Performance Evaluation of Deadline Monotonic Policy over protocol

Transcription

1 erformance Evaluaton of Deadlne Monotonc olcy over 80. rotocol Ines El Korb and Lela Azouz Sadane Natonal School of Comuter Scence Unversty of Manouba 00 Tunsa Emals: ABSTRACT Real tme alcatons are characterzed by ther delay bounds. To satsfy the Qualty of Servce (QoS) requrements of h flows over wreless communcatons we enhance the 80. rotocol to suort the Deadlne Monotonc (DM) schedulng olcy. Then we roose to evaluate the erformance of DM n terms of throughut average medum access delay and medum access delay dstrbuton. To evaluate the erformance of the DM olcy we develo a Markov chan based analytcal model and derve exressons of the throughut average MAC layer servce tme and servce tme dstrbuton. Therefore we valdate the mathematcal model and extend analytal results to a mult-ho network by smulaton usng the ns- network smulator. Keywords: Deadlne Monotonc 80. rotocol erformance evaluaton Medum access delay Throughut robablstc medum access delay bounds. INTRODUCTION Suortng alcatons wth QoS requrements has become an mortant challenge for all communcatons networks. In wreless LANs the IEEE 80. rotocol [5] has been enhanced and the IEEE 80.e rotocol [6] was roosed to suort qualty of servce over wreless communcatons. In the absence of a coordnaton ont the IEEE 80. defnes the Dstrbuted Coordnaton Functon (DCF) based on the Carrer Sense Multle Access wth Collson Avodance (CSMA/CA) rotocol. The IEEE 80.e rooses the Enhanced Dstrbuted Channel Access (EDCA) as an extenson for DCF. Wth EDCA each staton mantans four rortes called Access Categores (ACs). The qualty of servce offered to each flow deends on the AC to whch t belongs. Nevertheless the granularty of servce offered by 80.e (4 rortes at most) can not satsfy the real tme flows requrements (where each flow s characterzed by ts own delay bound). Therefore we roose n ths aer a new medum access mechansm based on the Deadlne Monotonc (DM) olcy [9] to schedule real tme flows over 80.. Indeed DM s a real tme schedulng olcy that assgns statc rortes to flow ackets accordng to ther deadlnes; the acket wth the shortest deadlne beng assgned the hghest rorty. To suort the DM olcy over 80. we use a dstrbuted schedulng and ntroduce a new medum access backoff olcy. Therefore we focus on erformance evaluaton of the DM olcy n terms of achevable throughut average MAC layer servce tme and MAC layer servce tme dstrbuton. Hence we follow these stes: Frst we roose a Markov Chan framework modelng the backoff rocess of n contendng statons wthn the same broadcast regon []. Due to the comlexty of the mathematcal model we restrct the analyss to n contendng statons belongng to two traffc categores (each traffc category s characterzed by ts own delay bound). From the analytcal model we derve the throughut acheved by each traffc category. Then we use the generalzed -transforms [3] to derve exressons of the average MAC layer servce tme and servce tme dstrbuton. As the analytcal model was restrcted to two traffc categores analytcal results are extended by smulaton to dfferent traffc categores. Fnally we consder a smle mult-ho scenaro to deduce the behavor of the DM olcy n a mult ho envronment. Ubqutous Comutng - and Communcaton Journal - -

