MAC Layer Service Time Distribution of a Fixed Priority Real Time Scheduler over


 Debra Watkins
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1 Internatonal Journal of Software Engneerng and Its Applcatons Vol., No., Aprl, 008 MAC Layer Servce Tme Dstrbuton of a Fxed Prorty Real Tme Scheduler over 80. Inès El Korb Ecole Natonale des Scences de l Informatque Laboratore Crstal Unversté de la Manouba, 00 Tunsa Lela Azouz Sadane Ecole Natonale des Scences de l Informatque Laboratore Crstal Unversté de la Manouba, 00 Tunsa Abstract In ths paper, we propose to support a fxed prorty real tme scheduler over 80. protocol called Deadlne Monotonc (DM. e evaluate the performances of ths polcy for a smple scenaro where two statons wth dfferent delay constrants contend for the channel. For ths scenaro a Markov chan based analytcal model s proposed. From the mathematcal model, we derve the probablty dstrbuton of the packet servce tme at MAC layer. Analytcal results are valdated by smulaton usng the ns network smulator.. Introducton The IEEE 80. wreless LANs [] become more and more relable to support applcatons wth Qualty of Servce (QoS requrements. Indeed, the IEEE 80.e standard [3] was recently proposed to offer servce dfferentaton over 80.. The IEEE 80.e standard proposes the Enhanced Dstrbuted Channel Access (EDCA as an extenson for the 80. Dstrbuted Coordnaton Functon (DCF. th EDCA, each staton mantans four prortes called Access Categores (ACs. Each access category s characterzed by a mnmum and a maxmum contenton wndow szes and an Arbtraton Inter Frame Space (AIFS. Even though the IEEE 80.e protocol ntroduces servce dfferentaton over 80., the granularty of servce offered by 80.e (4 prortes at most can not satsfy the real tme flows requrements (each flow s characterzed by ts own delay bound. Therefore, we propose n ths paper a new medum access mechansm based on the fxed prorty Deadlne Monotonc (DM polcy [8] to schedule real tme flows over 80.. To support the DM polcy over 80., we use a dstrbuted schedulng and ntroduce a new medum access backoff polcy. e then propose a Markov chan based analytcal model to evaluate the performances of DM for a smple scenaro where two statons wth dfferent deadlne constrants contend for the channel. Ths confguraton wll reflect the behavor of DM over 80. and the mathematcal model can be extended for more complex scenaros. 95
2 Internatonal Journal of Software Engneerng and Its Applcatons Vol., No., Aprl, 008 For the consdered confguraton, we evaluate for each staton the MAC layer servce tme dstrbuton. e can therefore derve the probablty that the packet servce tme exceeds a certan value. Analytcal results wll be valdated and extended by smulaton usng the ns network smulator [9]. The rest of ths paper s organzed as follows. In secton, we revew the works related to our study. In secton 3, we present the dstrbuted schedulng and ntroduce the new medum access backoff polcy to support DM over 80.. In secton 4, we present the mathematcal model based on the Markov chans analyss. In secton 5, we evaluate the servce tme dstrbuton and present analytcal and smulaton results. Fnally, we conclude the paper n secton 6.. Related orks In the absence of a coordnaton pont, the IEEE 80. defnes the Dstrbuted Coordnaton Functon (DCF based on the Carrer Sense Multple Access wth Collson Avodance (CSMA/CA protocol. In the DCF protocol, a staton shall ensure that the channel s dle when t attempts to transmt. Then t selects a random backoff n the contenton wndow [,C ] 0, where C s the current wndow sze and takes ts values between the mnmum and the maxmum contenton wndow szes. If the channel s sensed busy, the staton suspends ts backoff untl the channel becomes dle for a Dstrbuted Inter Frame Space (DIFS after a successful