can (8) express π (R,i,i j, D ) as a function of τ, τ and Solving the above system (8), allows deducing τ given respectively by equations (4), (6) and the expressions of τ, τ and τ, and deriving (7). the state probabilities of Markov chains modeling 4.4. Transition probability matrix of a category C and category C stations. category C station Let P be the transition probability matrix of 5 THROUGHPUT ANALYSIS the station S belonging to the traffic category C. The transition probabilities of S are: In this section, we propose to evaluate B i, the normalized throughput achieved by a station of (0) traffic category C i []. Hence, we define: P {(i, i, D j, D ), (i, i, D ( j + ), D )} = p, i = 0..W, j = 0..(D ) P i,s : the probability that a station S i P {(i,i, D j, D ), (i, i, D, D )} = p, belonging to traffic category C i transmits a () i = 0..W, j = 0..(D ) packet successfully. Let S and S be two P {(i, i,0, D ), (i, i,0, D )} = p, i =..W W The channel is idle if the n stations of category C don t transmit given that these stations By replacing p and p by their values in are in one of the states of ξ or if the n stations equations (8) and (9) and by replacing P and Π (both category C and category C stations) don t in (0) and solving the resulting system, we can transmit given that stations of category C are in (i,k,d express π j,d ) as a function of τ, τ one of the states of γ. Thus: and τ given respectively by equations (4), (6) () P {(,,0, D ), (0,0,0, D )} = p (3) P {(i,i,0, D ), (i, i, D, D )} = p, i =..W (4) P {(i,i,0, D ), (i,i, D, D )} = p, i =..W (5) P {(i, i,0, D ), (i, i,0, D )} = p, i = 3..W (6) P {(0,0,0, D ), (i, i, D, D )} =, i = 0..W (7) stations belonging respectively to traffic categories C and C. We have: P,s = Pr[S transmits successfully ξ ] Pr[ξ ] + Pr[S transmits successfully γ ] Pr[γ ] = τ ( p ) Pr[ξ ]+ τ ( p ) Pr[γ ] P,s = Pr[S transmits successfully ξ ] Pr[ξ ] + Pr[S transmits successfully γ ] Pr[γ ] = τ ( p ) Pr[γ ] (9) (30) P idle : the probability that the channel is idle. and (7). Moreover, by replacing π (R,i,i j, D ) and Pidle = ( τ ) n Pr[ξ ]+ ( τ ) n ( τ ) n Pr[γ ] π (i,k,d j,d ) by their values, in equations (4), (6) and (7), we obtain a system of non linear equations as follows: (3) Hence, the expression of the throughput of a category C i station is given by: Volume 3 Number 4 Page 5

10 B i = different stations present in the network as a P Idle T e + P s T s + P Idle n i P i,s T function of the contention window size W, c i = (D = ). We notice that the throughput achieved (3) by category C stations (stations numbered from S to S 4 ) is greater than the one achieved by Where T e denotes the duration of an empty category C stations (stations numbered from S slot, T s and T c denote respectively the duration of to S a successful transmission and a collision. 4 ). PIdle n i P i,s corresponds to the i = probability of collision. Finally T p denotes the average time required to transmit the packet data payload. We have: T s = (T PHY + T MAC + T p + T D )+ SIFS + (T PHY + T ACK + T D )+ DIFS T c = (T PHY + T MAC + T p + T D )+ EIFS (33) (34) Where T PHY, T MAC and T ACK are the durations of the PHY header, the MAC header and the ACK packet [], [3]. T D is the time required to transmit the two bytes deadline information. Stations hearing a collision wait during EIFS before resuming their packets. For numerical results stations transmit 5 bytes data packets using 80..b MAC and PHY layers parameters (given in table ) with a data rate equal to Mbps. For simulation scenarios, the propagation model is a two ray ground model. The transmission range of each node is 50m. The distance between two neighbors is 5m. The EIFS parameter is set to ACKTimeout as in ns-, where: Figure 3: Normalized throughput as a function of the contention window size (D =, n = 8 ) Analytically, stations belonging to the same traffic category have the same throughput given by equation (3). Simulation results validate analytical results and show that stations belonging to the same traffic category (either category C or category C ) have nearly the same throughput. Thus, we conclude the fairness of DM between stations of the same category. For subsequent throughput scenarios, we focus on one representative station of each traffic ACKTimeout = DIFS + (T PHY + T ACK + T D ) + SIFS (35) category. Figure 4, compares category C and category C stations throughputs to the one Table : 80. b parameters. obtained with 80.. Data Rate Mb/s Slot 0 µs SIFS 0 µs DIFS 50 µs PHY Header 9 µs MAC Header 7 µs ACK µs Short Retry Limit 7 For all the scenarios, we consider that we are in n presence of n contending stations with stations for each traffic category. In figure 3, n is fixed to Curves are represented as a function of W and for different values of D. Indeed as D increases, the category C station throughput increases, whereas the category C station throughput decreases. Moreover as W increases, the difference between stations throughputs is reduced. This is due to the fact that the shifting backoff becomes negligible compared to the contention window size. Finally, we notice that the category C station obtains better throughput with DM than with Volume 3 Number 4 Page 6