2 The rest of ths aer s organzed as follows. In secton we revew the state of the art of the IEEE 80. DCF QoS suort over 80. manly the IEEE 80.e EDCA and real tme schedulng over 80.. In secton 3 we resent the dstrbuted schedulng and ntroduce the new medum access backoff olcy to suort DM over 80.. In secton 4 we resent our mathematcal model based on Markov chan analyss. Secton 5 and 6 resent resectvely throughut and the servce tme analyss. Analytcal results are valdated by smulaton usng the ns- network smulator [6]. In secton 7 we extend our study by smulaton frst to take nto consderaton dfferent traffc categores second to study the behavor of the DM algorthm n a mult-ho envronment where factors lke nterferences or routng rotocols exst. Fnally we conclude n Secton 8. LITTERATURE REVIEWS. The 80. rotocol.. Descrton of the IEEE 80. DCF Usng DCF a staton shall ensure that the channel s dle when t attemts to transmt. Then t selects a random backoff n the contenton wndow [0CW-] where CW s the current wndow sze and vares between the mnmum and the maxmum contenton wndow szes. If the channel s sensed busy the staton susends ts backoff untl the channel becomes dle for a Dstrbuted Inter Frame Sace (DIFS) after a cessful transmsson or an Extended Inter Frame Sace (EIFS) after a collson. The acket s transmtted when the backoff reaches zero. A acket s droed f t colldes after maxmum retransmsson attemts. The above descrbed two way handshakng acket transmsson rocedure s called basc access mechansm. DCF defnes a four way handshakng technque called Request To Send/ Clear To Send (RTS/CTS) to revent the hdden staton roblem. A staton S j s sad to be hdden from S f S j s wthn the transmsson range of the recever of and out of the transmsson range of S... erformance evaluaton of the 80. DCF Dfferent works have been roosed to evaluate the erformance of the 80. rotocol based on Banch s work []. Indeed Banch roosed a Markov chan based analytcal model to evaluate the saturaton throughut of the 80. rotocol. By saturaton condtons t s meant that contendng have always ackets to transmt. Several works extended the Banch model ether to sut more realstc scenaros or to evaluate other erformance arameters. Indeed the authors of [] ncororate the frame retry lmts n the Banch s model and show that Banch overestmates the S maxmum achevable throughut. The natve model s also extended n [0] to a non saturated envronment. In [] the authors derve the average acket servce tme at a 80. node. A new generalzed -transform based framework has been roosed n [3] to derve robablstc bounds on MAC layer servce tme. Therefore t would be ossble to rovde robablstc end to end delay bounds n a wreless network.. Suortng QoS over Dfferentaton mechansms over 80. Emergng alcatons lke audo and vdeo alcatons requre qualty of servce guarantees n terms of throughut delay jtter loss rate etc. Transmttng h flows over wreless communcatons requre suortng servce dfferentaton mechansms over wreless networks. Many medum access schemes have been roosed to rovde some QoS enhancements over the IEEE 80. WLAN. Indeed [4] assgns dfferent rortes to the ncomng flows. rorty classes are dfferentated accordng to one of three 80. arameters: the backoff ncrease functon Inter Frame Sacng (IFS) and the maxmum frame length. Exerments show that all the three dfferentaton schemes offer better guarantees for the hghest rorty flow. But the backoff ncrease functon mechansm doesn t erform well wth TC flows because ACKs affect the dfferentaton mechansm. In [7] an algorthm s roosed to rovde servce dfferentaton usng two arameters of IEEE 80. the backoff nterval and the IFS. Wth ths scheme hgh rorty statons are more lkely to access the medum than low rorty ones. The above descrbed researches led to the standardzaton of a new rotocol that suorts QoS over 80. the IEEE 80.e rotocol [6]... The IEEE 80.e EDCA The IEEE 80.e rooses a new medum access mechansm called the Enhanced Dstrbuted Channel Access (EDCA) that enhances the IEEE 80. DCF. Wth EDCA each staton mantans four rortes called Access Categores (ACs). Each access category s characterzed by a mnmum and a maxmum contenton wndow szes and an Arbtraton Inter Frame Sacng (AIFS). Dfferent analytcal models have been roosed to evaluate the erformance of 80.e EDCA. In [7] Xao extends Banch s model to the rortzed schemes rovded by 80.e by ntroducng multle ACs wth dstnct mnmum and maxmum contenton wndow szes. But the AIFS dfferentaton arameter s lackng n Xao s model. Recently Osterbo and Al. have roosed Ubqutous Comutng - and Communcaton Journal - -

3 dfferent works to evaluate the erformance of the IEEE 80.e EDCA [3] [4] [5]. They roose a model that takes nto consderaton all the dfferentaton arameters of the EDFA esecally the AIFS one. Moreover dfferent arameters of QoS have been evaluated h as throughut average servce tme servce tme dstrbuton and robablstc resonse tme bounds for both saturated and non saturated cases. Although the IEEE 80.e EDCA classfes the traffc nto four rortzed ACs there s stll no guarantee of real tme transmsson servce. Ths s due to the lack of a satsfactory schedulng method for varous delay-senstve flows. Hence we need a schedulng olcy dedcated to h delay senstve flows..3 Real tme schedulng over 80. A dstrbuted soluton for the suort of realtme sources over IEEE 80. called Blackburst s dscussed n [8]. Ths scheme modfes the MAC rotocol to send short transmssons n order to gan rorty for real-tme servce. It s shown that ths aroach s able to suort bounded delays. The man drawback of ths scheme s that t requres constant ntervals for hgh rorty traffc; otherwse the erformance degrades very much. In [8] the authors roosed a dstrbuted rorty schedulng over 80. to suort a class of dynamc rorty schedulers h as Earlest Deadlne Frst (EDF) or Vrtual Clock (VC). Indeed the EDF olcy s used to schedule real tme flows accordng to ther absolute deadlnes where the absolute deadlne s the node arrval tme lus the delay bound. To realze a dstrbuted schedulng over 80. the authors of [8] used a rorty broadcast mechansm where each staton mantans an entry for the hghest rorty acket of all other statons. Thus statons can adjust ther backoff accordng to other statons rortes. The overhead ntroduced by the broadcast rorty mechansm s neglgble. Ths s due to the fact that rortes are exchanged usng natve DATA and ACK ackets. Nevertheless the authors of [8] roose a generc backoff olcy whch can be used by a class dynamc rorty schedulers no matter f ths scheduler targets delay senstve flows or rate senstve flows. In ths aer we focus on delay senstve flows and roose to suort the fxed rorty deadlne monotonc scheduler over 80. to schedule delay senstve flows. For nstance we use a rorty broadcast mechansm smlar to [5] and roose a new medum access backoff olcy where the backoff value s nferred from the deadlne nformaton. 3 SUORTING DEADLINE MONOTONIC (DM) OLICY OVER 80. Wth DCF all the statons share the same transmsson medum. Then the HOL (Head of Lne) ackets of all the statons (hghest rorty ackets) wll contend for the channel wth the same rorty even f they have dfferent deadlnes. Introducng DM over 80. allows statons havng ackets wth short deadlnes to access the channel wth hgher rorty than those havng ackets wth long deadlnes. rovdng h a QoS requres dstrbuted schedulng and a new medum access olcy. 3. Dstrbuted Schedulng over 80. To realze a dstrbuted schedulng over 80. we ntroduce a rorty broadcast mechansm smlar to [8]. Indeed each staton mantans a local schedulng table wth entres for HOL ackets of all other statons. Each entry n the schedulng table of node S comrses two felds ( S j D j ) where S j s the source node MAC address and D j s the deadlne of the HOL acket of node S j. To broadcast the HOL acket deadlnes we roose to use the DATA/ACK access mode. When a node S transmts a DATA acket t ggybacks the deadlne of ts HOL acket. The nodes hearng the DATA acket add an entry for S n ther local schedulng tables by fllng the corresondng felds. The recever of the DATA acket coes the rorty of the HOL acket n ACK before sendng the ACK frame. All the statons that dd not hear the DATA acket add an entry for S usng the nformaton n the ACK acket. 3. DM medum access backoff olcy Let s consder two statons S and S transmttng two flows wth the same deadlne D ( D s exressed as a number of 80. slots). The two statons havng the same delay bound can access the channel wth the same rorty usng the natve 80. DCF. Now we suose that S and S transmt flows wth dfferent delay bounds D and D h as D < D and generate two ackets at tme nstants t and t. If S had the same delay bound as S ts acket would have been generated at tme t h t t where D ( D ). as D D At that tme S and S would have the same rorty and transmt ther ackets accordng to the Ubqutous Comutng - and Communcaton Journal - 3 -

