VIEWS: 11 PAGES: 16 CATEGORY: Research POSTED ON: 6/17/2010 Public Domain
Performance Evaluation of Deadline Monotonic Policy over 802.11 protocol Ines El Korbi and Leila Azouz Saidane National School of Computer Science University of Manouba, 2010 Tunisia Emails: ines.korbi@gmail.com Leila.saidane@ensi.rnu.tn 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 802.11 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-2 network simulator. Keywords: Deadline Monotonic, 802.11, Performance evaluation, Average medium access delay, Throughput, Probabilistic medium access delay bounds. 1 INTRODUCTION use a distributed scheduling and introduce a new medium access backoff policy. Therefore, we focus Supporting applications with QoS requirements on performance evaluation of the DM policy in terms has become an important challenge for all of achievable throughput, average MAC layer communications networks. In wireless LANs, the service time and MAC layer service time IEEE 802.11 protocol [5] has been enhanced and the distribution. Hence, we follow these steps: IEEE 802.11e protocol [6] was proposed to support First, we propose a Markov Chain quality of service over wireless communications. framework modeling the backoff process of In the absence of a coordination point, the IEEE n contending stations within the same 802.11 defines the Distributed Coordination broadcast region [1]. Function (DCF) based on the Carrier Sense Multiple Due to the complexity of the mathematical Access with Collision Avoidance (CSMA/CA) model, we restrict the analysis to n protocol. The IEEE 802.11e proposes the Enhanced contending stations belonging to two traffic Distributed Channel Access (EDCA) as an extension categories (each traffic category is for DCF. With EDCA, each station maintains four characterized by its own delay bound). priorities called Access Categories (ACs). The From the analytical model, we derive the quality of service offered to each flow depends on throughput achieved by each traffic the AC to which it belongs. category. Nevertheless, the granularity of service offered Then, we use the generalized Z-transforms by 802.11e (4 priorities at most) can not satisfy the [3] to derive expressions of the average real time flows requirements (where each flow is MAC layer service time and the service characterized by its own delay bound). time distribution. As the analytical model was restricted to Therefore, we propose in this paper a new two traffic categories, analytical results are medium access mechanism based on the Deadline extended by simulation to different traffic Monotonic (DM) policy [9] to schedule real time categories. flows over 802.11. Indeed DM is a real time Finally, we consider a simple multi-hop scheduling policy that assigns static priorities to flow scenario to deduce the behavior of the DM packets according to their deadlines; the packet with policy in a multi hop environment. the shortest deadline being assigned the highest priority. To support the DM policy over 802.11, we Ubiquitous Computing and Communication Journal -1 - The rest of this paper is organized as follows. In maximum achievable throughput. The native model section 2, we review the state of the art of the IEEE is also extended in [10] to a non saturated 802.11 DCF, QoS support over 802.11 mainly the environment. In [12], the authors derive the average IEEE 80.211e EDCA and real time scheduling over packet service time at a 802.11 node. A new 802.11. In section 3, we present the distributed generalized Z-transform based framework has been scheduling and introduce the new medium access proposed in [3] to derive probabilistic bounds on backoff policy to support DM over 802.11. In section MAC layer service time. Therefore, it would be 4, we present our mathematical model based on possible to provide probabilistic end to end delay Markov chain analysis. Section 5 and 6 present bounds in a wireless network. respectively throughput and the service time analysis. Analytical results are validated by 2.2 Supporting QoS over 802.11 simulation using the ns-2 network simulator [16]. In 2.2.1 Differentiation mechanisms over 802.11 section 7, we extend our study by simulation, first to Emerging applications like audio and video take into consideration different traffic categories, applications require quality of service guarantees in second, to study the behavior of the DM algorithm in terms of throughput delay, jitter, loss rate, etc. a multi-hop environment where factors like Transmitting such flows over wireless interferences or routing protocols exist. Finally, we communications require supporting service conclude the paper in section 8. differentiation mechanisms over such networks. 