transmsson or an Extended Inter Frame Space (EIFS after a collson. hen the backoff reaches 0, the packet s transmtted. A packet s dropped f t colldes after maxmum retransmsson attempts. Dfferent works have been proposed to evaluate the performance of the 80. DCF. Indeed, Banch [] proposed a Markov chan based analytcal model to evaluate the saturaton throughput of the 80. protocol. Probablstc bounds on MAC layer servce tme were derved n [0]. The IEEE 80.e performs servce dfferentaton over 80. and aggregates the traffc nto four access categores. In [4] and [5] Osterbo and Al. proposed to evaluate the performance of EDCA under saturated and non saturated condtons. Although the IEEE 80.e EDCA classfes the traffc nto four prortzed ACs, there s stll no guarantee of real tme transmsson servce. Ths s due to the lack of a satsfactory schedulng method for varous delaysenstve flows. In ths paper, we focus on delay senstve flows and propose to support the fxed prorty Deadlne Monotonc (DM polcy over 80. to schedule delay senstve flows. For nstance, we use a prorty broadcast mechansm smlar to [6] and ntroduce a new medum access backoff polcy where the backoff value s nferred from the deadlne nformaton. 3. Supportng Deadlne Monotonc Polcy over 80. The Deadlne Monotonc polcy (DM [8] s a real tme schedulng polcy that assgns statc prortes to flows packets accordng to ther deadlnes; the packet wth the small deadlne beng assgned the hghest prorty. Indeed, when flows packets arrve to a staton, they are sorted by ncreasng order of ther deadlnes such as the Head of Lne (HOL packet has the shortest delay bound. The problem that occurs wth the DCF s that all the statons share the same transmsson medum and the HOL packets of all the statons wll contend for the channel wth the same prorty even f they have dfferent deadlnes. 96
3 Internatonal Journal of Software Engneerng and Its Applcatons Vol., No., Aprl, 008 The dea of ntroducng DM over 80. s to allow statons havng packets wth short deadlnes to access the channel wth hgher prorty than those havng packets wth long deadlnes. Provdng such a QoS requres a dstrbuted schedulng and a new medum access polcy. 3.. Dstrbuted Schedulng To realze a dstrbuted schedulng over 80., we ntroduce a broadcast prorty mechansm smlar to [6]. In each staton, we focus on two packets: The current packet: the packet beng served. The HOL packet: the packet at the head of the queue that wll be transmtted after the servce completon of the current packet. Each staton mantans a local schedulng table wth entres for HOL packets of all other statons. Each entry n the schedulng table of node S comprses two felds ( S k, D k where S k s the source node MAC address (Address feld n DATA packet and RA feld n the ACK packet and D k s the deadlne of staton S k HOL packet. To broadcast the HOL packet deadlnes, we propose to use the DATA/ACK access mode. The deadlne nformaton requres two addtonal bytes to be encoded n DATA and ACK packets. hen a node S transmts a DATA packet, t pggybacks the deadlne of ts HOL packet. The nodes hearng the DATA packet add an entry for S n ther local schedulng tables by fllng the correspondng felds. The recever of the DATA packet copes the prorty of the HOL packet n ACK before sendng the ACK frame. All the statons that dd not hear the DATA packet add an entry for S usng the nformaton n the ACK packet. In the followng, we propose a new medum access polcy, where the backoff value s nferred from the packet deadlne. 