4 80. rotocol. Thus to suort DM over 80. each staton uses a new backoff olcy where the backoff s gven by: The random backoff selected n [ 0CW ] accordng to 80. DCF referred as BAsc Backoff (BAB). The DM Shftng Backoff (DMSB): corresonds to the addtonal backoff slots that a staton wth low rorty (the HOL acket havng a large deadlne) adds to ts BAB to have the same rorty as the staton wth the hghest rorty (the HOL acket havng the shortest deadlne). Whenever a staton S sends an ACK or hears an ACK on the channel ts DMSB s revaluated as follows: DMSB ( S ) Deadlne( HOL( S ) ) DT ( S ) () mn Where DT mn ( S ) s the mnmum of the HOL acket deadlnes resent n S schedulng table and Deadlne( HOL( S ) ) s the HOL acket deadlne of node S. Hence when S has to transmt ts HOL acket wth a delay bound D t selects a BAB n the contenton wndow [ 0CWmn ] and comutes the WHole Backoff (WHB) value as follows: ( S ) DMSB( S ) BAB( S ) WHB () The staton S decrements ts BAB when t senses an dle slot. Now we suose that S senses the channel busy. If a cessful transmsson s heard then S revaluates ts DMSB when a correct ACK s heard. Then the staton S adds the new DMSB value to ts current BAB as n equaton (). Whereas f a collson s heard S rentalzes ts DMSB and adds t to ts current BAB to allow colldng statons contendng wth the same rorty as for ther frst transmsson attemt. S transmts when ts WHB reaches 0. If the transmsson fals doubles ts contenton wndow sze and reeats the above rocedure untl the acket s cessfully transmtted or droed after maxmum retransmsson attemts. 4 MATHEMATICAL MODEL OF THE DM OLICY OVER 80. S In ths secton we roose a mathematcal model to evaluate the erformance of the DM olcy usng Markov chan analyss []. We consder the followng assumtons: Assumton : The system under study comrses n contendng statons hearng each other transmssons. Assumton : Each staton S transmts a flow F wth a delay bound D. The n statons are dvded nto two traffc categores C and C h as: C reresents n nodes transmttng flows wth delay bound D. C reresents n nodes transmttng flows wth delay bound D h as D < D D ( D D ) and ( n n ) n. Assumton 3: We oerate n saturaton condtons: each staton has mmedately a acket avalable for transmsson after the servce comleton of the revous acket []. Assumton 4: A staton selects a BAB n a constant contenton wndow [ 0W ] ndeendently of the transmsson attemt. Ths s a smlfyng assumton to lmt the comlexty of the mathematcal model. Assumton 5: We are n statonary condtons.e. the n statons have already sent one acket at least. Deendng on the traffc category to whch t belongs each staton S wll be modeled by a Markov Chan reresentng ts whole backoff (WHB) rocess. 4. Markov chan modelng a staton of category C Fgure llustrates the Markov chan modelng a staton S of category C. The states of ths Markov chan are descrbed by the followng quadrulet ( R jd ) where: R : takes two values denoted by C and ~ C. When R ~ C the n statons of category C are decrementng ther shftng backoff (DMSB) durng D slots and wouldn t contend for the channel. When R C the D slots had already been elased and statons of category C wll contend for the channel.. Ubqutous Comutng - and Communcaton Journal - 4 -