2 LITTERATURE REVIEWS Many medium access schemes have been proposed to provide some QoS enhancements over 2.1 The 802.11 protocol the IEEE 802.11 WLAN. Indeed, [4] assigns 2.1.1 Description of the IEEE 802.11 DCF different priorities to the incoming flows. Priority Using DCF, a station shall ensure that the classes are differentiated according to one of three channel is idle when it attempts to transmit. Then it 802.11 parameters: the backoff increase function, the selects a random backoff in the contention Inter Frame Spacing (IFS) and the maximum frame window 0 , CW 1 , where CW is the current length. Experiments show that all the three window size and varies between the minimum and differentiation schemes offer better guarantees for the maximum contention window sizes. If the the highest priority flow. But the backoff increase channel is sensed busy, the station suspends its function mechanism doesn’t perform well with TCP backoff until the channel becomes idle for a flows because ACKs affect the differentiation Distributed Inter Frame Space (DIFS) after a mechanism. successful transmission or an Extended Inter Frame Space (EIFS) after a collision. The packet is In [7], an algorithm is proposed to provide transmitted when the backoff reaches zero. A packet service differentiation using two parameters of IEEE is dropped if it collides after maximum 802.11, the backoff interval and the IFS. With this retransmission attempts. scheme high priority stations are more likely to The above described two way handshaking access the medium than low priority ones. The above packet transmission procedure is called basic access described researches led to the standardization of a mechanism. DCF defines a four way handshaking new protocol that supports QoS over 802.11, the technique called Request To Send/Clear To Send IEEE 802.11e protocol [6]. (RTS/CTS) to prevent the hidden station problem. A station S j is said to be hidden from S i if S j is 2.2.2 The IEEE 802.11e EDCA The IEEE 802.11e proposes a new medium within the transmission range of the receiver of S i access mechanism called the Enhanced Distributed and out of the transmission range of S i . Channel Access (EDCA), that enhances the IEEE 2.1.2 Performance evaluation of the 802.11 802.11 DCF. With EDCA, each station maintains DCF four priorities called Access Categories (ACs). Each Different works have been proposed to evaluate access category is characterized by a minimum and a the performance of the 802.11 protocol based on maximum contention window sizes and an Bianchi’s work [1]. Indeed, Bianchi proposed a Arbitration Inter Frame Spacing (AIFS). Markov chain based analytical model to evaluate the saturation throughput of the 802.11 protocol. By Different analytical models have been proposed saturation conditions, it’s meant that contending to evaluate the performance of 802.11e EDCA. In stations have always packets to transmit. [17], Xiao extends Bianchi’s model to the prioritized Several works extended the Bianchi model either schemes provided by 802.11e by introducing to suit more realistic scenarios or to evaluate other multiple ACs with distinct minimum and maximum performance parameters. Indeed, the authors of [2] contention window sizes. But the AIFS incorporate the frame retry limits in the Bianchi’s differentiation parameter is lacking in Xiao’s model. model and show that Bianchi overestimates the Recently Osterbo and Al. have proposed Ubiquitous Computing and Communication Journal -2 - different works to evaluate the performance of the backoff value is inferred from the deadline IEEE 802.11e EDCA [13], [14], [15]. They proposed information. a model that takes into consideration all the differentiation parameters of the EDCA especially 3 SUPPORTING DEADLINE MONOTONIC the AIFS one. Moreover different parameters of QoS (DM) POLICY OVER 802.11 have been evaluated such as throughput, average service time, service time distribution and With DCF all the stations share the same probabilistic response time bounds for both saturated transmission medium. Then, the HOL (Head of Line) and non saturated cases. packets of all the stations (highest priority packets) will contend for the channel with the same priority Although the IEEE 802.11e EDCA classifies the even if they have different deadlines. traffic into four prioritized ACs, there is still no Introducing DM over 802.11 allows stations guarantee of real time transmission service. This is having packets with short deadlines to access the due to the lack of a satisfactory scheduling method channel with higher priority than those having for various delay-sensitive flows. Hence, we need a packets with long deadlines. Providing such a QoS scheduling policy dedicated to such delay sensitive requires distributed scheduling and a new medium flows. access policy. 2.3 Real time scheduling over 802.11 3.1 Distributed Scheduling over 802.11 To realize a distributed scheduling over 802.11, A distributed solution for the support of real- we introduce a priority broadcast mechanism similar time sources over IEEE 802.11, called Blackburst, is to [18]. Indeed each station maintains a local discussed in [8]. This scheme modifies the MAC scheduling table with entries for HOL packets of all protocol to send short transmissions in order to gain other stations. Each entry in the scheduling table of priority for real-time service. It is shown that this node S i comprises two fields S j , D j where S j is approach is able to support bounded delays. The main drawback of this scheme is that it requires 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. broadcast HOL packets deadlines, we propose to use the two way handshake DATA/ACK access mode. In [18], the authors introduced a distributed priority scheduling over 802.11 to support a class of When a node S i transmits a DATA packet, it dynamic priority schedulers such as Earliest 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 corresponding fields. The receiver of the DATA delay bound. packet copies the priority of the HOL packet in ACK To realize a distributed scheduling over 802.11, before sending the ACK frame. All the