VIEWS: 17 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, average MAC layer service time and 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 protocol, Performance evaluation, Medium access delay, Throughput, Probabilistic medium access delay bounds. 1 INTRODUCTION priority. To support the DM policy over 802.11, we use a distributed scheduling and introduce a new Supporting applications with QoS requirements medium access backoff policy. Therefore, we focus has become an important challenge for all on performance evaluation of the DM policy in terms communications networks. In wireless LANs, the of achievable throughput, average MAC layer IEEE 802.11 protocol [5] has been enhanced and the service time and MAC layer service time IEEE 802.11e protocol [6] was proposed to support distribution. Hence, we follow these steps: quality of service over wireless communications. − First, we propose a Markov Chain In the absence of a coordination point, the IEEE framework modeling the backoff process of 802.11 defines the Distributed Coordination n contending stations within the same Function (DCF) based on the Carrier Sense Multiple broadcast region [1]. Access with Collision Avoidance (CSMA/CA) Due to the complexity of the mathematical protocol. The IEEE 802.11e proposes the Enhanced model, we restrict the analysis to n Distributed Channel Access (EDCA) as an extension contending stations belonging to two traffic for DCF. With EDCA, each station maintains four categories (each traffic category is priorities called Access Categories (ACs). The characterized by its own delay bound). quality of service offered to each flow depends on − From the analytical model, we derive the the AC to which it belongs. throughput achieved by each traffic Nevertheless, the granularity of service offered category. by 802.11e (4 priorities at most) can not satisfy the − Then, we use the generalized Z-transforms real time flows requirements (where each flow is [3] to derive expressions of the average characterized by its own delay bound). MAC layer service time and service time distribution. Therefore, we propose in this paper a new − As the analytical model was restricted to medium access mechanism based on the Deadline two traffic categories, analytical results are Monotonic (DM) policy [9] to schedule real time extended by simulation to different traffic flows over 802.11. Indeed DM is a real time categories. scheduling policy that assigns static priorities to flow − Finally, we consider a simple multi-hop packets according to their deadlines; the packet with scenario to deduce the behavior of the DM the shortest deadline being assigned the highest policy in a multi hop environment. Ubiquitous Computing- and Communication Journal -1 - maximum achievable throughput. The native model The rest of this paper is organized as follows. In is also extended in [10] to a non saturated section 2, we review the state of the art of the IEEE environment. In [12], the authors derive the average 802.11 DCF, QoS support over 802.11 mainly the packet service time at a 802.11 node. A new IEEE 80.211e EDCA and real time scheduling over generalized Z-transform based framework has been 802.11. In section 3, we present the distributed proposed in [3] to derive probabilistic bounds on scheduling and introduce the new medium access MAC layer service time. Therefore, it would be backoff policy to support DM over 802.11. In section possible to provide probabilistic end to end delay 4, we present our mathematical model based on bounds in a wireless network. Markov chain analysis. Section 5 and 6 present respectively throughput and the service time 2.2 Supporting QoS over 802.11 analysis. Analytical results are validated by 2.2.1 Differentiation mechanisms over 802.11 simulation using the ns-2 network simulator [16]. In Emerging applications like audio and video section 7, we extend our study by simulation, first to applications require quality of service guarantees in take into consideration different traffic categories, terms of throughput delay, jitter, loss rate, etc. second, to study the behavior of the DM algorithm in Transmitting such flows over wireless a multi-hop environment where factors like communications require supporting service interferences or routing protocols exist. Finally, we differentiation mechanisms over wireless networks. conclude in Section 8. Many medium access schemes have been 2 LITTERATURE REVIEWS proposed to provide some QoS enhancements over the IEEE 802.11 WLAN. Indeed, [4] assigns 2.1 The 802.11 protocol different priorities to the incoming flows. Priority 2.1.1 Description of the IEEE 802.11 DCF classes are differentiated according to one