5 Fgure : Markov chan modelng a category C Staton : the value of the BAB selected by S n [ 0W ]. ( j ) : corresonds to the current backoff of the staton S. D : corresonds to ( D D ). We choose the negatve notaton D for statons of C to exress the fact that only statons of category C have a ostve DMSB equal to D. Intally S selects a random BAB and s n one of the states ( ~ C D ) 0.. W. Durng ( D ) slots S decrements ts backoff f none of the ( n ) remanng statons of category C transmts. Indeed durng these slots the n statons of category C are decrementng ther DMSB and wouldn t contend for the channel. When S s n one of the states ~ C ( D ) D.. W and ( ) D th senses the channel dle t decrements ts D slot. But S knows that henceforth the n statons of category C can contend for the channel (the D slots had been elased). Hence S moves to one of the states ( C D ) D.. W. D However when the staton S s n one of the ~ C j.. W states ( D ) j 0..mn( D ) and at least one of the ( n ) remanng statons of category C transmts then the statons of category C wll rentalze ther DMSB and wouldn t contend for channel durng addtonal D slots. Therefore S moves to the state ( ~ C j j D ).. W j 0..mn( D ). Now If S s n one of the states D ( D ).. W and at ( C D ) least one of the ( ) n remanng statons (ether a category C or a category C staton) transmts then S moves to one of the states ( ~ C D D ) ( D ).. W. D 4. Markov chan modelng a staton of category C Fgure llustrates the Markov chan modelng a staton S of category C. Each state of S Markov chan s reresented by the quadrulet ( kd j D ) where: : refers to the BAB value selected by S n [ 0W ]. k : refers to the current BAB value of S. D j : refers to the current DMSB of S j [ 0D ]. D : corresonds to ( D ). D When S selects a BAB ts DMSB equals D and s n one of the states ( D D ) 0.. W. Durng D slots only the n statons of category C contend for the channel. If S senses the channel dle durng D slots t moves to one of the states ( 0 D ) 0.. W where t ends ts shftng backoff. Ubqutous Comutng - and Communcaton Journal - 5 -

6 Fgure : Markov chan modelng a category C Staton other statons of category C have also decremented ther DMSB and can contend for the channel. Thus S decrements ts BAB and moves to the state ( 0 D ).. W only f none of ( n ) remanng statons transmts. When S s n one of the states ( 0 D ) 0.. W the ( n ) If S s n one of the states ( 0 D ).. W and at least one of the ( n ) remanng statons transmts the n statons of category C wll rentalze ther DMSB and S moves to the state ( D D ).. W. 4.3 Blockng robabltes n the Markov chans Accordng to the exlanatons gven n aragrahs 4. and 4. the states of the Markov chans modelng statons S and S can be dvded nto the followng grous: ξ : the set of states of S where none of the n statons of category C contends for the channel (blue states n fgure ). ξ ~ C j D 0.. W {( ) ( max( 0 ) D )} j 0..mn γ : the set of states of S where statons of category C can contend for the channel (nk states n fgure ). γ D D D.. W {( ) } C ξ : the set of states of S where statons of category C do not contend for the channel (blue states n fgure ). ξ D jd 0.. W j 0.. {( ) ( D )} γ : the set of states of S where statons of category C contend for the channel (nk states n fgure ). γ 0 D 0.. W {( ) ( 0D ).. W } Therefore when statons of category C are n one the states of ξ statons of category C are n one of the states of ξ. Smlarly when statons of category C are s n one of the states of γ statons of category C are n one of the states of γ. Hence we derve the exressons of S blockng robabltes and shown n fgure as follows: : the robablty that S s blocked gven that S s n one of the states of ξ. s the robablty that at least a staton the other ( n ) statons of gven that S of C transmts S s n one of the states of ξ. n ( ) τ (3) where τ s the robablty that a staton of C transmts gven that the states of ξ : τ r [ S transmts ξ ] 0 W mn S S s n one of ( ~ C 00 D ) π ( max( 0 ) D ) ( ~ C j D ) π j 0 (4) ( R j D ) π s defned as the robablty of the state ( j D ) n the statonary R Ubqutous Comutng - and Communcaton Journal - 6 -

7 ( R j D ) condtons and Π { π } s the robablty vector of a category C staton. : the robablty that S s blocked gven that S s n one of the states of γ. s the robablty that at least a staton the other ( n ) statons of gven that at least a staton S of C transmts S s n one of the states of γ or S of the n statons of C transmts gven that states of γ. S s n one of the n n ( τ ) ( τ ) where τ s the robablty that a staton of C transmts gven that the states of γ. τ r [ S transmts γ ] ( C D 0 D ) π W D ( C D D ) π (5) S S s n one of and τ the robablty that a staton C transmts gven that states of γ. τ r [ S transmts γ ] W 0 ( 000D ) π (6) S of S s n one of the W ( 0D ) ( 0D ) π π (7) ( k D j D ) π s defned as the robablty of the state ( kd jd ) n the ( k D D ) statonary condton. Π π j { } s the robablty vector of a category C staton. In the same way we evaluate and the blockng robabltes of staton S as shown n fgure : : the robablty that S s blocked gven that S s n one of the states of ξ. n ( τ ) (8) : the robablty that S s blocked gven that S s n one of the states of γ. n ( ) n ( ) τ τ (9) The blockng robabltes descrbed above allow deducng the transton state robabltes and havng the transton robablty matrx for a staton of traffc category C. Therefore we can evaluate the state robabltes by solvng the followng system []: Π j Π π j (0) 4.4 Transton robablty matrces 4.4. Transton robablty matrx of a category C staton Let be the transton robablty matrx of the staton S of category C. { j} s the robablty to transt from state to state j. We have: {( ~ C j D )( ~ C ( j ) D )}.. W j 0..mn( D ) {( ~ C D )( ~ C 00 D )}..mn( W D ) () () D {( ~ C D D )( C D )} D.. W {( ~ C j D ) ( ~ C j j D )}.. W j..mn( D ) {( ~ C D ) ( ~ C D )}.. W (3) (4) (5) {( C D D )( ~ C D D D )} ( D ).. W (6) {( C D D )( C ( ) ( D ) D )} ( D ).. W {( ~ C 00 D ) ( ~ C D )} 0.. W If ( D < W ) then: W (7) (8) Ubqutous Comutng - and Communcaton Journal - 7 -