stations that the authors of [18] used a priority broadcast did not hear the DATA packet add an entry for S i mechanism where each station maintains an entry for using the information in the ACK packet. the highest priority packet of all other stations. Thus, stations can adjust their backoff according to other 3.2 DM medium access backoff policy stations priorities. Let’s consider two stations S 1 S2and The overhead introduced by the broadcast transmitting two flows with the same deadline D1 priority mechanism is negligible. This is due to the ( D1 is expressed as a number of 802.11 slots). The fact that priorities are exchanged using native DATA two stations having the same delay bound can access and ACK packets. Nevertheless, authors of [18] the channel with the same priority using the native proposed a generic backoff policy that can be used 802.11 DCF. by a class of dynamic priority schedulers no matter if Now, we suppose that S 1 and S 2 transmit flows this scheduler targets delay sensitive flows or rate sensitive flows. with different delay bounds D1 and D2 such as D1 D2 , and generate two packets at time instants In this paper, we focus on delay sensitive flows t 1 and t 2 . If S 2 had the same delay bound as S 1 , and propose to support the fixed priority Deadline Monotonic (DM) policy over 802.11 to schedule its packet would have been generated at time t '2 such delay sensitive flows. For instance, we use a priority as t '2 t 2 D 21 , where D 21 D 2 D1 . broadcast mechanism similar to [18] and introduce a At that time, S 1 and S 2 would have the same new medium access backoff policy where the priority and transmit their packets according to the Ubiquitous Computing and Communication Journal -3 - 802.11 protocol. following assumptions: Thus, to support DM over 802.11, each station uses a new backoff policy where the backoff is given Assumption 1: by: The system under study comprises n contending The random backoff selected in 0 , CW 1 stations hearing each other transmissions. according to 802.11 DCF, referred as BAsic Backoff (BAB). Assumption 2: The DM Shifting Backoff (DMSB): Each station S i transmits a flow Fi with a delay corresponds to the additional backoff slots that bound Di . The n stations are divided into two a station with low priority (the HOL packet traffic categories C1 and C 2 such as: having a large deadline) adds to its BAB to have the same priority as the station with the C1 represents n1 nodes transmitting flows highest priority (the HOL packet having the with delay bound D1 . shortest deadline). C 2 represents n 2 nodes transmitting flows Whenever a station S i sends an ACK or hears with delay bound D2 , such as D1 D2 , an ACK on the channel its DMSB is revaluated as D 21 D 2 D1 and n1 n 2 n . follows: Assumption 3: DMSBS i DeadlineHOLS i DTmin S i (1) We operate in saturation conditions: each station has immediately a packet available for transmission after the service completion of the previous packet [1]. Where DTmin S i is the minimum of the HOL packet deadlines present in S i scheduling table and Assumption 4: DeadlineHOLS i is the HOL packet deadline of A station selects a BAB in a constant contention node S i . window 0 ,W 1 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 Di , it selects a BAB in the contention window 0 , CW min 1 and computes the Assumption 5: WHole Backoff (WHB) value as follows: We are in stationary conditions, i.e. the n stations have already sent one packet at least. WHBS i DMSBS i BAB S i (2) Depending on the traffic category to which it belongs, each station S i will be modeled by a The station S i decrements its BAB when it 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 4.1 Markov chain modeling a station of category ACK is heard. Then the station S i adds the new C1 Figure 1 illustrates the Markov chain modeling a DMSB value to its current BAB as in equation (2). station S 1 of category C1 . The states of this Markov Whereas, if a collision is heard, S i reinitializes its DMSB and adds it to its current BAB to allow chain are described by the following quadruplet colliding stations contending with the same priority R , i , i j , D21 where: as for their first transmission attempt. S i transmits R : takes two values denoted by C 2 and when its WHB reaches 0. If the transmission fails, S i doubles its contention window size and repeats the ~ C 2 . When R ~ C 2 , the n 2 stations of above procedure until the packet is successfully category C 2 are decrementing their shifting transmitted or dropped after maximum backoff (DMSB) during D21 slots and retransmission attempts. wouldn’t contend for the channel. When R C 2 , the D21 slots had already been 4 MATHEMATICAL MODEL OF THE DM elapsed and stations of category C 2 will POLICY OVER 802.11 contend for the channel. i : the value of the BAB selected by S 1 in In this section, we propose a mathematical model to evaluate the performance of the DM policy 0 ,W 1 . using Markov chain analysis [1]. We consider the Ubiquitous Computing and Communication Journal -4 - Figure 1: Markov chain modeling a category C1 Station i j : corresponds to the current backoff moves to the state ~ C 2 , i j , i j , D 21 , of the station S 1 . i 1..W 1 , j 0.. minD21 1, i 1 . D21 : corresponds to D 2 D1 . We choose the negative notation D21 for stations of Now, If S1 is in one of the states C1 to express the fact that only stations of C 2 , i , i D21 , D21 , i D21 