of three Using DCF, a station shall ensure that the 802.11 parameters: the backoff increase function, channel is idle when it attempts to transmit. Then it Inter Frame Spacing (IFS) and the maximum frame selects a random backoff in the contention window length. Experiments show that all the three [0,CW-1], where CW is the current window size and differentiation schemes offer better guarantees for varies between the minimum and the maximum the highest priority flow. But the backoff increase contention window sizes. If the channel is sensed function mechanism doesn’t perform well with TCP busy, the station suspends its backoff until the flows because ACKs affect the differentiation channel becomes idle for a Distributed Inter Frame mechanism. Space (DIFS) after a successful transmission or an Extended Inter Frame Space (EIFS) after a collision. In [7], an algorithm is proposed to provide The packet is transmitted when the backoff reaches service differentiation using two parameters of IEEE zero. A packet is dropped if it collides after 802.11, the backoff interval and the IFS. With this maximum 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 have to evaluate the performance of 802.11e EDCA. In 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 information. IEEE 802.11e EDCA [13], [14], [15]. They propose a model that takes into consideration all the 3 SUPPORTING DEADLINE MONOTONIC differentiation parameters of the EDFA especially (DM) POLICY OVER 802.11 the AIFS one. Moreover different parameters of QoS have been evaluated such as throughput, average With DCF all the stations share the same service time, service time distribution and transmission medium. Then, the HOL (Head of Line) probabilistic response time bounds for both saturated packets of all the stations (highest priority packets) and non saturated cases. 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 the HOL packet deadlines, we propose to use the DATA/ACK access mode. In [18], the authors proposed 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. The the EDF policy is used to schedule real time flows nodes hearing the DATA packet add an entry for S i according to their absolute deadlines, where the in 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 and S 2 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, the authors of [18] the channel with the same priority using the native propose a generic backoff policy which can be used 802.11 DCF. by a class 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 D 2 such as D1 < D 2 , 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 scheduler over 802.11 to schedule delay its packet would have been generated at time t '2 such sensitive flows. For instance, we use a priority as t '2 = t 2 + D 21 , where D21 = ( D2 − D1 ) . broadcast mechanism similar to [5] and propose a At that time, S 1 and S 2 would have the same new medium access backoff policy where the backoff value is inferred from the deadline priority and transmit their packets according to the Ubiquitous Computing- and Communication Journal -3 - 802.11 protocol. In this section, we propose a mathematical Thus, to support DM over 802.11, each station model to evaluate the performance of the DM policy uses a new backoff policy where the backoff is given using Markov chain analysis [1]. We consider the by: following assumptions: • The random backoff selected in [ 0 , CW − 1] according to 802.11 DCF, referred as BAsic Assumption 1: Backoff (BAB). The system under study comprises n contending • The DM Shifting Backoff (DMSB): stations hearing each other transmissions. corresponds to the additional backoff slots that Assumption 2: a station with low priority (the HOL packet Each station S i transmits a flow Fi with a delay having a large deadline) adds to its BAB to bound Di . The n stations are divided into two traffic have the same priority as the station with the categories C1 and C 2 such as: highest priority (the HOL packet having the shortest deadline). − C1 represents n1 nodes transmitting flows with delay bound D1 . Whenever a station S i sends an ACK or hears − C 2 represents n 2 nodes transmitting flows an ACK on the channel its DMSB is revaluated as with delay bound D 2 , such as D1 < D 2 , follows: D21 = ( D 2 − D1 ) and ( n1 + n 2 ) = n . DMSB( S i ) = Deadline( HOL( S i ) ) − DTmin ( S i ) (1) Assumption 3: We operate in saturation conditions: each station has immediately a packet available for transmission after Where DTmin ( S i ) is the minimum of the HOL the service completion of the previous packet [1]. 