11 category C station. service time distribution. The service time depends on the duration of an idle slot T e, the duration of a successful transmission T s and the duration of a collision T c [], [3],[4]. As T e is the smallest duration event, the duration of all events will be T given by event. T e 6. Z-Transform of the MAC layer service time Figure 4: Normalized throughput as a function of the contention window size (different D values) In figure 5, we generalize the results for different numbers of contending stations and fix the contention window size W to Service time Z-transform of a category C station: Let TS (Z ) be the service time Z-transform of a station define: S belonging to traffic category C. We H (R,i,i j, D ) (Z ) : The Z-transform of the time already elapsed from the instant S selects a basic backoff in [0,W ] (i.e. being in one of the states (~ C,i,i, D ) ) to the time it is found in the state (R,i,i j, D ). Moreover, we define: P suc : the probability that S observes a successful transmission on the channel, while S is in one of the states of ξ. P = (n )τ ( τ ) n (36) suc P suc : the probability that S observes a successful transmission on the channel, while S is in one of the states of γ. Figure 5: Normalized throughput as a function of P = (n )τ ( τ ) n ( τ ) n the number of contending stations suc (37) + n τ ( τ ) n ( τ ) n All the curves show that DM performs service differentiation over 80. and offers better We evaluate H (R,i,i j, D ) (Z ) for each state throughput for category C stations independently of S Markov chain as follows: of the number of contending stations. 6 SERVICE TIME ANALYSIS In this section, we evaluate the average MAC layer service time of category C and category C T s T H ( ~ C,i,i, D )(Z ) = + suc W P Z e + T c min ( i + D,W ) ( ) T ( ) stations using the DM policy. The service time is p P suc Z e H (~C,k,i, D ) Z the time interval from the time instant that a packet becomes at the head of the queue and starts to contend for transmission to the time instant that either the packet is acknowledged for a successful transmission or dropped [3]. k =i + T s T T + Ĥ (C,i + D,i, D ) (Z ) P suc Z e + (p P suc )Z e We propose to evaluate the Z- T c Transform of the MAC layer service time [3], [4], [5] to derive Volume 3 Number 4 Page 7

12 an Where: (38) Volume 3 Number 4 Page 8

13 Ĥ (C,i + D,i, D ) (Z ) = H (C,i + D,i, D ) (Z ) T s (i + D ) W (39) if D T s T j = D TS (Z ) = Z Moreover, we define: ( p )ZH (~ C,,, D ) (Z ) H (~ C,0,0, D )(Z ) = T s T c P suc : the probability that S observes a P Z T e (p P )Z T e successful transmission on the channel, suc suc min(w,d ) while S is in one of the states of ξ. + ( p )Z H ( ~ C,i,, D ) (Z ) + P = n τ ( τ ) n W (45) i = suc (43) P suc : the probability that S observes a If S transmission state is (~ C,0,0, D ), successful transmission on the channel, the transmission will be successful only if none of while S is in one of the states of γ. the (n ) remaining stations of C transmits. P = n τ ( τ ) n ( τ ) n suc Whereas when the station S transmission state is (46) + (n )τ ( τ ) n ( τ ) n (C, D,0, D ), the transmission occurs T e (( p )H ( ) (Z ) ~ C,0,0, D Ĥ m (C,i + D,i, D )(Z ) = 0 Otherwise ( ) ( )) T c T e + p H (C,D,0, D ) Z Z p H (~C,0,0, D ) Z i =0 We also have: i + p H ( C,D,0, D ) (Z ))) H (~ C,i,i j, D ) (Z ) T s (( p )Z ) H (~ C,i,i, D ) (Z ) P Z T e (p suc i =..W, j =..min(i,d ) T c P )Z T e suc (40) T c + Z e (p H (Z ~ C,0,0, D ) + p H C,D ) ( T ( ( ( ),0, D ) (( p )Z ) H (~ C,i,i, D ) (Z ) 6.. Service time Z-transform of a category H (C,i,i D, D ) (Z ) = T s T c C station: P Z T e (p P )Z T e In the same way, let TS (Z ) be the service time Z-transform of a station S of category C. suc suc + ( p )ZH (C,i +,i + D, D )(Z ),i = D..W (4) m + (Z )) (44) We define: H (i,k,d j,d )(Z ): The Z-transform of the H (C,W,W D, D ) (Z ) time already elapsed from the instant S selects a basic backoff in [0,W ] (i.e. being in one of the = (( p )Z ) H (~C,W,W, D ) (Z ) (4) T c ( ) T state (i, k, D j, D ). P suc Z e p P suc Z e states (i,i, D, D ) ) to the time it is found in the successfully only if none of (n ) remaining We evaluate H (i,i,d j,d ) (Z ) for each state stations (either a category C station) transmits. or a category C If the transmission fails, S tries another of S Markov chain as follows: H (i,i,d,d ) (Z ) =,i = 0 and i = W W transmission. After m retransmissions, if the T s packet is not acknowledged, it will be dropped. H (i,i,d,d ) (Z ) = + P suc Z T e + Thus, the Z-transform of station S service time is: W T c (47) Volume 3 Number 4 Page 9