1..W 1 and at category C 2 have a positive DMSB equal to least one of the n 1 remaining stations (either a D21 . category C1 or a category C 2 station) transmits, Initially S 1 selects a random BAB and is in then S1 moves to one of the states one of the states ~ C 2 , i , i , D 21 , i 0..W 1 . ~ C 2 , i D21 , i D21 , D21 , i D21 1..W 1 . During D21 1 slots, S 1 decrements its backoff if Markov chain modeling a station of none of the n1 1 remaining stations of category 4.2 category C2 C1 transmits. Indeed, during these slots, the n 2 Figure 2 illustrates the Markov chain modeling a station S 2 of category C 2 . Each state of S 2 stations of category C 2 are decrementing their Markov chain is represented by the quadruplet DMSB and wouldn’t contend for the channel. i , k , D21 j , D21 where: When S1 is in one of the states i : refers to the BAB value selected by S 2 in ~ C 2 , i , i D21 1, D21 , i D 21 ..W 1 and 0 ,W 1 . senses the channel idle, it decrements its th D21 slot. k : refers to the current BAB value of S 2 . But S 1 knows that henceforth the n 2 stations of D 21 j : refers to the current DMSB of S 2 , category C 2 can contend for the channel (the D21 j 0 , D21 . slots had been elapsed). Hence, S 1 moves to one of D21 : corresponds to D D . 2 1 the states C 2 , i , i D21 , D 21 , i D21 ..W 1 . When S 2 selects a BAB, its DMSB equals However, when the station S 1 is in one of the D 21 and is in one of the states i , i , D 21 , D 21 , states ~ C 2 , i , i j , D 21 , for i 1..W 1 , i 0..W 1 . During D 21 slots, only the n1 j 0.. minD 21 1, i 1 and at least one of the stations of category C1 contend for the channel. n1 1 remaining stations of category C1 transmits, then the stations of category C 2 will If S 2 senses the channel idle during D21 slots, it reinitialize their DMSB and wouldn’t contend for moves to one of the states i , i ,0 , D 21 , i 0..W 1 , channel during additional D21 slots. Therefore, S 1 where it ends its shifting backoff. Ubiquitous Computing and Communication Journal -5 - Figure 2: Markov chain modeling a category C 2 Station When S 2 is in one of the states i , i ,0 , D 21 , 2 i , i , D 21 j , D 21 , i 0..W 1, i 0..W 1 , the n 2 1 other stations of category j 0..D 21 1 C 2 have also decremented their DMSB and can 2 : the set of states of S 2 , where stations contend for the channel. Thus, S 2 decrements its of category C 2 contend for the channel BAB and moves to the state i , i 1,0 , D 21 , (pink states in figure 2). i 2..W 1 , only if none of the n 1 remaining 2 i , i ,0 , D21 , i 0..W 1 stations transmits. i , i 1,0 , D 21 , i 2..W 1 If S 2 is in one of the states i , i 1,0 , D 21 , Therefore, when stations of category C1 are in i 2..W 1 , and at least one of the n 1 one the states of 1 , stations of category C 2 are in remaining stations transmits, the n 2 stations of one of the states of 2 . Similarly, when stations of category C 2 will reinitialize their DMSB and S 2 category C1 are is in one of the states of 1 , moves to the state i 1, i 1, D21 , D21 , stations of category C 2 are in one of the states of i 2..W 1 . 2. 4.3 Blocking probabilities in the Markov chains Hence, we derive the expressions of S1 According to the explanations given in blocking probabilities p 11 and p 12 shown in paragraphs 4.1 and 4.2, the states of the Markov figure 1 as follows: chains modeling stations S 1 and S 2 can be divided into the following groups: p 11 : the probability that S 1 is blocked given that S 1 is in one of the states of 1 . p 11 is 1 : the set of states of S 1 where none of the ' the probability that at least a station S 1 of n 2 stations of category C 2 contends for the the other n1 1 stations of C1 transmits channel (blue states in figure 1). 1 ~ C 2 , i , i j , D 21 , i 0..W 1, ' given that S 1 is in one of the states of 1 . j 0.. minmax0 , i 1, D 21 1 p 11 1 1 11 n1 1 (3) ' where 11 is the probability that a station S 1 1 : the set of states of S 1 where stations of ' of C1 transmits given that S 1 is in one of category C 2 can contend for the channel the states of 1 : (pink states in figure 1). 1 C 2 , i , i D 21 , D 21 , i D 21 ..W 1 ' 11 Pr S 1 transmits 1 ~ C2 ,0 ,0 , D21 1 2 : the set of states of S 2 where stations of (4) W 1 min max 0 ,i 1,D21 1 category C 2 do not contend for the channel i 0 1~ C2 ,i ,i j , D21 (blue states in figure 2). j 0 Ubiquitous Computing and Communication Journal -6 - 1R ,i ,i j , D21 is defined as the probability of p 22 : the probability that S 2 is blocked the state R , i , i j , D21 , in the stationary given that S 2 is in one of the states of 2 . conditions and 1 1 R ,i ,i j , D21 is the p 22 1 1 12 n1 1 22 n2 1 (9) probability vector of a category C1 station. The blocking probabilities described above p 12 : the probability that S 1 is blocked allow deducing the transition state probabilities and given that S 1 is in one of the states of 1 . having the transition probability matrix Pi , for a p 12 is the probability that at least a station station of traffic category C i . ' S1 of the other n1 1 stations of C1 Therefore, we can evaluate the state ' probabilities by solving the following system [11]: transmits given that S1 is in one of the states of 1 or at least a station S '2 of the n 2 i Pi i stations of C 2 transmits given that S '2 is in ij 1 j (10) one of the states of 2 . p 12 1 1 12 n1 1 1 22 n2 (5) 4.4 Transition probability matrices 4.4.1 Transition probability matrix of a