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 − 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 Assumption 5: contention window [ 0 , CW min − 1] and computes the We are in stationary conditions, i.e. the n stations WHole Backoff (WHB) value as follows: have already sent one packet at least. WHB( S i ) = DMSB( S i ) + BAB( S i ) (2) Depending on the traffic category to which it belongs, each station S i will be modeled by a Markov Chain representing its whole backoff (WHB) The station S i decrements its BAB when it process. senses an idle slot. Now, we suppose that S i senses the channel busy. If a successful transmission is 4.1 Markov chain modeling a station of category heard, then S i revaluates its DMSB when a correct C1 ACK is heard. Then the station S i adds the new 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 chain are described by the following quadruplet DMSB and adds it to its current BAB to allow ( R , i , i − j , D21 ) where: colliding stations contending with the same priority • R : takes two values denoted by C 2 and as for their first transmission attempt. S i transmits ~ C 2 . When R = ~ C 2 , the n 2 stations of when its WHB reaches 0. If the transmission fails, S i category C 2 are decrementing their shifting doubles its contention window size and repeats the backoff (DMSB) during D21 slots and above procedure until the packet is successfully wouldn’t contend for the channel. When transmitted or dropped after maximum R = C 2 , the D 21 slots had already been retransmission attempts. elapsed and stations of category C 2 will contend for the channel.. 4 MATHEMATICAL MODEL OF THE DM POLICY OVER 802.11 Ubiquitous Computing- and Communication Journal -4 - Figure 1: Markov chain modeling a category C1 Station • i : the value of the BAB selected by S 1 in channel during additional D21 slots. Therefore, S 1 [0 ,W − 1] . moves to the state ( ~ C 2 , i − j , i − j ,− D 21 ) , • ( i − j ) : corresponds to the current backoff of i = 1..W − 1 , j = 0.. min( D21 − 1, i − 1) . the station S 1 . • D 21 : corresponds to ( D2 − D1 ) . We choose Now, If S 1 is in one of the states the negative notation − D 21 for stations of ( C 2 , i , i − D21 ,− D21 ) , i = ( D21 + 1) ..W − 1 and at C1 to express the fact that only stations of least one of the ( n − 1) remaining stations (either a category C 2 have a positive DMSB equal to category C1 or a category C 2 station) transmits, D 21 . then S 1 moves to one of the states Initially S 1 selects a random BAB and is in ( ~ C 2 , i − D21 , i − D21 ,− D21 ) , i = ( D21 + 1) ..W − 1 . one of the states ( ~ C2 , i , i ,− D21 ) , i = 0..W − 1 . During ( D 21 − 1) slots, S 1 decrements its backoff if 4.2 Markov chain modeling a station of category C2 none of the ( n1 − 1) remaining stations of category Figure 2 illustrates the Markov chain modeling C1 transmits. Indeed, during these slots, the n 2 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: • i : refers to the BAB value selected by S 2 in When S 1 is in one of the states [0 ,W − 1] . ( ~ C 2 , i , i − ( D21 − 1) ,− D21 ) , i = D 21 ..W − 1 and • k : refers to the current BAB value of S 2 . th senses the channel idle, it decrements its D 21 slot. • D21 − j : refers to the current DMSB of S 2 , But S 1 knows that henceforth the n 2 stations of j ∈ [ 0 , D21 ] . category C 2 can contend for the channel (the D 21 • D21 : corresponds to ( D 2 − D1 ) . slots had been elapsed). Hence, S 1 moves to one of the states ( C 2 , i , i − D21 ,− D 21 ) , i = D 21 ..W − 1 . When S 2 selects a BAB, its DMSB equals D21 and is in one of the states ( i , i , D 21 , D 21 ) , However, when the station S 1 is in one of the i = 0..W − 1 . During D21 slots, only the n1 states ( ~ C 2 , i , i − j ,− D 21 ) , i = 1..W − 1 , stations of category C1 contend for the channel. j = 0.. min( D 21 − 1, i − 1) and at least one of the ( n1 − 1) remaining stations of category C1 If S 2 senses the channel idle during D21 slots, it transmits, then the stations of category C 2 will moves to one of the states ( i , i ,0 , D 21 ) , i = 0..W − 1 , reinitialize their DMSB and wouldn’t contend for 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 ) , i = 0..W − 1 , the ( n 2 − 1) other stations of category • γ : the set of states of S 2 , where stations 2 C 2 have also decremented their DMSB and can of category C 2 contend for the channel (pink states in figure 2). contend for the channel. Thus, S 2 decrements its γ 2 = { ( i , i ,0 , D21 ) , i = 0..W − 1 BAB and moves to the state ( i , i − 1,0 , D 21 ) , ∪ ( i , i − 1,0 , D 21 ) , i = 2..W − 1} i = 2..W − 1 , only if none of ( n − 1) remaining stations transmits. Therefore, when stations of category C 1 are in If S 2 is in one of the states ( i , i − 1,0 , D 21 ) , one the states of ξ 1 , stations of category C 2 are in i = 2..W − 1 , and at least one of the ( n − 1) one of the states of ξ 2 . Similarly, when stations of remaining stations transmits, the n 2 stations of category C 1 are is in one of the states of γ 1 , category C 2 will reinitialize their DMSB and S 2 stations of category C 2 are in one of the states of moves to the state ( i − 1, i − 1, D21 , D21 ) , γ 2. i = 2..W − 1 . Hence, we derive the expressions of S 1 4.3 Blocking probabilities in the Markov chains blocking probabilities p11 and p12 shown in According to the explanations given in figure 1 as follows: paragraphs 4.1 and 4.2, the states of the Markov chains modeling stations S 1 and S 2 can be divided − p11 : the probability that S 1 is blocked given into the following groups: that S 1 is in one of the states of ξ 1 . p11 is ' • ξ 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 C 1 transmits channel (blue states in figure 1). given that S 1 is in one of the states of ξ 1 . ' ξ 1 = { ( ~ C 2 , i , i − j ,− D 21 ) , i = 0..W − 1, p 11 = 1 − ( 1 − τ ) n1 − 1 (3) j = 0.. min( max( 0 , i − 1) , D 21 − 1)} 11 where τ 11 ' is the probability that a station S 1 ' • γ : the set of states of S 1 where stations of 1 of C1 transmits given that S 1 is in one of category C 2 can contend for the channel the states of ξ 1 : (pink states in figure 1). τ 11 ' [ = Pr S 1 transmits ξ 1 ] γ 1 = { ( C 2 , i , i − D 21 ,− D 21 ) , i = D 21 ..W − 1} ( ~ C2 ,0 ,0 ,− D21 ) π 1 = (4) W − 1 min ( max ( 0 ,i − 1) ,D21 − 1) ξ • : the set of states of S 2 where stations of 2 category C 2 do not contend for the channel ∑ i= 0 ∑ π 1~C2 ,i ,i − j ,− D21 ) ( j= 0 (blue states in figure 2). ξ 2 = { ( i , i , D 21 − j , D 21 ) , i = 0..W − 1, ( j ,− D21 ) π 1R ,i ,i − is defined as the probability of j = 0..( D 21 − 1)} the state ( R , i , i − j ,− D21 ) , in the stationary Ubiquitous Computing- and Communication Journal -6 - conditions and Π 1 = π { ( R ,i ,i − 1 j ,− D21 ) } is the − p 22 : the probability that S 2 is blocked probability vector of a category C 1 station. given that S 2 is in one of the states of γ 2 . p 22 = 1 − ( 1 − τ 12 ) n1 ( 1 − τ 22 ) n2 − 1 (9) − p12 : the probability that S 1 is blocked given that S 1 is in one of the states of γ 1 . p12 is The blocking probabilities described above ' allow deducing the transition state probabilities and the probability that at least a station S 1 of having the transition probability matrix Pi , for a the other ( n1 − 1) stations of C 1 transmits station of traffic category C i . given that S 1 is in one of the states of γ 1 or ' Therefore, we can evaluate the state ' at least a station S 2 of the n 2 stations of probabilities by solving the following system [11]: ' C 2 transmits given that S 2 is in one of the Π i Pi = Π i states of γ 2 . p 12 = 1 − ( 1 − τ ) n1 − 1 ( 1 − τ 22 ) n2 ∑ j π ij = 1 (10) 12 (5) 4.4 Transition probability matrices where τ 12 is the probability that a station S 1 ' 4.4.1 Transition probability matrix of a ' category C1 station of C 1 transmits given that S 1 is in one of Let P1 be the transition probability matrix of the states of γ 1 . the station S 1 of category C1 . P1 { i , j} is the τ 12 ' [ = Pr S 1 transmits γ 1 ] probability to transit from state i to state j . We ( π 1C2 ,D21 ,0 ,− D21 ) have: = W−1 (6) P1 { ( ~ C 2 , i , i − j ,− D 21 ) , ( ~ C 2 , i , i − ( j + 1) ,− D 21 )} ∑ π 1 ( C2 ,i ,i − D21 ,− D21 ) i = D21 = 1 − p11 , i = 2..W − 1, j = 0.. min( i − 2 , D 21 − 2 ) (11) and τ 22 ' the probability that a station S 2 of P1 { ( ~ C 2 , i ,1,− D 21 ) , ( ~ C 2 ,0 ,0 ,− D 21 )} = 1 − p11 , ' C 2 transmits given that S 2 is in one of the i = 1.. min(W − 1, D 21 − 1) states of γ 2 . (12) P1 { ( ~ C 2 , i , i − D 21 + 1,− D 21 ) , ( C 2 , i , i − D 21 ,− D 21 )} τ 12 = Pr [ S '2 transmits γ 2 ] = 1 − p11 , i = D 21 ..W − 1 ( 0 ,0 ,0 ,D21 ) (13) π = 2 (7) P1{ ( ~ C2 , i , i − j ,− D21 ) , ( ~ C2 , i − j , i − j ,− D21 )} W−1 W−1 (14) = p11 , i = 2..W − 1, j = 1.. min( i − 1, D21 − 1) ∑i= 0 π ( i ,i ,0 ,D21 ) 2 + ∑ i= 2 π ( i ,i − 1,0 ,D21 ) 2 P { ( ~ C2 , i , i ,− D21 ) , ( ~ C2 , i , i ,− D21 )} = p11 , 1 ( i ,k ,D21 − j ,D21 ) (15) π 2 is defined as the probability i = 1..W − 1 of the state ( i , k , D21 − j , D 21 ) , in the P { ( C2 , i , i − D21 ,− D21 ) , ( ~ C2 , i − D21 , i − D21 ,− D21 )} stationary condition. Π 2 = π { ( i ,k ,D21 − 2 j ,D21 ) } 1 = p12 , i = ( D21 + 1) ..W − 1 is the probability vector of a category C 2 (16) station. P1{ ( C2 ,i ,i − D21 ,− D21 ) ,( C2 ,( i − 1) ,( i − 1 − D21 ) ,− D21 )} In the same way, we evaluate p 21 and p 22 the = 1 − p12 ,i = ( D21 + 1) ..W − 1 blocking probabilities of station S 2 as shown in (17) figure 2: − p 21 : the probability that S 2 is blocked 1 P { ( ~ C2 ,0 ,0 ,− D21 ) , ( ~ C2 , i , i ,− D21 )} = 1 , given that S 2 is in one of the states of ξ 2 . W (18) i = 0..W − 1 p 21 = 1 − ( 1 − τ 11 ) n1 (8) If ( D 21 < W ) then: Ubiquitous Computing- and Communication Journal -7 - P { ( C2 , D21 ,0 ,− D21 ) , ( ~ C2 , i , i ,− D21 )} = 1 , τ 11 = f (τ 11 ,τ 12 ,τ 22 ) 1 τ 12 = f (τ 11 ,τ 12 ,τ 22 ) W (19) i = 0..W − 1 τ 22 = f (τ 11 ,τ 12 ,τ 22 ) under the constraint By replacing p11 and p 12 by their values in equations (3) and (5) and by replacing P1 and Π 1 τ 11 > 0 ,τ 12 > 0 ,τ 22 > 0 ,τ 11 < 1,τ 12 < 1,τ 22 < 1 in (10) and solving the resulting system, we can (28) ( R ,i ,i − j ,− D21 ) express π 1 as a function of τ 11 , τ 12 and Solving the above system (28), allows deducing τ 22 given respectively by equations (4), (6) and the expressions of τ 11 , τ 12 and τ 22 , and deriving (7). the state probabilities of Markov chains modeling category C 1 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 S i belonging P2 { ( i , i , D21 − j , D21 ) , ( i , i , D21 , D21 )} = p21 , to the traffic category C i transmits a packet (21) i = 0..W − 1, j = 0..( D21 − 1) successfully. Let S 1 and S 2 be two stations belonging respectively to traffic categories C 1 P2 { ( i , i ,0 , D21 ) , ( i , i − 1,0 , D21 )} = 1 − p22 , and C 2 . We have: (22) i = 2..W − 1 P1,s = Pr [ S1 transmits successfully ξ 1 ] Pr [ξ 1 ] P2 { ( 1,1,0 , D21 ) , ( 0 ,0 ,0 , D21 )} = 1 − p22 (23) + Pr [ S1 transmits successfully γ 1 ] Pr [γ 1 ] = τ 11 ( 1 − p11 ) Pr [ξ 1 ] + τ 12 ( 1 − p12 ) Pr [γ 1 ] P2 { ( i , i ,0 , D21 ) , ( i , i , D21 , D21 )} = p22 , (24) (29) i = 1..W − 1 P2 ,s = Pr [ S 2 transmits successfully ξ ] Pr[ξ 2 ] P2 { ( i , i − 1,0 , D21 ) , ( i − 1, i − 1, D21 , D21 )} = p22 , 2 i = 2..W − 1 (25) + Pr [ S 2 transmits successfully γ 2 ] Pr[γ 2 ] =τ 22 ( 1 − p 22 ) Pr [γ 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 C 1 don’t transmit given that these stations By replacing p 21 and p22 by their values in are in one of the states of ξ 1 or if the n stations equations (8) and (9) and by replacing P2 and Π 2 (both category C 1 and category C2 stations) don’t in (10) and solving the resulting system, we can ( i ,k ,D − j ,D21 ) transmit given that stations of category C 1 are in express π 2 21 as a function of τ 11 , τ 12 one of the states of γ 1 . Thus: and τ 22 given respectively by equations (4), (6) ( R ,i ,i − j ,− D21 ) and (7). Moreover, by replacing π 1 and Pidle = ( 1 − τ 11 ) n1 Pr [ξ 1 ] + ( 1 − τ 12 ) n1 ( 1 − τ 22 ) n2 Pr [γ 1 ] ( i ,k ,D21 − j ,D21 ) (31) π 2 by their values, in equations (4), (6) 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 Bi = 2 PIdle Te + Ps Ts + 1 − PIdle − ∑ ni Pi ,s Tc For all the scenarios, we consider that we are in n i= 1 presence of n contending stations with stations (32) 2 for each traffic category. In figure 3, n is fixed to Where Te denotes the duration of an empty 8 and we depict the throughput achieved by the different stations present in the network as a slot, Ts and Tc denote respectively the duration of function of the contention window size W , a successful transmission and a collision. ( D21 = 1) . We notice that the throughput achieved 2 1 − PIdle − ∑ ni Pi ,s corresponds to the by category C1 stations (stations numbered from i= 1 S 11 to S 14 ) is greater than the one achieved by probability of collision. Finally T p denotes the category C 2 stations (stations numbered from S 21 average time required to transmit the packet data to S 24 ). 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]. T D is the time required to transmit the two bytes deadline information. Stations hearing a collision wait during EIFS before resuming their backoff. For numerical results stations transmit 512 Figure 3: Normalized throughput as a function of bytes data packets using 802.11.b MAC and PHY the contention window size ( D 21 = 1, n = 8 ) layers parameters (given in table 1) with a data rate equal to 11Mbps. For simulation scenarios, the Analytically, stations belonging to the same propagation model is a two ray ground model. The traffic category have the same throughput given by transmission range of each node is 250m. The equation (31). Simulation results validate analytical distance between two neighbors is 5m. The EIFS results and show that stations belonging to the same parameter is set to ACKTimeout as in ns-2, where: traffic category (either category C1 or category C 2 ) have nearly the same throughput. Thus, we ACKTimeout = DIFS + ( T PHY + T ACK + T D ) + SIFS conclude the fairness of DM between stations of the (35) same category. Table 1: 802.11 b parameters. For subsequent throughput scenarios, we focus on one representative station of