3.. DM medum access backoff polcy Let s consder two statons S and S transmttng two flows wth the same deadlne D ( D s expressed as a number of 80. slots. The two statons havng the same delay bounds can access the channel wth the same prorty usng the natve 80. DCF. Now, we suppose that S and S transmt flows wth dfferent delay bounds D and D such as D < D and generate two packets at tme nstants t and t. If S had the same delay bound as S, ts packet would have been generated at tme t ' such as t ' = t + D, where D = ( D D. At that tme S and S would have the same prorty and transmt ther packets accordng to the 80. protocol. Hence, when S has a packet to transmt, t selects a 80. backoff, but suspends ths backoff durng D dle slots. The D slots elapsed, 80. backoff can therefore be decremented. Thus to support DM over 80., each staton uses a new backoff polcy where the backoff s gven by: The random backoff selected n [,C ] BAsc Backoff (BAB. 0, accordng to 80. DCF, called The DM Shftng Backoff (DMSB: corresponds to the addtonal backoff slots that a staton wth low prorty (transmttng a packet wth a large deadlne adds to ts 97
4 Internatonal Journal of Software Engneerng and Its Applcatons Vol., No., Aprl, 008 BAB to have the same prorty as the staton wth the hghest prorty (transmttng the packet wth the shortest deadlne. henever a staton reevaluated as follows: S sends an ACK or hears an ACK on the channel ts DMSB s DMSB ( S Deadlne( HOL( S DT ( S = ( mn where mn ( S table and ( HOL( DT s the mnmum of the HOL packet deadlnes present n S schedulng Deadlne S s staton S HOL packet deadlne. Hence, when S has to transmt ts HOL packet wth a delay bound D, t selects a BAB n the contenton wndow [ 0,Cmn ] and computes the hole Backoff (HB value as follows: ( S DMSB( S BAB( S HB = + ( The staton S decrements ts HB when t senses an dle slot. Now, we suppose that S senses the channel busy. If a successful transmsson s heard, then S revaluates ts DMSB when a correct ACK s heard. Then, S adds the new DMSB value to ts current BAB as n equaton (. hereas, f a collson s heard, S rentalzes ts DMSB and adds t to ts current BAB to allow colldng statons contendng wth the same prorty as for ther frst transmsson attempt. S transmts when ts HB reaches Mathematcal Model of the DM polcy over 80. In the hereby secton, we propose a mathematcal model to evaluate the performance of the DM polcy usng Markov chans analyss []. e consder the followng assumptons: The system under study comprses two statons S and S, such as S transmts a flow F havng a deadlne D and D < D. e defne D = ( D D as the dfference between the two delay bounds. e operate n saturaton condtons: each staton has mmedately a packet avalable for transmsson after the servce completon of the prevous packet []. 3 A staton selects a BAB n a contenton wndow[ 0, ]. e consder that each staton selects a 80. backoff n the same contenton wndow of sze ndependently of the transmsson attempt. Ths s a smplfyng assumpton to lmt the complexty of the mathematcal model. 4 e suppose that we are n statonary condtons,.e. the two statons have already sent one packet to each other. Thus, the two statons have the same schedulng table. Each staton S wll be modeled by a Markov chan representng the whole backoff (HB process. 98
5 Internatonal Journal of Software Engneerng and Its Applcatons Vol., No., Aprl, Markov chan modelng staton S Fgure represents the Markov chan modelng staton S. Fgure : Markov chan modelng staton S The states of ths Markov chan are descrbed by the followng quadruplet ( R,, j, where: R : takes two values ~ S and S. hen R = ~ S, staton S s decrementng ts shftng backoff (DMSB durng D slots and wouldn t contend for the channel. hen R = S, the D slots were elapsed and S wll contend for the channel at the same tme as S. : the value of the BAB selected by S n [ 0, ]. ( j : corresponds to the remanng backoff slots before reachng 0. D : corresponds to ( D D. e choose the negatve notaton D for S to express the fact that S has a postve ΜΣΒ equals to D and DMSB( S = 0. D Intally ~ S,,, D, = 0... Durng ( D slots, S