where 12 is the probability that a station category C1 station ' ' S 1 of C1 transmits given that S 1 is in one Let P1 be the transition probability matrix of the station S 1 of category C1 . P1 i , j is the of the states of 1 . ' 12 Pr S 1 transmits 1 probability to transit from state i to state j . We have: C2 ,D21 ,0 , D21 1 W 1 (6) P1 ~ C 2 , i , i j , D 21 , ~ C 2 , i , i j 1, D 21 i D21 1C2 ,i ,i D21 , D21 1 p11 , i 2..W 1, j 0.. mini 2 , D 21 2 (11) P1 ~ C 2 , i ,1, D 21 , ~ C 2 ,0 ,0 , D 21 1 p11 , ' and 22 the probability that a station S 2 of i 1.. minW 1, D 21 1 ' C 2 transmits given that S 2 is in one of the (12) states of 2 . P1 ~ C 2 , i , i D 21 1, D 21 , C 2 , i , i D 21 , D 21 1 p 11 , i D 21 ..W 1 ' 12 Pr S 2 transmits 2 (13) 2 0 ,0 ,0 ,D21 P1~ C2 , i , i j , D21 , ~ C2 , i j , i j , D21 (14) W 1 W 1 (7) p11 , i 2..W 1, j 1.. mini 1, D21 1 i ,i ,0 ,D21 2 i ,i 1,0 ,D21 2 i 0 i2 P1~ C2 , i , i , D21 , ~ C2 , i , i , D21 p11 , (15) i 1..W 1 2i ,k ,D21 j ,D21 is defined as the probability of the state i , k , D21 j , D 21 , in the P1C2 ,i ,i D21 , D21 ,~ C2 ,i D21 ,i D21 , D21 p12 ,i D21 1..W 1 stationary condition. 2 2 i ,k ,D21 j ,D21 (16) is the probability vector of a category C 2 station. P1C2 ,i ,i D21 , D21 ,C2 ,i 1,i 1 D21 , D21 1 p12 ,i D21 1..W 1 In the same way, we evaluate p 21 and p 22 the (17) blocking probabilities of station S 2 shown in figure 2: 1 P1~ C2 ,0 ,0 , D21 , ~ C2 , i , i , D21 , p 21 : the probability that S 2 is blocked W (18) given that S 2 is in one of the states of 2 . i 0..W 1 p 21 1 1 11 n1 (8) If D 21 W then: Ubiquitous Computing and Communication Journal -7 - P1C2 , D21 ,0 , D21 , ~ C2 , i , i , D21 1 , 11 f 11 , 12 , 22 W (19) f , , 12 11 12 22 i 0..W 1 22 f 11 , 12 , 22 under the constraint By replacing p11 and p 12 by their values in equations (3) and (5) and by replacing P1 and 1 11 0 , 12 0 , 22 0 , 11 1, 12 1, 22 1 in (10) and solving the resulting system, we can (28) R ,i ,i j , D21 express 1 as a function of 11 , 12 and Solving the above system (28), allows deducing 22 given respectively by equations (4), (6) and the expressions of 11 , 12 and 22 , and deriving (7). the state probabilities of Markov chains modeling category C1 and category C 2 stations. 4.4.2 Transition probability matrix of a category C2 station Let P2 be the transition probability matrix of 5 THROUGHPUT ANALYSIS the station S 2 belonging to the traffic category C 2 . The transition probabilities of S 2 are: In this section, we propose to evaluate Bi , the normalized throughput achieved by a station of P2 i , i , D21 j , D21 , i , i , D21 j 1, D21 traffic category C i [1]. Hence, we define: (20) 1 p21 , i 0..W 1, j 0..D21 1 Pi ,s : the probability that a station Si P2 i , i , D21 j , D21 , i , i , D21 , D21 p21 , belonging to traffic category C i transmits a (21) i 0..W 1, j 0..D21 1 packet successfully. Let S 1 and S 2 be two stations belonging respectively to traffic P2 i , i ,0 , D21 , i , i 1,0 , D21 1 p22 , categories C1 and C 2 . We have: (22) i 2..W 1 P1,s Pr S1 transmits successfully 1 Pr1 P2 1,1,0 , D21 , 0 ,0 ,0 , D21 1 p22 (23) Pr S1 transmits successfully 1 Pr 1 11 1 p11 Pr 1 12 1 p12 Pr 1 P2 i , i ,0 , D21 , i , i , D21 , D21 p22 , (24) (29) i 1..W 1 P2 ,s Pr S 2 transmits successfully 2 Pr 2 P2 i , i 1,0 , D21 , i 1, i 1, D21 , D21 p22 , (25) Pr S 2 transmits successfully 2 Pr 2 i 2..W 1 22 1 p 22 Pr 2 P2 i , i 1,0 , D21 , i 1, i 2 ,0 , D21 1 p22 , (30) (26) i 3..W 1 Pidle : the probability that the channel is idle. 1 P2 0 ,0 ,0 , D21 , i , i , D21 , D21 , i 0..W 1 (27) W The channel is idle if the n1 stations of category C1 don’t transmit given that these stations By replacing p 21 and p 22 by their values in are in one of the states of 1 or if the n stations equations (8) and (9) and by replacing P2 and 2 (both category C1 and category C 2 stations) don’t in (10) and solving the resulting system, we can transmit given that stations of category C1 are in i ,k ,D21 j ,D21 express 2 as a function of 11 , 12 one of the states of 1 . Thus: and 22 given respectively by equations (4), (6) R ,i ,i j , D21 and (7). Moreover, by replacing 1 and Pidle 1 11 n1 Pr 1 1 12 n1 1 22 n2 Pr 1 2i ,k ,D21 j ,D21 by their values, in equations (4), (6) (31) and (7), we obtain a system of non linear equations Hence, the expression of the throughput of a as follows: category C i station is given by: Ubiquitous Computing and Communication Journal -8 - Pi ,s T p 8 and we depict the throughput achieved by the Bi different stations present in the network as a 2 PIdle Te Ps T s 1 PIdle n P i 1 i i ,s Tc function of the contention window size W , D 21 1 . We notice that the throughput achieved (32) by category C1 stations (stations numbered from S 11 to S 14 ) is greater than the one achieved by Where Te denotes the duration of an empty category C 2 stations (stations numbered from S 21 slot, Ts and Tc denote respectively the duration of to S 24 ). a successful transmission and a collision. 