8 {( C D 0 D ) ( ~ C D )} 0.. W W (9) By relacng and by ther values n equatons (3) and (5) and by relacng and Π n (0) and solvng the resultng system we can ( R j D ) exress π as a functon of τ τ and τ gven resectvely by equatons (4) (6) and (7) Transton robablty matrx of a category C staton Let be the transton robablty matrx of the staton S belongng to the traffc category C. The transton robabltes of S are: {( D jd ) ( D ( j ) D )} 0.. W j 0.. ( D ) {( D j D ) ( D D )} 0.. W j 0.. ( D ) {( 0 D )( 0 D )}.. W {( 0 D )( 000 D )} {( 0 D )( D D )}.. W {( 0 D )( D D )} (0) () () (3).. W {( 0 D )( 0 D )} (4) (5) (6) 3.. W {( 000 D ) ( D D )} 0.. W (7) W By relacng and by ther values n equatons (8) and (9) and by relacng and Π n (0) and solvng the resultng system we can ( k D j D ) exress π as a functon of τ τ and τ gven resectvely by equatons (4) (6) ( R j D ) and (7). Moreover by relacng π and ( k D j D ) π by ther values n equatons (4) (6) and (7) we obtan a system of non lnear equatons as follows: ( τ τ τ ) ( τ τ τ ) ( τ τ τ ) τ f τ f τ f under the constrant τ > 0 τ > 0 τ > 0 τ < τ < τ < (8) Solvng the above system (8) allows deducng the exressons of τ τ and τ and dervng the state robabltes of Markov chans modelng category C and category C statons. 5 THROUGHUT ANALYSIS In ths secton we roose to evaluate B the normalzed throughut acheved by a staton of traffc category C []. Hence we defne: s τ r s s : the robablty that a staton S belongng to the traffc category C transmts a acket cessfully. Let S and S be two statons belongng resectvely to traffc categores C and C. We have: r[ S transmts cessfully ξ ] r[ ξ ] [ S transmts cessfully γ ] r[ γ ] ( ) r[ ξ ] τ ( ) r[ γ ] r τ r[ S transmts cessfully ξ ] r[ ξ ] [ S transmts cessfully γ ] r[ γ ] ( ) r[ γ ] dle (9) (30) : the robablty that the channel s dle. The channel s dle f the n statons of category C don t transmt gven that these statons are n one of the states of ξ or f the n statons (both category C and category C statons) don t transmt gven that statons of category C are n one of the states of γ. Thus: n n n ( τ ) r[ ξ ] ( τ ) ( τ ) r[ γ ] dle (3) Hence the exresson of the throughut of a category C staton s gven by: Ubqutous Comutng - and Communcaton Journal - 8 -

9 B Idle s T Te s Ts Idle n s T c (3) Where T e denotes the duraton of an emty slot T s and T c denote resectvely the duraton of a cessful transmsson and a collson. Idle ns corresonds to the robablty of collson. Fnally T denotes the average tme requred to transmt the acket data ayload. We have: T s ( T T T T ) ( T T T ) DIFS HY HY ACK MAC D D SIFS (33) For all the scenaros we consder that we are n resence of n contendng statons wth n statons for each traffc category. In fgure 3 n s fxed to 8 and we dect the throughut acheved by the dfferent statons resent n the network as a functon of the contenton wndow szew ( D ). We notce that the throughut acheved by category C statons (statons numbered from S to S 4 ) s greater than the one acheved by category C statons (statons numbered from S S ). to 4 T ( T T T T ) EIFS (34) c HY MAC D Where T HY T MAC and T ACK are the duratons of the HY header the MAC header and the ACK acket [] [3]. T D s the tme requred to transmt the two bytes deadlne nformaton. Statons hearng a collson wat durng EIFS before resumng ther backoff. For numercal results statons transmt 5 bytes data ackets usng 80..b MAC and HY layers arameters (gven n table ) wth a data rate equal to Mbs. For smulaton scenaros the roagaton model s a two ray ground model. The transmsson range of each node s 50m. The dstance between two neghbors s 5m. The EIFS arameter s set to ACKTmeout as n ns- where: ACKTmeout DIFS Table : 80. b arameters. ( T T T ) SIFS HY ACK D Data Rate Mb/s Slot 0 µs SIFS 0 µs DIFS 50 µs HY Header 9 µs MAC Header 7 µs ACK µs Short Retry Lmt 7 (35) Fgure 3: Normalzed throughut as a functon of D n 8 the contenton wndow sze ( ) Analytcally statons belongng to the same traffc category have the same throughut gven by equaton (3). Smulaton results valdate analytcal results and show that statons belongng to the same traffc category (ether category C or category C ) have nearly the same throughut. Thus we conclude the farness of DM between statons of the same category. For subsequent throughut scenaros we focus on one reresentatve staton of each traffc category. Fgure 4 comares category C and category C statons throughuts to the one obtaned wth 80.. Curves are reresented as a functon of W and for dfferent values of D. Indeed as D ncreases the category C staton throughut ncreases whereas the category C staton throughut decreases. Moreover as W ncreases the dfference between statons throughuts s reduced. Ths s due to the fact that the shftng backoff becomes neglgble comared to the contenton wndow sze. Ubqutous Comutng - and Communcaton Journal - 9 -