decrements ts backoff wth the probablty and moves to one of the states ( ~ S,, j, D, = 0.., j = mn( max( 0,,D. Indeed durng these slots, S s decrementng ts DMSB and wouldn t contend for the channel. hen S th decrements ts D slot t knows that henceforth, S can contend for the channel (the D slots were elapsed. Hence, S moves to one of the states ( S,, D, D, = D... If the BAB ntally selected by S s smaller than D, then S transmts when ts backoff reaches 0. If S transmts before S backoff reaches 0, the next packet of S wll decrement another DMSB and S wll see the channel free agan for D slots. S selects a random BAB and s n one of the states ( 99
6 Internatonal Journal of Software Engneerng and Its Applcatons Vol., No., Aprl, Markov chan modelng staton S Fgure represents the Markov chan modelng staton S. Fgure : Markov chan modelng staton S Each state of S Markov chan s represented by the quadruplet (,k,d j, D S n [ 0, ]. : refers to the BAB value selected by k : refers to the current BAB value. D j : refers to the current DMSB of S, j n[ 0,D ]. D : corresponds to ( D. D where: hen S selects a BAB, ts DMSB equals,,d, D, = 0... If S observes the channel dle durng D slots, t moves to one of the states (,,0,D, = 0.., where t ends ts shftng backoff. At that tme, S begns decrementng ts basc backoff. If S transmts from the state (,,0,D, S rentalzes ts,,d,, =... shftng backoff and moves agan to one of the states ( 4.3. Blockng probabltes n the Markov chans D and s n one of states ( D e notce from fgure that when ~ S,, j, D, = 0.., j = mn( max( 0,,D, t decrements ts backoff wth the probablty. S s n one of the states ( That means that when S s n one of these states ( ~ S,, j, D decrementng ts DMSB and s n one of the states (,,D j, D j = 0.. ( D. S s n one of the states ( S,, D,, D.. (, t knows that S s, = 0.., However, when D =, S has already decremented ts DMSB and can now contend for the channel by decrementng ts basc backoff. In ths case, S wll be n one of the states,,0, D,,0,. ( ( = 0.. D =.. From the explanatons above, each staton Markov chan states can be dvded n two groups: 00
7 Internatonal Journal of Software Engneerng and Its Applcatons Vol., No., Aprl, 008 ξ : the set of states of S for whch S wll not contend (blue states n fgure. ξ {( S,, j, D, = 0.., j = 0..mn( max( 0,,D } = ~ γ : the set of states of staton S for whch S can con contend and decrements ts BAB (pnk states n fgure. γ {(,, D, D, = D.. } = S ξ : the set of states of S where S does not contend for the channel (blue states n fgure. ξ {(,,D j,d, = 0.., j = 0.. ( D } = γ : the set of states of S, where S contends for the channel (pnk states n fgure. γ {(,,0,D, = 0.. (,,0,D, =.. } = Thus when S s n one of the states of ξ, S s oblgatory n of the states of ξ. Smlarly, when S s n one of the states of γ, S s oblgatory n of the states of γ. hen the staton S s n one states of ξ, S s blocked wth the probablty τ, ths probablty corresponds to the probablty that S transmts gven that t s n one of the states of ξ. Thus: [ S transmts ξ ] ( ~S,0,0, D π τ = Pr = (3 mn( max( 0,,D ( ~S,, j, D π = 0 j= 0 ( R,, j, D here π s the probablty that S s n the state ( R,, j, D, n the ( R,,, D statonary condtons and { } j Π = π s the probablty vector of S. e also defne τ, the probablty that S s blocked gven that staton S s n one of the states of γ. Hence: ( S,D,0, D π τ = Pr[ S transmts γ ] = (4 ( S,, D, D π = D In the same way, when S s n one of the states of ξ, S wll decrement ts backoff wth the probablty. Indeed, no one of the ξ states corresponds to a transmsson state (those states descrbe the shftng backoff decremented by S. However, when S s n one of the states of γ, t contends for the channel and S s blocked wth the probablty τ, such as: [ S transmts γ ] ( 0,0,0,D π τ = Pr = (5 (,,0,D (,,0,D + (,k,d j, D where π s defned as the probablty of the state (,k,d j,d, n the (,k,d D statonary condton. Π { } j, = π s the probablty vector of S. = 0 π = π 0