each traffic category. Figure 4, compares category C1 and category C 2 stations throughputs to the one obtained with 802.11. Curves are represented as a function of W and Data Rate 11 Mb/s for different values of D21 . Indeed as D21 Slot 20 µs increases, the category C1 station throughput SIFS 10 µs 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. Ubiquitous Computing- and Communication Journal -9 - We propose to evaluate the Z-Transform of the Finally, we notice that the category C1 station MAC layer service time [3], [14], [15] to derive an obtains better throughput with DM than with expression of the average service time. The service 802.11, but the opposite scenario happens to the time depends on the duration of an idle slot Te , the category C 2 station. 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 Tevent will be given by . 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 S1 belonging to traffic category C 1 . We define: Figure 4: Normalized throughput as a function of H 1( R ,i ,i − j ,− D21 ) (Z) : The Z-transform of the the contention window size (different D21 values) time already elapsed from the instant S 1 selects a In figure 5, we generalize the results for basic backoff in [ 0 ,W − 1] (i.e. being in one of the different numbers of contending stations and fix the states ( ~ C 2 , i , i ,− D 21 ) ) to the time it is found in the contention window size W to 32. state ( R ,i ,i − j ,− D21 ) . 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 ξ 1 . Psuc = ( n1 − 1)τ 11 ( 1 − τ 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 γ 1 . Psuc = ( n1 − 1)τ 12 ( 1 − τ 12 ) n1 − 2 ( 1 − τ 22 ) n2 12 (37) Figure 5: Normalized throughput as a function of + n2τ 22 ( 1 − τ 22 ) n2 − 1 ( 1 − τ 12 ) n1 − 1 the number of contending stations We evaluate H 1( R ,i ,i − j ,− D21 ) ( Z ) for each state All the curves show that DM performs service differentiation over 802.11 and offers better of S1 Markov chain as follows: throughput for category C1 stations independently Ts of the number of contending stations. 1 11 Te H 1( ~ C2 ,i ,i ,− D21 ) ( Z ) = + Psuc Z + W 6 SERVICE TIME ANALYSIS Tc min ( i + D21 − 1,W − 1) In this section, we evaluate the average MAC (p 11 − 11 Psuc ) T Z e ∑ H 1( ~ C 2 ,k ,i ,− D21 ) (Z) k = i+ 1 layer service time of category C 1 and category C 2 stations using the DM policy. The service time is Ts Tc 12 Te ( ) + H ( C 2 ,i + D21 ,i ,− D21 ) ( Z ) Psuc Z ˆ1 T the time interval from the time instant that a packet 12 + p11 − Psuc Z e 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 (38) transmission or dropped. Where: Ubiquitous Computing- and Communication Journal - 10 - Ts (( 1 − H 1( C ,i + D ,i ,− D ) ( Z ) = H 1( C ,i + D ,i ,− D ) ( Z ) ˆ TS1 ( Z ) = p11 ) H 1( ~ C 2 ,0 ,0 ,− D21 ) ( Z ) T Z e 2 21 21 2 21 21 if ( i + D 21 ) ≤ W − 1 Tc Te )∑ ( m ˆ + ( 1 − p12 ) H 1( C2 ,D21 ,0 ,− D21 ) ( Z ) p11 H 1( ~ C2 ,0 ,0 ,− D21 ) ( Z ) H 1( C2 ,i + D21 ,i ,− D21 ) ( Z ) = 0 Otherwise Z i= 0 (39) + p12 H 1( C2 ,D21 ,0 ,− D21 ) ( Z ) )) i We also have: m+ 1 Tc T ( (1 − p11 ) Z ) j H 1( ~ C2 ,i ,i ,− D21 ) ( Z ) ( + Z e p11H 1( ~ C2 ,0 ,0 ,− D21 ) ( Z ) + p12 H 1( C 2 ,D21 ,0 ,− D21 ) ( Z ) ) j ,− D21 ) ( Z ) = H 1( ~ C2 ,i ,i − Ts Tc ( ) 11 1 − Psuc Z Te 11 − p11 − Psuc Z Te (44) i = 2..W − 1, j = 1..min( i − 1, D21 − 1) 6.1.2 Service time Z-transform of a category (40) C2 station: In the same way, let TS2 (Z) be the service ( (1 − p11 ) Z ) D21 H 1( ~ C2 ,i ,i ,− D21 ) ( Z ) time Z-transform of a station S 2 of category C 2 . H 1( C2 ,i ,i − D21 ,− D21 ) ( Z ) = Ts Tc We define: ( ) 1− 11 Te Psuc Z − p11 − 11 Psuc T Z e H 2( i ,k ,D21 − j ,D21 ) ( Z ) : The Z-transform of the + ( 1 − p12 ) ZH 1( C 2 ,i + 1,i + 1− D21 ,− D21 ) ( Z ) ,i = D21 ..W − 2 time already elapsed from the instant S 2 selects a (41) basic backoff in [0 ,W − 1] (i.e. being in one of the states ( i , i , D21 , D 21 ) ) to the time it is found in the H 1( C 2 ,W − 1,W − 1− D21 ,− D21 ) ( Z ) state ( i , k , D21 − j , D 21 ) . ( (1 − p11 ) Z ) D21 H 1( ~ C2 ,W − 1,W − 1,− D21 ) ( Z ) Moreover, we define: = Ts Tc ( ) 11 Te 11 T 21 1− Psuc Z − p11 − Psuc Z e • Psuc : the probability that S 2 observes a + ( 1 − p12 ) ZH 1( C 2 ,i + 1,i + 1− D21 ,− D21 ) ( Z ) ,i = D21 ..W − 2 successful transmission on the channel, (42) while S 2 is in one of the states of ξ 2 . Psuc = ( n1 − 1)τ 12 ( 1 − τ 12 ) n1 − 1 11 (45) (1 − p11 ) ZH 1( ~ C2 ,1,1,− D21 ) ( Z ) H 1( ~ C 2 ,0 ,0 ,− D21 ) ( Z ) = Ts Tc 22 ( )Z • Psuc : the probability that S 2 observes a 11 Te 11 Te 1− Psuc Z − p11 − Psuc successful transmission on the channel, min ( W − 1,D21 − 1) 1 while S 2 is in one of the states of γ 2 . + ( 1 − p11 ) Z ∑ H 1( ~ C2 ,i ,1,− D21 ) ( Z ) + W i= 2 Psuc = n1τ 12 ( 1 − τ 12 ) n1 − 1 ( 1 − τ 22 ) n2 − 1 22 (43) (46) + ( n2 − 1)τ 22 ( 1 − τ 22 ) n2 − 2 ( 1 − τ 12 ) n1 If S 1 transmission state is ( ~ C 2 ,0 ,0 ,− D 21 ) , the transmission will be successful only if none of We evaluate H 2( i ,i ,D21 − j ,− D21 ) ( Z ) for each state the ( n1 − 1) remaining stations of C 1 transmits. of S1 Markov chain as follows: 1 Whereas when the station S 1 transmission state is H 2( i ,i ,D21 − j ,D21 ) ( Z ) = , i = 0 and i = W − 1 (47) ( C 2 , D21 ,0 ,− D21 ) , the transmission occurs W successfully only if none of ( n − 1) remaining Ts 1 22 Te H 2( i ,i ,D21 ,D21 ) ( Z ) = + Psuc Z + stations (either a category C 1 or a category C 2 W station) transmits. Tc ( ) If the transmission fails, S 1 tries another p 22 − Psuc Z e H 2( i + 1,i ,0 ,D21 ) ( Z ) , i = 1..W − 2 22 T transmission. After m retransmissions, if the packet is not acknowledged, it will be dropped. (48) To compute H 2( i ,i ,D21 − j ,D21 ) (Z) , we define Thus: Tdec ( Z ) , such as: j Ubiquitous Computing- and Communication Journal - 11 - m+ 1 Tc 0 Tdec (Z) = 1 (49) TS 2 ( Z ) = p 22 Z e H 2( 0 ,0 ,0 ,D21 ) ( Z ) T + (1 − p 21 ) Z Tdec ( Z ) = j i Ts Tc Ts Tc m 21 ( ) j− 1 ∑ 1 − Psuc Z Te 21 + p 21 − Psuc Z Te Tdec ( Z ) (1 − p 22 ) Z Te H 2( 0 ,0 ,0 ,D21 ) ( Z ) p 22 Z Te H 2 ( 0 ,0 ,0 ,D21 ) ( Z ) i= 0 for j = 1..D 21 (54) (50) 6.2 Average Service Time So: From equations (43) (respectively equation (54)), we derive the average service time of a H 2( i ,i ,D21 − j ,D21 ) (Z) = H 2( i ,i ,D21 − j + 1,D21 ) ( Z )Tdec ( Z ) , j category C 1 station ( respectively a category C 2 i = 0..W − 1, j = 1..D 21 , ( i , j ) ≠ ( 0 , D 21 ) station). The average service time of a category C i (51) station is given by: And: X i = TS i( 1) ( 1) (55) H 2( i ,i − 1,0 ,D21 ) ( Z ) = ( 1 − p 22 ) ZH 2( i + 1,i ,0 ,D21 ) ( Z ) (1 − p 22 ) ZH 2( i ,i ,0 ,D21 ) ( Z ) Where TS i( 1) ( Z ) , is the derivate of the service + Ts Tc time Z-transform of station S i [11]. 22 Te ( ) D21 Tdec ( Z ) 22 T 1 − Psuc Z + p 22 − Psuc Z e By considering the same configuration as in figure 3, we depict in figure 5, the average service i = 2..W − 2 time of category C 1 and category C2 stations as a (51) function of W . As for the throughput analysis, stations belonging to the same traffic category have H 2( W − 1,W − 2 ,0 ,D21 ) ( Z ) nearly the same average service value. Simulation (1 − p 22 ) ZH 2( W − 1,W − 1,0 ,D21 ) ( Z ) service time values coincide with analytical values = given by equation (55). These results confirm the Ts Tc (52) 22 Te ( ) D21 fairness of DM in serving stations of the same Tdec ( Z ) 22 T 1 − Psuc Z + p 22 − Psuc Z e category. According to figure 2 and using equations (44), we have: H 2( 0 ,0 ,0 ,D21 ) ( Z ) = H 2( 0 ,1,0 ,D21 ) ( Z )Tdec ( Z ) 21 D ( 1 − p 22 ) ZH 2( 1,1,0 ,D21 ) ( Z ) + Ts Tc (53) 22 Te ( ) 1 − Psuc Z 22 + p 22 − Psuc Z Te T D21 ( Z ) dec Therefore, we can derive an expression of S 2 Z-transform service time as follows: Figure 6: Average service time as a function of the contention window size (D21=1, n=8) In figure 8, we show that category C 1 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 D 21 = 4 , the probability that S 1 service time stations within the network. exceeds 0.005s equals 0.28%. Whereas, station S 2 service time exceeds 0.005s with the probability 5.67%. 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 1 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 near 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 (43) and (54). But we are most interested in probabilistic service time bounds derived by inverting the complementary service time Z transform given by [11]: ~ 1 − TS i ( Z ) Xi (Z) = (55) Figure 9: Complementary service time distribution 1− Z for different values of D21 (W=64) In figure 8, we depict analytical and simulation In figure 10, we depict the complementary values of the complementary service time service time distribution for both category C 1 and distribution of both category C 1 and category C 2 category C 2 stations and for values of n , the station (W = 32 ) . number of contending nodes. Figure 8: Complementary service time distribution Figure 10: Complementary service time 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 C 1 stations curves drop to 0 complementary service time curves drop faster faster than category C 2 curves. Indeed, when when the number of contending stations is small for both category C 1 and category C 2 stations. This Ubiquitous Computing- and Communication Journal - 13 - means that all stations service time increases as the CW max < 1024 and K =1. number of contending nodes increases. Analytical and simulation results show