10 Fnally we notce that the category C staton obtans better throughut wth DM than wth 80. but the ooste scenaro haens to the category C staton. We roose to evaluate the -Transform of the MAC layer servce tme [3] [4] [5] to derve an exresson of the average servce tme. The servce tme deends on the duraton of an dle slot T e the duraton of a cessful transmsson T s and the duraton of a collson T c [] [3][4]. As T e s the smallest duraton event the duraton of all events Tevent wll be gven by. 6. -Transform of the MAC layer servce tme Fgure 4: Normalzed throughut as a functon of the contenton wndow sze (dfferent D values) In fgure 5 we generalze the results for dfferent numbers of contendng statons and fx the contenton wndow sze W to Servce tme -transform of a category C staton: Let TS ( ) be the servce tme -transform of a staton S belongng to traffc category C. We defne: H ( R j ) ( ) D : The -transform of the tme already elased from the nstant S selects a basc backoff n [ 0W ] (.e. beng n one of the states ( ~ C D ) ) to the tme t s found n the state ( R j D ). Moreover we defne: : the robablty that S observes a cessful transmsson on the channel whle S s n one of the states of ξ. n ( n ) ( ) τ τ (36) Fgure 5: Normalzed throughut as a functon of the number of contendng statons All the curves show that DM erforms servce dfferentaton over 80. and offers better throughut for category C statons ndeendently of the number of contendng statons. 6 SERVICE TIME ANALYSIS In ths secton we evaluate the average MAC layer servce tme of category C and category C statons usng the DM olcy. The servce tme s the tme nterval from the tme nstant that a acket becomes at the head of the queue and starts to contend for transmsson to the tme nstant that ether the acket s acknowledged for a cessful transmsson or droed. : the robablty that S observes a cessful transmsson on the channel whle S s n one of the states of γ. n n ( n ) τ ( τ ) ( τ ) n n τ ( τ ) ( τ ) We evaluate H( R j ) ( ) n (37) D for each state of S Markov chan as follows: H ( ~ C D ) ( ) ( ) c mn D W ( ) H( ~ C ) ( ) k D Ĥ T s ( ) ( ) ( ) C D D Where: W k T Tc T e (38) Ubqutous Comutng - and Communcaton Journal - 0 -

11 H H Ĥ f Ĥ ( C ) ( ) H( ) ( ) D D C D D ( D ) W ( C D D ) ( ) 0 Otherwse We also have: ( ~ C j D ) ( ).. W j..mn ( C D D ) ( ) (39) j ( ( ) ) H( ) ( ) ( D ) ~ C D Te ( ) (40) D ( ( ) ) H( ) ( ) ( ) ( ) H( ) ( ) D.. W H C D D ( C ) ( ) W W D D D ( ( ) ) H( ) ( ) ( ) ~ C D Te ( ) H( ) ( ) D.. W H ( ~ C 00 D ) ( ) mn ~ C W W D Te C D D ( W D ) ( ) H( ) ( ) ( ) H( ) ( ) ~ C D ~ C D ( ) W (4) (4) (43) If ~ C 00 D the transmsson wll be cessful only f none of the ( n ) remanng statons of C transmts. Whereas when the staton S transmsson state s ( C D 0 D ) the transmsson occurs cessfully only f none of ( n ) remanng statons (ether a category C or a category C staton) transmts. S transmsson state s ( ) If the transmsson fals S tres another transmsson. After m retransmssons f the acket s not acknowledged t wll be droed. Thus: TS ( Te ( ) ( ) H( ) ( ) Te ( ) H( ) ( ) ) H( ) ( ) H ( C D 0 D ) ( ) )) ( H ) C D 0 D ~ C 00 D m 0 ( ~ C 00 D ) ( ) H( C D 0 D ) ( ) ( ~ C 00 D (44) 6.. Servce tme -transform of a category C staton: In the same way let TS () be the servce tme -transform of a staton S of category C. We defne: H k D j : The -transform of the ( ) ( ) D tme already elased from the nstant S selects a basc backoff n [ 0W ] (.e. beng n one of the states ( D D ) ) to the tme t s found n the state ( kd j D ). Moreover we defne: : the robablty that S observes a cessful transmsson on the channel whle S s n one of the states of ξ. n ( n ) ( ) τ τ (45) : the robablty that S observes a cessful transmsson on the channel whle S s n one of the states of γ. n n nτ ( τ ) ( τ ) n n ( n ) τ ( τ ) ( τ ) We evaluate H ( D j ) ( ) (46) D for each state of S Markov chan as follows: H ( D ) ( ) 0 W j D and (47) W H ( D D ) ( ) T W c T e ( ) H ( ) ( ).. W T j dec 0D To comute H ( D ) ( ) j D ( ) h as: (48) we defne m Ubqutous Comutng - and Communcaton Journal - -