8 Internatonal Journal of Software Engneerng and Its Applcatons Vol., No., Aprl, 008 The blockng probabltes descrbed above allow deducng the transton state probabltes and havng the transton probablty matrx P, for each staton S. Therefore, we can evaluate the state probabltes by solvng the followng system [7]: Π P = Π j = π j ( Transton probablty matrx of S Let P be the transton probablty matrx of P, j s the probablty to transt from state to state j. The transtons probabltes of staton S are: S and { } P {( ~ S,, j, D,( ~ S,, ( j +, D } =, =.. j = 0..mn(,D P {( ~ S,, D +, D,( S,, D, D } =, = D..( P {( ~ S,,, D,( ~ S,0,0, D } =, =.. (,D P {( S,, D, D,( S,(,( D, D } = τ = ( D +.. P {( S,, D, D,( ~ S,( D,( D, D } = τ, = ( D +.., (9 {( ~ S,0,0, D,( ~ S,,, D } =, = 0.., (7 (8 (0 ( ( P If ( D < then: {( S, D,0, D,( ~ S,,, D } =, = 0.. P (3 By replacng P and Π n (6 and solvng the resultng system, we can express ( R,, j, D π as a functon of τ, where τ s gven by ( Transton probablty matrx of S Let P be the transton probablty matrx of S. The transtons probabltes of S are: P = {(,,D j,d,(,,d ( j +,D } = τ, 0.., j = 0.. ( D {(,,D j,d,(,,d,d } =, = 0.., j = 0.. ( D {(,,0, D,(,,0,D } =, =.. {(,,0,D,( 0,0,0, D } τ {(,,0, D,(,,D,D }, =.. {(,,0,D,(,,D,D } =, =.. P P P P P (4 τ (5 τ (6 = (7 = τ (8 τ (9 0
9 Internatonal Journal of Software Engneerng and Its Applcatons Vol., No., Aprl, 008 {(,,0,D,(,,0,D } =, = 3.. P τ (0 {( 0,0,0, D,(,, D, D }, = 0.. P = ( By replacng P and Π n (6 and solvng the resultng system, we can express (,k,d j, D π as a functon of τ, τ gven respectvely by equatons (3, (4. Moreover, by ( R,, j, D replacng (,k,d j, D π and π by ther values, n equatons (3, (4 and (5, we obtan a system of non lnear equatons as follows: ( τ ( τ ( τ, τ τ = f τ = f τ = f under the constrant τ > 0, τ > 0, τ > 0, τ <, τ <, τ ( < Solvng the above system (, allows deducng the expressons of τ, τ and τ, and dervng the state probabltes of S and S Markov chans. 5. Servce Tme Analyss In ths secton, we evaluate the MAC layer servce tme dstrbuton of S and S, usng the DM polcy. The MAC layer servce tme s the tme nterval from the tme nstant that a packet becomes at the head of the queue and starts to contend for channel to the tme nstant that ether the packet s acknowledged for a successful transmsson or dropped. e propose to evaluate the ZTransform of the MAC layer servce tme [0] to derve expressons of the servce tme dstrbutons. The servce tme depends on the duraton of an dle slot T e, the duraton of a successful transmsson T s and the duraton of a collson T c [4], [0]. e have: T T ( TPHY + TMAC + T p + TD + SIFS + ( TPHY + TACK + TD DIFS ( T + T + T + T EIFS = (3 s + = (4 c PHY MAC p D + where T PHY, T MAC and T ACK are the duratons of the PHY header, the MAC header and the ACK packet. T D s the tme requred to transmt the two bytes deadlne nformaton and T p s the tme requred to transmt the data payload. Statons hearng a collson wat durng EIFS before resumng ther packets. Tevent As T e s the smallest duraton event, the duraton of all events wll be gven by. Te 5.. Ztransform of staton S servce tme To evaluate the Ztransform of staton S servce tme TS ( Z, we defne: H( R,, j, D ( Z a basc backoff n [ 0, ] (.e. beng n one of the states ( S,,, D found n the state ( R,, j,. : The Ztransform of the tme already elapsed from the nstant S selects ~ to the tme t s D 03