14 T (p P )Z e H (i,i,0,d ) (Z ),i =..W suc + (48) Volume 3 Number 4 Page 0

15 To compute H (i,i,d j,d ) (Z ), we define T j (Z ), such as: dec 0 Tdec (Z ) = (49) j Tdec (Z ) = for j =..D ( p )ZH (W,W,0,D )(Z ) category. = T s T c (53) P Z T e + (p P )Z T e T D suc suc dec (Z ) T c T TS (Z ) = p Z e H (0,0,0,D i i =0 i m + )(Z ) + i T s T c m T T ( p )Z T s (55) P Z T e + (p P )Z T e T j suc suc (Z ) dec T c ( p )Z e H (0,0,0,D ) (Z ) p Z e H (0,0,0,D (50) 6. Average Service Time From equations (44) (respectively equation (55)), we derive the average service time of a category C So: station ( respectively a category C station). The average service time of a category C i H ( ) (Z ) = H ( ) (Z )T j station is given by: i,i,d j,d i,i,d j +,D dec (Z ), X i = TS () () (56) i = 0..W, j =..D, (i, j ) (0, D ) And: (5) Where TS () (Z ), is the derivate of the service H (i,i,0,d ) (Z ) = ( p )ZH (i +,i,0,d ) (Z ) time Z-transform of a category C i station []. + ( p )ZH (i,i,0,d ) (Z ) By considering the same configuration as in T s T c figure 3, we depict in figure 5, the average service P Z T e + (p P )Z T e T D (Z ) time of category C and category C stations as a suc suc dec function of W. As for the throughput analysis, stations belonging to the same traffic category have i =..W H (W,W,0,D )(Z ) (5) nearly the same average service value. Simulation service time values coincide with analytical values given by equation (56). These results confirm the fairness of DM in serving stations of the same ) (Z ) According to figure and using equation (5), we have: H ( ) (Z ) = H ( ) (Z )T D (Z ) + 0,0,0,D 0,,0,D dec ( p )ZH (,,0,D )(Z ) T s T c (54) P Z T e + (p P )Z T e T D suc suc dec (Z ) Therefore, we can derive an expression of S Z-transform service time as follows: Figure 6: Average service time as a function of the contention window size (D =, n = 8) In figure 7, we show that category C stations obtain better average service time than the one obtained with 80. protocol. Whereas, the opposite scenario happens for category C stations Volume 3 Number 4 Page

16 independently of n, the number of contending stations in the network. exceeds 0.0s equals 0.%. Whereas, station S service time exceeds 0.0s with the probability 57,6%. Thus, DM offers better service time guarantees for the stations with the highest priority. In figure 9, we double the size of the contention window size and set it to 64. We notice that category C and category C stations service time curves become closer. Indeed, when W becomes large, the BAB values increase and the DMSB becomes negligible compared to the basic backoff. The whole backoff values of S and S become closer and their service time accordingly. Figure 7: Average service time as a function of the number of contending stations 6.3 Service Time Distribution Service time distribution is obtained by inverting the service time Z transforms given by equations (44) and (55). But we are most interested in probabilistic service time bounds derived by inverting the complementary service time Z transform given by []: Figure 9: Complementary service time distribution TS (Z ) X (Z ) = (56) ~ i for different values of D ( W = 64 ) i Z In figure 0, we depict the complementary In figure 8, we depict analytical and simulation service time distribution for both category C and values of the complementary service time category C stations and for different values of n, distribution of a category C and a category C the number of contending nodes. stations for different values of D and (W = 3). Figure 8: Complementary service time distribution for different values of D, (W = 3) Figure 0: Complementary service time distribution for different values of the contending stations All the curves drop gradually to 0 as the delay Analytical and simulation results show that increases. Category C stations curves drop to 0 complementary service time curves drop faster when the number of contending stations is small for faster than category C curves. Indeed, when both category C and category C stations. This D = 4 slots, the probability that S service time means that all stations service time increases as the Volume 3 Number 4 Page