12 T 0 dec ( ) (49) T j dec ( ) for j..d H H So: ( ) T c T j ( ) e T ( ) dec j ( D jd ) ( ) H ( D j D ) ( ) Tdec ( ) 0.. W j..d ( j ) ( 0D ) And: ( 0D ) ( ) ( ) H ( ) ( ) 0D ( ) H ( ) ( ).. W H 0D T c T e D ( ) T ( ) ( W W 0D ) ( ) ( ) H ( ) ( ) T dec c T e D ( ) T ( ) W W 0D dec (50) (5) (5) (5) TS ( ) H ( ) ( ) ( ) ( ) ( ) H H ( ) ( ) 000D 000D m 0 m 000D (54) 6. Average Servce Tme From equatons (43) (resectvely equaton (54)) we derve the average servce tme of a category C staton ( resectvely a category C C staton). The average servce tme of a category staton s gven by: ( X ) TS ( ) (55) Where TS ( ) ( ) tme -transform of staton s the dervate of the servce S []. By consderng the same confguraton as n fgure 3 we dect n fgure 5 the average servce tme of category C and category C statons as a functon ofw. As for the throughut analyss statons belongng to the same traffc category have nearly the same average servce value. Smulaton servce tme values concde wth analytcal values gven by equaton (55). These results confrm the farness of DM n servng statons of the same category. Accordng to fgure and usng equatons (44) we have: H D ( 000D ) ( ) H ( ) ( ) T ( ) 00D dec ( ) H ( ) ( ) 0D (53) Te T e D ( ) Tdec ( ) Therefore we can derve an exresson of S -transform servce tme as follows: Fgure 6: Average servce tme as a functon of the contenton wndow sze (D n8) In fgure 8 we show that category C statons obtan better average servce tme than the one obtaned wth 80. rotocol. Whereas the ooste scenaro haens for category C statons Ubqutous Comutng - and Communcaton Journal - -

13 ndeendently of n the number of contendng statons wthn the network. D 4 the robablty that S servce tme exceeds 0.005s equals 0.8%. Whereas staton S servce tme exceeds 0.005s wth the robablty 5.67%. Thus DM offers better servce tme guarantees for the statons wth the hghest rorty. In fgure 9 we double the sze of the contenton wndow sze and set t to 64. We notce that category C and category C statons servce tme curves become closer. Indeed when W becomes large the BAB values ncrease and the (DMSB) becomes neglgble comared to the basc backoff. The whole backoff values of S and S become near and ther servce tme accordngly. Fgure 7: Average servce tme as a functon of the number of contendng statons 6.3 Servce Tme Dstrbuton Servce tme dstrbuton s obtaned by nvertng the servce tme transforms gven by equatons (43) and (54). But we are most nterested n robablstc servce tme bounds derved by nvertng the comlementary servce tme transform gven by []: X ~ ( ) ( ) TS (55) In fgure 8 we dect analytcal and smulaton values of the comlementary servce tme dstrbuton of both category C and category C staton ( W 3). Fgure 9: Comlementary servce tme dstrbuton for dfferent values of D (W64) In fgure 0 we dect the comlementary servce tme dstrbuton for both category C and category C statons and for values of n the number of contendng nodes. Fgure 8: Comlementary servce tme dstrbuton for dfferent values of D ( W 3) All the curves dro gradually to 0 as the delay ncreases. Category C statons curves dro to 0 faster than category C curves. Indeed when Fgure 0: Comlementary servce tme dstrbuton for dfferent values of the contendng statons Analytcal and smulaton results show that comlementary servce tme curves dro faster when the number of contendng statons s small for both category C and category C statons. Ths Ubqutous Comutng - and Communcaton Journal - 3 -

14 means that all statons servce tme ncreases as the number of contendng nodes ncreases. 7 EXTENTIONS OF THE ANAYTICAL RESULTS BY SIMULATION The mathematcal analyss undertaken above show that DM erforms servce dfferentaton over 80. rotocol and offers better QoS guarantees for hghest rorty statons Nevertheless the analyss was restrcted to two traffc categores. In ths secton we frst generalze the results by smulaton for dfferent traffc categores. Therefore we consder a smle multho and evaluate the erformance of the DM olcy when the statons belong to dfferent broadcast regons. 7. Extenson of the analytcal results In ths secton we consder n statons contendng for the channel n the same broadcast regon. The n statons belong to 5 traffc categores where n 5m and m s the number of statons of the same traffc category. A traffc category C s characterzed by a delay bound D and Dj D D j s the dfference between the C j deadlne values of category C and category statons. We have: D j ( j )K (53) Where K s the deadlne multlcty factor and s gven by: D D D K (53) Indeed when K vares the deadlne values of all other statons also vary. Statons belongng to the traffc category C are numbered from S to S. m CW max < 04 and K. Analytcal and smulaton results show that throughut values ncrease wth statons rorty. Indeed the staton wth the lowest delay bound has the maxmum throughut. Moreover fgure shows that statons belongng to the same traffc category have the same throughut. For nstance when n s set to 5 (.e. m 3 ) the three statons of the same traffc category have almost the same throughut. Fgure : Normalzed throughut: dfferent statons belongng to the same traffc category In fgure 3 we dect the average servce tme of the dfferent traffc category statons as a functon of K the deadlne multlcty factor. We notce that the hghest rorty staton average servce tme decreases as the deadlne multlcty factor ncreases. Whereas the lowest rorty staton average servce tme ncreases wth K. Fgure : Normalzed throughut for dfferent traffc category statons In fgure we dect the throughut acheved by dfferent traffc categores statons as a functon of the mnmum contenton wndow sze CW mn h as CW mn s always smaller than CW max Fgure 3: Average servce tme as a functon of the deadlne multlcty factor K In the same way the robablstc servce tme bounds offered to S (the hghest rorty staton) are better than those offered to staton S 5 (the lowest rorty staton). Indeed the robablty that S servce tme exceeds 0.0s0.3%. But staton Ubqutous Comutng - and Communcaton Journal - 4 -