10 Internatonal Journal of Software Engneerng and Its Applcatons Vol., No., Aprl, 008 e evaluate H( ( Z for each state of S Markov chan as follows: R,, j, D j H( ~ S,, j, D ( Z Z, j 0.. D = = (5 H( ~ S,,, D ( Z Z, D..(.. = = (6 Ts T e H( ~S,,, D ( Z Z H( ~S, D,, D ( Z = τ + + (7 =..max 0, D j ( ( j ( ~ S ( Z Z H( ( Z,..,, j, D = ~S,,, D = =..mn(,d D ( S ( Z Z H( ( Z,, D, D = ~S,,, D ( τ Z H( ( Z, = D..( H H + S,+, + D, D, (8 (9 mn(,d ( ( H ~S,0,0, D Z = + H( ~S,,, D ( Z (30 = If the staton ~ S,0,0, D, the transmsson wll be successful snce S was decrementng ts shftng backoff. hereas when the staton S transmsson state s ( S,D,0, D, the transmsson occurs successfully only f S doesn t transmt wth the probablty ( τ. Otherwse S selects another backoff and tres another transmsson. After m retransmssons, f the packet s not acknowledged, t wll be dropped. S transmsson state s ( TS + Z m c ( + ( τ H( ( Z Z τ H( ( Z T ( Z Z e H( ( Z Tc = Ts ~S,0,0, D S,D,0, D = 0 τ H ( S,D,0, D ( Z m+ T C,D,0, D (3 5.. Ztransform of staton S servce tme In the same way, we defne ( Z have: TS, the Ztransform of staton S servce tme. e H (,k,d ( Z j, D selects a basc backoff n [ 0, ] (.e. beng n one of the states (,,D, D tme t s found n the state (,k,d j,. : The Ztransform of the tme already elapsed from the nstant S to the H D = (3 (,,D, ( Z, = 0 and = D 04
11 Internatonal Journal of Software Engneerng and Its Applcatons Vol., No., Aprl, 008 H Ts T D e (,,D,D ( Z = + Z H ( +,,0, ( Z, =.. To compute H (,,D j, ( Z, we defne T j ( Z D τ (33 dec such as: So: And: T 0 ( Z dec = (34 j ( τ Z T Z =, j =.. D (35 dec H j = ( τ Z Ts T j dec ( Z j (,,D j,d ( Z H (,,D j,d ( Z Tdec ( Z = +..D,(, j ( 0,D H (,,0,D ( Z = ( τ ZH ( ( Z +,,0,D ( τ ZH ( ( Z H τ Z,,0,D Ts D Tdec (,,0,D ( Z ( Z =, =.. ( τ ZH ( ( Z τ Z Ts T D dec +,,0,D ( Z, = 0..,, =.. (36 (37 (38 TS D ( 0,0,0,D ( Z = ( τ ZH ( ( Z T ( Z 0,,0,D dec ( τ ZH ( ( Z H + τ Z Ts,,0,D T D dec ( Z Therefore, we can derve an expresson of S Ztransform servce tme as follows: m+ Tc Ts T m c 0,0,0,D 0,0,0,D 0,0,0,D Z = 0 ( Z = τ Z H ( ( Z + ( τ Z H ( ( Z τ Z H ( ( 5.3. Servce Tme Dstrbuton Servce tme dstrbuton s obtaned by nvertng the servce tme Z transforms gven by equatons (3 and (40. But we are most nterested n tal behavour n terms of servce tme bounds,.e. the probablty that the servce tme exceeds a certan value. Probablstc bounds on servce tme can be derved by nvertng the complementary servce tme Z transform [4] gven by: (39 (40 05
12 Internatonal Journal of Software Engneerng and Its Applcatons Vol., No., Aprl, 008 X ~ ( Z ( Z TS = (4 Z In fgures 3(a to 3(d, we depct analytcal and smulaton values of the Complementary servce tme dstrbuton of both statons S and S. The curves are obtaned for dfferent values of the contenton wndow sze and for dfferent values of D ( D s gven n slots. The statons transmt 5 bytes data payload packets and we use the 80..b parameters (gven n table to determne the values of T e, T s and T c. Smulaton results are obtaned wth ns network smulator [9]. Table : : 80. b parameters. Data Rate Mb/s Slot 0 µs SIFS 0 µs DIFS 50 µs PHY Header 9 µs MAC Header 7 µs ACK µs Short Retry Lmt 7 All the curves drop gradually to 0 as the delay ncreases. Staton S curves drop to 0 faster than staton S curves. Indeed, when = 3 and D = 4, the probablty that S servce tme exceeds 0.005s equals 0.8%. hereas, staton S servce tme exceeds 0.005s wth the probablty of 5.67%. Thus, DM offers better servce tme guarantees for the flow wth the hghest prorty. (a =6 (b =3 06