2 1 PIdle i 1 ni Pi ,s corresponds to the probability of collision. Finally T p denotes the average time required to transmit the packet data payload. We have: Ts T PHY TMAC T p T D SIFS (33) TPHY T ACK T D DIFS Tc TPHY TMAC T p TD EIFS (34) Where T PHY , TMAC and T ACK are the durations of the PHY header, the MAC header and the ACK packet [1], [13]. TD is the time required to Figure 3: Normalized throughput as a function of transmit the two bytes deadline information. the contention window size D 21 1, n 8 Stations hearing a collision wait during EIFS before resuming their packets. Analytically, stations belonging to the same traffic category have the same throughput given by For numerical results stations transmit 512 equation (32). Simulation results validate analytical bytes data packets using 802.11.b MAC and PHY results and show that stations belonging to the same layers parameters (given in table 1) with a data rate traffic category (either category C1 or category equal to 11Mbps. For simulation scenarios, the C 2 ) have nearly the same throughput. Thus, we propagation model is a two ray ground model. The conclude the fairness of DM between stations of the transmission range of each node is 250m. The same category. distance between two neighbors is 5m. The EIFS parameter is set to ACKTimeout as in ns-2, where: For subsequent throughput scenarios, we focus on one representative station of each traffic ACKTimeout DIFS T PHY T ACK T D SIFS category. Figure 4, compares category C1 and (35) category C 2 stations throughputs to the one Table 1: 802.11 b parameters. obtained with 802.11. 11 Mb/s Curves are represented as a function of W and Data Rate Slot 20 µs for different values of D 21 . Indeed as D 21 SIFS 10 µs increases, the category C1 station throughput DIFS 50 µs increases, whereas the category C 2 station PHY Header 192 µs throughput decreases. Moreover as W increases, MAC Header 272 µs the difference between stations throughputs is ACK 112 µs reduced. This is due to the fact that the shifting Short Retry Limit 7 backoff becomes negligible compared to the contention window size. For all the scenarios, we consider that we are in n Finally, we notice that the category C1 station presence of n contending stations with stations obtains better throughput with DM than with 2 for each traffic category. In figure 3, n is fixed to Ubiquitous Computing and Communication Journal -9 - 802.11, but the opposite scenario happens to the expression of the average service time and the category C 2 station. service time distribution. The service time depends on the duration of an idle slot Te , the duration of a successful transmission Ts and the duration of a collision Tc [1], [3],[14]. As Te is the smallest duration event, the duration of all events will be T given by event . Te 6.1 Z-Transform of the MAC layer service time 6.1.1 Service time Z-transform of a category C1 station: Let TS 1 Z be the service time Z-transform of a station S 1 belonging to traffic category C1 . We Figure 4: Normalized throughput as a function of define: the contention window size (different D 21 values) H 1R ,i ,i j , D21 Z : The Z-transform of the In figure 5, we generalize the results for different numbers of contending stations and fix the time already elapsed from the instant S 1 selects a contention window size W to 32. basic backoff in 0 ,W 1 (i.e. being in one of the states ~ C 2 , i , i , D21 ) to the time it is found in the state R , i , i j , D 21 . Moreover, we define: 11 Psuc : the probability that S 1 observes a successful transmission on the channel, while S 1 is in one of the states of 1 . Psuc n1 1 11 1 11 n1 2 11 (36) 12 Psuc : the probability that S 1 observes a successful transmission on the channel, while S 1 is in one of the states of 1 . Figure 5: Normalized throughput as a function of Psuc n1 1 12 1 12 n1 2 1 22 n2 12 the number of contending stations (37) n2 22 1 22 n2 1 1 12 n1 1 All the curves show that DM performs service differentiation over 802.11 and offers better We evaluate H 1R ,i ,i j , D21 Z for each state throughput for category C1 stations independently of S 1 Markov chain as follows: of the number of contending stations. Ts 1 11 Te 6 SERVICE TIME ANALYSIS H 1~ C2 ,i ,i , D21 Z Psuc Z W In this section, we evaluate the average MAC Tc layer service time of category C1 and category C 2 min i D21 1,W 1 stations using the DM policy. The service time is 11 p11 Psuc Z e T H 1~ C 2 ,k ,i , D21 Z the time interval from the time instant that a packet k i 1 becomes at the head of the queue and starts to Ts Tc 12 Te contend for transmission to the time instant that H C 2 ,i D21 ,i , D21 Z Psuc Z ˆ1 12 T p11 Psuc Z e either the packet is acknowledged for a successful transmission or dropped [3]. (38) We propose to evaluate the Z-Transform of the Where: MAC layer service time [3], [14], [15] to derive an Ubiquitous Computing and Communication Journal - 10 - H 1C ,i D ,i , D Z H 1C ,i D ,i , D Z ˆ Ts 1 p11 H 1~ C ,0 ,0 , D TS1 Z Z Z 2 21 21 2 21 21 Te if i D 21 W 1 (39) 2 21 ˆ m c T H 1C2 ,i D21 ,i , D21 Z 0 Otherwise 1 p12 H 1C2 ,D21 ,0 , D21 Z Te Z p11H 1~C ,0 ,0 , D Z 2 21 i 0 We also have: p12 H 1C 2 ,D21 ,0 , D21 Z i 1 p11 Z j H 1~ C2 ,i ,i , D21 Z m 1 H 1~ C2 ,i ,i j , D21 Z Tc T Ts Tc Z e p11 H 1~ C2 ,0 ,0 , D21 Z p12 H 1C 2 ,D21 ,0 , D21 Z 11 Te 11 T 1 Psuc Z p11 Psuc Z e i 2..W 1, j 1..mini 1, D21 1 (40) (44) 1 p11 Z D21 H 1~ C2 ,i ,i , D21 Z 6.1.2 Service time Z-transform of a category H 1C2 ,i ,i D21 , D21 Z C2 station: Ts Tc In the same way, let TS 2 Z be the service 11 1 Psuc Z Te p11 11 T Psuc Z e 1 p12 ZH 1C2 ,i 1,i 1 D21 , D21 Z ,i D21 ..W 2 time Z-transform of a station S 2 of category C 2 . We define: (41) H 2i ,k ,D21 j ,D21 Z : The Z-transform of the H 1C2 ,W 1,W 1 D21 , D21 Z time already elapsed from the instant S 2 selects a 1 p11 Z D21 H 1~ C 2 ,W 1,W 1, D21 Z basic backoff in 0 ,W 1 (i.e. being in one of the (42) Ts Tc states i , i , D 21 , D 21 ) to the time it is found in the 11 1 Psuc Z Te 11 p11 Psuc Z Te state i , k , D21 j , D21 . Moreover, we define: 1 p11 ZH 1~ C2 ,1,1, D21 Z H 1~ C2 ,0 ,0 , D21 Z 21 Ts Tc Psuc : the probability that S 2 observes a 11 Te 11 T 1 Psuc Z p11 Psuc Z e successful transmission on the channel, min W 1,D21 1 while S 2 is in one of the states of 2 . 