that 7 EXTENTIONS OF THE ANAYTICAL throughput values increase with stations priority. RESULTS BY SIMULATION Indeed, the station with the lowest delay bound has the maximum throughput. The mathematical analysis undertaken above show that DM performs service differentiation over Moreover, figure 12 shows that stations 802.11 protocol and offers better QoS guarantees belonging to the same traffic category have the for highest priority stations same throughput. For instance, when n is set to 15 Nevertheless, the analysis was restricted to two (i.e. m = 3 ), the three stations of the same traffic traffic categories. In this section, we first generalize category have almost the same throughput. the results by simulation for different traffic categories. Therefore, we consider a simple multi- hop and evaluate the performance of the DM policy 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 = 5 m 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 Figure 12: Normalized throughput: different stations. We have: stations belonging to the same traffic category Dij = ( i − j ) K (53) In figure 13, we depict the average service Where K is the deadline multiplicity factor time of the different traffic category stations as a and is given by: function of K , the deadline multiplicity factor. We Di + 1,i = Di + 1 − Di = K (53) notice that the highest priority station average service time decreases as the deadline multiplicity Indeed, when K varies, the deadline values of factor increases. Whereas, the lowest priority all other stations also vary. Stations belonging to station average service time increases with K . the traffic category C i are numbered from S i1 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) by different traffic categories stations as a function are better than those offered to station S 51 (the of the minimum contention window size CW min lowest priority station). Indeed, the probability that such as CW min is always smaller than CW max , S 11 service time exceeds 0.01s=0.3%. But, station Ubiquitous Computing- and Communication Journal - 14 - S 51 service time exceeds 0.01s with the probability and D21 = D 2 − D1 =5 slots. Flows F3 and F4 are of 36%. transmitted respectively by S 12 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 D1 and D2 and D 2 ,1 = D2 − D1 = 5 slots. Figure 16 shows that the throughput achieved by F1 is smaller than the one achieved by F2 . Figure 14: Complementary service time distribution (W=32, n=8) 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. Figure 16: Normalized throughput using DM policy 7.2 Simple Multi hop scenario In the above study, we considered that Indeed, both flows cross nodes 6 and 7, where contending stations belong to the same broadcast F1 got a higher priority to access the medium than region. In reality, stations may not be within one F2 when the DM policy is used. We obtain the hop from each other. Thus a packet can go through same results for flows F5 and F6 . Flows F3 and several hops before reaching its destination. Hence, factors like routing protocols or interferences may F4 have almost the same throughput since they preclude the DM policy from working correctly. have equal deadlines. Figure 17 show that the complementary service In the following paragraph, we evaluate the time distribution curves drop to 0 faster for flow F1 performance of the DM policy in a multi-hop than for flow F2 . environment. Hence, we consider a 13 node simple mtlti-hop scenario described in figure 15. Figure 17: End to end complementary service time distribution Figure 15: Simple multi hop scenario Six flows are transmitted over the network. Flows The same behavior is obtained for flow F5 and F6, packets are routed using the AODV protocol. where F5 has the shortest delay bound. Flows F1 and F2 are respectively transmitted by stations S 1 and S 2 with delay bounds D1 and D2 Hence, we conclude that even in a multi-hop Ubiquitous Computing- and Communication Journal - 15 - environment, the DM policy performs service [6] IEEE 802.11 WG, ”Draft Supplement to Part differentiation over 802.11 and provides better QoS 11: Wireless Medium Access Control (MAC) guarantees for flows with short deadlines. and physical layer (PHY) specifications: Medium Access Control (MAC) Enhancements 8 CONCLUSION for Quality of Service (QoS)”, IEEE In this paper we first proposed to support the 802.11e/D13.0, (January 2005). DM policy over 802.11 protocol. Therefore, we [7] J. Deng, R. S. Chang: A priority Scheme for used a distributed backoff scheduling algorithm and IEEE 802.11 DCF Access Method, IEICE introduced a new medium access backoff policy. 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