13 Internatonal Journal of Software Engneerng and Its Applcatons Vol., No., Aprl, 008 (c =64 (d =8 Fgure 3: Complementary Servce Tme Dstrbuton Moreover, we notce that each tme doubles ts sze, S and S servce tme curves become closer. Indeed, when becomes large, the basc backoff values selected by S and S ncrease. Hence, the shftng backoff slots (DMSB added by DM become neglgble compared to the basc backoff. The whole backoff values (HB of the two statons become near and ther servce tme accordngly Extended Smulaton Results In the above secton, we consdered a two staton scenaro where each staton transmts a real tme flow wth a gven delay bound. e showed that DM performs servce dfferentaton over 80. and offers better servce tme bounds for the flow wth the short deadlne. In ths secton, we consder a fve staton scenaro where each staton transmts a real tme flow wth a characterzed delay bound. For ths scenaro, we consder the default 80.b mnmum and maxmum wndows szes ( C mn = 3, C max = 04. Smulaton results show that the delay bounds on servce tme decrease wth the deadlne bounds. Moreover, as the dfference between flows deadlnes ncreases, the dfference between ther delay bounds ncreases. 07
14 Internatonal Journal of Software Engneerng and Its Applcatons Vol., No., Aprl, 008 (a D5=4 (b D5=8 (c D5= (d D5=6 Fgure 4: Complementary Servce Tme Dstrbuton (Extended Smulaton Results 6. Concluson In ths paper we proposed to support the DM polcy over 80. protocol. Therefore, we used a dstrbuted schedulng algorthm and ntroduced a new medum access backoff polcy. Then we proposed a mathematcal model to evaluate the performance of the DM polcy n terms of servce tme guarantees for a scenaro where two statons wth dfferent delay bounds contend for the channel. Analytcal and smulaton results show that DM performs servce dfferentaton over 80. and offers better servce tme guarantees for the flow havng the small deadlne. Moreover, as the dfference between flows deadlnes ncreases, the dfference between ther delay bounds ncreases. 7. References [] Banch, G., Performance Analyss of the IEEE 80. Dstrbuted Coordnaton Functon, IEEE JSAC Vol. 8 N. 3, Mar. 000, pp [] IEEE 80. G, Part : reless LAN Medum Access Control (MAC and Physcal Layer (PHY specfcaton, IEEE
15 Internatonal Journal of Software Engneerng and Its Applcatons Vol., No., Aprl, 008 [3] IEEE 80. G, Draft Supplement to Part : reless Medum Access Control (MAC and physcal layer (PHY specfcatons: Medum Access Control (MAC Enhancements for Qualty of Servce (QoS, IEEE 80.e/D3.0, Jan [4] Engelstad, P.E. and Osterbo O.N., The Delay Dstrbuton of IEEE 80.e EDCA and 80. DCF, Proceedngs of the Internatonal Performance Computng and Communcatons Conference, Arzona, Apr [5] Engelstad, P.E., Osterbo, O.N, Delay and Throughput Analyss of IEEE 80.e EDCA wth Starvaton Predcton, In proceedngs of the The IEEE Conference on Local Computer Networks, LCN 05 (005. [6] Kanoda, V., L, C., Dstrbted Prorty Schedulng and Medum Access n Adhoc Networks, ACM reless Networks, Volume 8, Nov. 00. [6] Klenrock, L., Queung Systems,Vol., John ley, 975. [7] Klenrock, L., Queung Systems,Vol., John ley, 975. [8] Leung, J. Y. T., htehead, J, On the Complexty of FxedProrty Schedulng of Perodc, Real Tme Tasks, Performance Evaluaton (Netherlands, pp , Dec. 98. [9] McCanne, S., Floyd, S., The network smulator  ns, [0] Zha, H., Kwon, Y., Fang, Y.,.Performance Analyss of IEEE 80. MAC protocol n wreless LANs., reless Computer and Moble Computng, 004. Authors Inès El Korb receved the engneerng degree and the Master degree n computer scence n 003 and 005 respectvely from l Ecole Natonale des Scences de l Informatque (ENSI, Unversté de la Manouba, Tunsa. Currently she s applyng for a PHD degree. From 004 she operates as a student researcher n cooperaton projects between l ENSI (Tunsa and l Insttut Natonal de Recherche en Informatque et en Automatque (INRIA n France. Lela Azouz Sadane s Professor at l ENSI, Tunsa. Her research nterests nclude performance evaluaton of QoS networks, wreless and sensor networks. From 004, she ntates many cooperaton projects between l ENSI and l INRIA n France. 09
16 Internatonal Journal of Software Engneerng and Its Applcatons Vol., No., Aprl, 008 0
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