1 1 p11 Z H 1 i2 ~ C 2 ,i ,1, D21 Z W Psuc n1 11 1 11 n1 1 21 (45) (43) 22 Psuc : the probability that S 2 observes a If S 1 transmission state is ~ C 2 ,0 ,0 , D 21 , successful transmission on the channel, the transmission will be successful only if none of while S 2 is in one of the states of 2 . the n1 1 remaining stations of C1 transmits. Psuc n1 12 1 12 n1 1 1 22 n2 1 22 Whereas when the station S 1 transmission state is (46) n2 1 22 1 22 n2 2 1 12 n1 C 2 , D21 ,0 , D 21 , the transmission occurs successfully only if none of n 1 remaining We evaluate H 2i ,i ,D21 j ,D21 Z for each state stations (either a category C1 or a category C 2 of S 2 Markov chain as follows: station) transmits. 1 H 2i ,i ,D21 ,D21 Z , i 0 and i W 1 (47) If the transmission fails, S 1 tries another W transmission. After m retransmissions, if the Ts 1 22 Te packet is not acknowledged, it will be dropped. H 2i ,i ,D21 ,D21 Z Psuc Z Thus, the Z-transform of station S 1 service time is: W Tc Z Te H 2i 1,i ,0 ,D21 Z , i 1..W 2 22 p 22 Psuc (48) Ubiquitous Computing and Communication Journal - 11 - To compute H 2i ,i ,D21 j ,D21 Z , we define Tc m 1 Tdec Z , such as: j TS 2 Z p 22 Z Te H 2 0 ,0 ,0 ,D21 Z Tdec Z 1 0 (49) Ts Tc i m 1 p 21 Z 1 p 22 Z Te H 2 0 ,0 ,0 ,D21 Z p 22 Z Te H 2 0 ,0 ,0 ,D21 Z Tdec Z j i 0 Ts Tc 21 Te (55) 1 Psuc Z p 21 Te T j 1 Z 21 Psuc Z dec 6.2 Average Service Time for j 1..D 21 From equations (44) (respectively equation (50) (55)), we derive the average service time of a category C1 station ( respectively a category C 2 So: station). The average service time of a category C i station is given by: H 2i ,i ,D21 j ,D21 Z H 2i ,i ,D21 j 1,D21 Z j Tdec Z , X i TS i1 1 (56) i 0..W 1, j 1..D21 , i , j 0 , D 21 (51) And: Where TS i1 Z , is the derivate of the service H 2i ,i 1,0 ,D21 Z 1 p 22 ZH 2i 1,i ,0 ,D21 Z time Z-transform of a category C i station [11]. 1 p 22 ZH 2i ,i ,0 ,D21 Z By considering the same configuration as in Ts Tc figure 3, we depict in figure 5, the average service 22 Te 1 Psuc Z p 22 Te T D21 Z time of category C1 and category C 2 stations as a 22 Psuc Z dec function of W . As for the throughput analysis, stations belonging to the same traffic category have i 2..W 2 nearly the same average service value. Simulation (52) service time values coincide with analytical values given by equation (56). These results confirm the H 2W 1,W 2 ,0 ,D21 Z fairness of DM in serving stations of the same 1 p 22 ZH 2W 1,W 1,0 ,D21 Z category. Ts Tc (53) 22 Te 1 Psuc Z p 22 Te T D21 Z 22 Psuc Z dec According to figure 2 and using equation (51), we have: H 20 ,0 ,0 ,D21 Z H 20 ,1,0 ,D21 Z Tdec Z D21 1 p 22 ZH 21,1,0 ,D21 Z Ts Tc (54) 22 Te 1 Psuc Z p 22 Te T D21 Z 22 Psuc Z dec Figure 6: Average service time as a function of the contention window size D 21 1, n 8 Therefore, we can derive an expression of S 2 Z-transform service time as follows: In figure 7, we show that category C1 stations obtain better average service time than the one obtained with 802.11 protocol. Whereas, the opposite scenario happens for category C 2 stations Ubiquitous Computing and Communication Journal - 12 - independently of n , the number of contending exceeds 0.01s equals 0.2%. Whereas, station S 2 stations in the network. service time exceeds 0.01s 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 C1 and category C 2 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 1 and S 2 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 [11]: Figure 9: Complementary service time distribution ~ 1 TS i Z for different values of D21 ( W 64 ) X i Z (56) 1 Z In figure 10, we depict the complementary In figure 8, we depict analytical and simulation service time distribution for both category C1 and values of the complementary service time category C 2 stations and for different values of n , distribution of a category C1 and a category C 2 the number of contending nodes. stations for different values of D21 and W 32 . Figure 10: Complementary service time Figure 8: Complementary service time distribution distribution for different values of the contending for different values of D21 , W 32 stations All the curves drop gradually to 0 as the delay Analytical and simulation results show that increases. Category C1 stations curves drop to 0 complementary service time curves drop faster when the number of contending stations is small for faster than category C 2 curves. Indeed, when both category C1 and category C 2 stations. This D21 4 slots, the probability that S 1 service time means that all stations service time increases as the Ubiquitous Computing and Communication Journal - 13 - number of contending nodes increases. 