17 number of contending nodes increases. 7 EXTENTIONS OF THE ANAYTICAL RESULTS BY SIMULATION The mathematical analysis undertaken above showed that DM performs service differentiation over 80. protocol and offers better QoS guarantees for highest priority stations Nevertheless, the analysis was restricted to two traffic categories. In this section, we first generalize the results by simulation for different traffic categories. Then, we consider a simple multi-hop and evaluate the performance of the DM policy when the stations belong to different broadcast regions. 7. Extension of the analytical results In this section, we consider n stations contending for the channel in the same broadcast region. The n stations belong to 5 traffic categories where n = 5m and m is the number of stations of the same traffic category. A traffic category C i is characterized by a delay bound D i, and D ij = D i D j is the difference between the by different traffic categories stations as a function of the minimum contention window size CW min such as CW min is always smaller than CW max, CW max < 04 and K =. Analytical and simulation results show that throughput values increase with stations priorities. Indeed, the station with the lowest delay bound has the maximum throughput. Moreover, figure shows that stations belonging to the same traffic category have the same throughput. For instance, when n is set to 5 (i.e. m = 3 ), the three stations each traffic category have almost the same throughput. deadline values of category C i stations. We have: and category C j D ij = (i j )K (57) Figure : Normalized throughput: different Where K is the deadline multiplicity factor stations belonging to the same traffic category and is given by: D i +,i = D i + D i = K (58) In figure 3, we depict the average service time of the different traffic categories stations as a Indeed, when K varies, the D ij the difference function of K, the deadline multiplicity factor. We notice that the highest priority station average between deadline values of category C i and service time decreases as the deadline multiplicity category C j stations also varies. Stations factor increases. Whereas, the lowest priority station average service time increases with K. belonging to the traffic category C i are numbered from S i to S im. Figure : Normalized throughput for different traffic category stations In figure, we depict the throughput achieved Figure 3: Average service time as a function of the deadline multiplicity factor K In the same way, the probabilistic service time bounds offered to S (the highest priority station) Volume 3 Number 4 Page 3

18 are better than those offered to station S 5 (the Flows packets are routed using the Ad-hoc On lowest priority station). Indeed, the probability that Demand (AODV) protocol. Flows F and F are S service time exceeds 0.0s=0.3%. But, station respectively transmitted by stations S and S S 5 service time exceeds 0.0s with the probability with delay bounds D and D and of 36%. D = D D =5 slots. Flows F 3 and F 4 are transmitted respectively by S 3 and S 4 and have the same delay bound. Finally, F 5 and F 6 are transmitted respectively by S 5 and S 6 with delay bounds D 5 and D 6 and D 65 = D 6 D 5 = 4 slots. Figure 6 shows that the throughput achieved by F is smaller than the one achieved by F. Indeed, both flows cross nodes 6 and 7, where F got a higher priority to access the medium than F when the DM policy is used. We obtain the same Figure 4: Complementary service time distribution (CW min = 3, n = 8) results for flows F 5 and F 6. Flows F 3 and F 4 have almost the same throughput since they have equal deadlines. The above results generalize the analytical model results and show once again that DM performs service differentiation over 80. and offer better guarantees in terms of throughput, average service time and probabilistic service time bounds for flows with short deadlines. 7. Simple Multi hop scenario In the above study, we considered that contending stations belong to the same broadcast region. In reality, stations may not be within one hop from each other. Thus a packet can go through several hops before reaching its destination. Hence, factors like routing protocols or interferences may preclude the DM policy from working correctly. In the following paragraph, we evaluate the performance of the DM policy in a multi-hop environment. Hence, we consider a 3 node simple mtlti-hop scenario described in figure 5. Six flows are transmitted over the network. Figure 6: Normalized throughput using DM policy Figure 7 show that the complementary service time distribution curves drop to 0 faster for flow F than for flow F. Figure 5: Simple multi hop scenario Figure 7: End to end complementary service time distribution Volume 3 Number 4 Page 4