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 , 7 EXTENTIONS OF THE ANAYTICAL RESULTS BY SIMULATION CW max 1024 and K =1. Analytical and simulation results show that The mathematical analysis undertaken above throughput values increase with stations priorities. showed that DM performs service differentiation Indeed, the station with the lowest delay bound has over 802.11 protocol and offers better QoS the maximum throughput. guarantees for highest priority stations Nevertheless, the analysis was restricted to two Moreover, figure 12 shows that stations traffic categories. In this section, we first generalize belonging to the same traffic category have the the results by simulation for different traffic same throughput. For instance, when n is set to 15 categories. Then, we consider a simple multi-hop (i.e. m 3 ), the three stations each traffic category and evaluate the performance of the DM policy have almost the same throughput. when the stations belong to different broadcast regions. 7.1 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 Di , and Dij Di D j is the difference between the deadline values of category C i and category C j stations. We have: Dij i j K (57) Figure 12: Normalized throughput: different Where K is the deadline multiplicity factor stations belonging to the same traffic category and is given by: Di 1,i Di 1 Di K (58) In figure 13, we depict the average service time of the different traffic categories stations as a function of K , the deadline multiplicity factor. We Indeed, when K varies, the Dij the difference notice that the highest priority station average between deadline values of category C i and service time decreases as the deadline multiplicity category Cj 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 1 to S im . Figure 13: Average service time as a function of Figure 11: Normalized throughput for different the deadline multiplicity factor K traffic category stations In the same way, the probabilistic service time In figure 11, we depict the throughput achieved bounds offered to S 11 (the highest priority station) Ubiquitous Computing and Communication Journal - 14 - are better than those offered to station S 51 (the Flows packets are routed using the Ad-hoc On lowest priority station). Indeed, the probability that Demand (AODV) protocol. Flows F1 and F2 are S 11 service time exceeds 0.01s=0.3%. But, station respectively transmitted by stations S 1 and S 2 S 51 service time exceeds 0.01s with the probability with delay bounds D1 and D2 and of 36%. D 21 D 2 D1 =5 slots. Flows F3 and F4 are transmitted respectively by S 3 and S 4 and have the same delay bound. Finally, F5 and F6 are transmitted respectively by S 5 and S 6 with delay bounds D5 and D6 and D65 D6 D5 = 4 slots. Figure 16 shows that the throughput achieved by F1 is smaller than the one achieved by F2 . Indeed, both flows cross nodes 6 and 7, where F1 got a higher priority to access the medium than F2 when the DM policy is used. We obtain the same results for flows F and F . Flows F3 and F4 5 6 Figure 14: Complementary service time have almost the same throughput since they have distribution CWmin 32 , n 8 equal deadlines. The above results generalize the analytical model results and show once again that DM performs service differentiation over 802.11 and offer better guarantees in terms of throughput, average service time and probabilistic service time bounds for flows with short deadlines. 7.2 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. Figure 16: Normalized throughput using DM policy In the following paragraph, we evaluate the performance of the DM policy in a multi-hop Figure 17 show that the complementary environment. Hence, we consider a 13 node simple service time distribution curves drop to 0 faster for mtlti-hop scenario described in figure 15. Six flows flow F1 than for flow F2 . are transmitted over the network. Figure 17: End to end complementary service time Figure 15: Simple multi hop scenario distribution Ubiquitous Computing and Communication Journal - 15 - The same behavior is obtained for flow F5 and (PHY) specification, IEEE (1999). F6 , where F5 has the shortest delay bound. IEEE 802.11 WG: Draft Supplement to Part 11: Wireless Medium Access Control (MAC) and physical layer (PHY) specifications: Medium Hence, we conclude that even in a multi-hop Access Control (MAC) Enhancements for environment, the DM policy performs service Quality of Service (QoS), IEEE 802.11e/D13.0, differentiation over 802.11 and provides better QoS (January 2005). guarantees for flows with short deadlines. J. Deng, R. S. Chang: A priority Scheme for IEEE 802.11 DCF Access Method, IEICE Transactions in Communications, vol. 82-B, 8 CONCLUSION no. 1, (January 1999). J.L. Sobrinho, A.S. 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Analytical and simulation results 802.11 Distributed Coordination Function in showed that DM performs service differentiation Non-saturated Conditions, IEEE/ACM over 802.11 and offers better guarantees in terms of Transactions on Networking (TON), throughput, average service time and probabilistic Vol. 15 , pp. 159-172 (February 2007) service time bounds for flows with small deadlines. L. Kleinrock: Queuing Systems,Vol. 1: Theory, Moreover, DM achieves fairness between stations Wiley Interscience, 1976. belonging to the same traffic category. P. Chatzimisios, V. Vitsas, A. C. Boucouvalas: Throughput and delay analysis of IEEE 802.11 Then, we extended by simulation the analytical protocol, in Proceedings of 2002 IEEE 5th results obtained for two traffic categories to International Workshop on Networked different traffic categories. Simulation results Appliances, (2002). showed that even if contending stations belong to P.E. Engelstad, O.N. 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