19 The same behavior is obtained for flow F 5 and (PHY) specification, IEEE (999). F 6, where F 5 has the shortest delay bound. IEEE 80. WG: Draft Supplement to Part : Wireless Medium Access Control (MAC) and physical layer (PHY) specifications: Medium Hence, we conclude that even in a multi-hop environment, the DM policy performs service differentiation over 80. and provides better QoS guarantees for flows with short deadlines. 8 CONCLUSION In this paper we proposed to support the DM policy over 80. protocol. Therefore, we used a distributed backoff scheduling algorithm and introduced a new medium access backoff policy. Then we proposed a Markov Chain based mathematical model to evaluate the performance of the DM policy in terms of throughput, average medium access delay and medium access delay distribution. Analytical and simulation results showed that DM performs service differentiation over 80. and offers better guarantees in terms of throughput, average service time and probabilistic service time bounds for flows with small deadlines. Moreover, DM achieves fairness between stations belonging to the same traffic category. Then, we extended by simulation the analytical results obtained for two traffic categories to different traffic categories. Simulation results showed that even if contending stations belong to K traffic categories, K >, the DM policy offers better QoS guarantees for highest priority stations. Finally, we considered a simple multi-hop scenario and concluded that factors like routing messages or interferences don t impact the behavior of the DM policy and DM still provides better QoS guarantees for stations with short deadlines. 9 REFERENCES G. Bianchi: Performance Analysis of the IEEE 80. Distributed Coordination Function, IEEE J-SAC Vol. 8 N. 3, (March 000). H. Wu, Y. Peng, K. Long, S. Cheng, J. Ma: Performance of Reliable Transport Protocol over IEEE 80. Wireless LAN: Analysis and Enhancement, In Proceedings of the IEEE INFOCOM 0, June 00. H. Zhai, Y. Kwon, Y., Fang: Performance Analysis of IEEE 80. MAC protocol in wireless LANs, Wireless Computer and Mobile Computing, (004). I. Aad and C. Castelluccia: Differentiation mechanisms for IEEE 80., In Proc. of IEEE Infocom 00, (April 00). IEEE 80. WG: Part : Wireless LAN Medium Access Control (MAC) and Physical Layer Access Control (MAC) Enhancements for Quality of Service (QoS), IEEE 80.e/D3.0, (January 005). J. Deng, R. S. Chang: A priority Scheme for IEEE 80. DCF Access Method, IEICE Transactions in Communications, vol. 8-B, no., (January 999). J.L. Sobrinho, A.S. Krishnakumar: Real-time traffic over the IEEE 80. medium access control layer, Bell Labs Technical Journal, pp. 7-87, (996). J. Y. T. Leung, J. Whitehead: On the Complexity of Fixed-Priority Scheduling of Periodic, Real- Time Tasks, Performance Evaluation (Netherlands), pp , (98). K. Duffy, D. Malone, D. J. Leith: Modeling the 80. Distributed Coordination Function in Non-saturated Conditions, IEEE/ACM Transactions on Networking (TON), Vol. 5, pp (February 007) L. Kleinrock: Queuing Systems,Vol. : Theory, Wiley Interscience, 976. P. Chatzimisios, V. Vitsas, A. C. Boucouvalas: Throughput and delay analysis of IEEE 80. protocol, in Proceedings of 00 IEEE 5th International Workshop on Networked Appliances, (00). P.E. Engelstad, O.N. Osterbo: Delay and Throughput Analysis of IEEE 80.e EDCA with Starvation Prediction, In proceedings of the The IEEE Conference on Local Computer Networks, LCN 05 (005). P.E. Engelstad, O.N. Osterbo: Queueing Delay Analysis of 80.e EDCA, Proceedings of The Third Annual Conference on Wireless On demand Network Systems and Services (WONS 006), France, (January 006). P.E. Engelstad, O.N. Osterbo: The Delay Distribution of IEEE 80.e EDCA and 80. DCF, in the proceeding of 5th IEEE International Performance Computing and Communications Conference (IPCCC 06), (April 006), USA. The network simulator ns-, Y. Xiao: Performance analysis of IEEE 80.e EDCF under saturation conditions, Proceedings of International Conference on Communication (ICC 04), Paris, France, (June 004). V. Kanodia, C. Li: Distribted Priority Scheduling and Medium Access in Ad-hoc Networks, ACM Wireless Networks, Volume 8, (November 00). Volume 3 Number 4 Page 5