15 S 5 servce tme exceeds 0.0s wth the robablty of 36%. and D D D 5 slots. Flows F 3 and F 4 are transmtted resectvely by S and S 4 and have the same delay bound. Fnally F 5 and F 6 are transmtted resectvely by S 5 and S 6 wth delay bounds D and D and D D D 5 slots. Fgure 6 shows that the throughut acheved by F s smaller than the one acheved by F. Fgure 4: Comlementary servce tme dstrbuton (W3 n8) The above results generalze the analytcal model results and show once agan that DM erforms servce dfferentaton over 80. and offer better guarantees n terms of throughut average servce tme and robablstc servce tme bounds for flows wth short deadlnes. 7. Smle Mult ho scenaro In the above study we consdered that contendng statons belong to the same broadcast regon. In realty statons may not be wthn one ho from each other. Thus a acket can go through several hos before reachng ts destnaton. Hence factors lke routng rotocols or nterferences may reclude the DM olcy from workng correctly. In the followng aragrah we evaluate the erformance of the DM olcy n a mult-ho envronment. Hence we consder a 3 node smle mtlt-ho scenaro descrbed n fgure 5. Fgure 6: Normalzed throughut usng DM olcy Indeed both flows cross nodes 6 and 7 where F got a hgher rorty to access the medum than F when the DM olcy s used. We obtan the same results for flows F 5 and F 6. Flows F 3 and F 4 have almost the same throughut snce they have equal deadlnes. Fgure 7 show that the comlementary servce tme dstrbuton curves dro to 0 faster for flow F than for flow F. Fgure 5: Smle mult ho scenaro Sx flows are transmtted over the network. Flows ackets are routed usng the AODV rotocol. Flows F and F are resectvely transmtted by statons S and S wth delay bounds D and D Fgure 7: End to end comlementary servce tme dstrbuton The same behavor s obtaned for flow F5 and F6 where F5 has the shortest delay bound. Hence we conclude that even n a mult-ho Ubqutous Comutng - and Communcaton Journal - 5 -

16 envronment the DM olcy erforms servce dfferentaton over 80. and rovdes better QoS guarantees for flows wth short deadlnes. 8 CONCLUSION In ths aer we frst roosed to suort the DM olcy over 80. rotocol. Therefore we used a dstrbuted backoff schedulng algorthm and ntroduced a new medum access backoff olcy. Then we roosed a mathematcal model to evaluate the erformance of the DM olcy. Indeed we consdered n contendng statons belongng to two traffc categores characterzed by dfferent delay bounds. Analytcal and smulaton results show that DM erforms servce dfferentaton over 80. and offers better guarantees n terms of throughut average servce tme and robablstc servce tme bounds for the flows havng small deadlnes. Moreover DM acheves farness between statons belongng to the same traffc category. Then we extended by smulaton the analytcal results obtaned for two traffc categores to dfferent traffc categores. Smulaton results showed that even f contendng statons belong to K traffc categores K > the DM olcy offers better QoS guarantees for hghest rorty statons. Fnally we consdered a smle mult-ho scenaro and concluded that factors lke routng messages or nterferences don t mact the behavor of the DM olcy and DM stll rovdes better QoS guarantees for statons wth short deadlnes. 9 REFERENCES [] G. Banch: erformance Analyss of the IEEE 80. Dstrbuted Coordnaton Functon IEEE J-SAC Vol. 8 N. 3 (March 000). [] H. Wu Y. eng K. Long S. Cheng J. Ma: erformance of Relable Transort rotocol over IEEE 80. Wreless LAN: Analyss and Enhancement In roceedngs of the IEEE INFOCOM`0 June 00. [3] H. ha Y. Kwon Y. Fang: erformance Analyss of IEEE 80. MAC rotocol n wreless LANs Wreless Comuter and Moble Comutng (004). [4] I. Aad and C. Castellucca Dfferentaton mechansms for IEEE 80. In roc. of IEEE Infocom 00 (Arl 00). [5] IEEE 80. WG: art : Wreless LAN Medum Access Control (MAC) and hyscal Layer (HY) secfcaton IEEE (999). [6] IEEE 80. WG Draft Sulement to art : Wreless Medum Access Control (MAC) and hyscal layer (HY) secfcatons: Medum Access Control (MAC) Enhancements for Qualty of Servce (QoS) IEEE 80.e/D3.0 (January 005). [7] J. Deng R. S. Chang: A rorty Scheme for IEEE 80. DCF Access Method IEICE Transactons n Communcatons vol. 8-B no. (January 999). [8] J.L. Sobrnho A.S. Krshnakumar: Real-tme traffc over the IEEE 80. medum access control layer Bell Labs Techncal Journal (996). [9] J. Y. T. Leung J. Whtehead: On the Comlexty of Fxed-rorty Schedulng of erodc Real-Tme Tasks erformance Evaluaton (Netherlands) (98). [0]K. Duffy D. Malone D. J. Leth: Modelng the 80. Dstrbuted Coordnaton Functon n Non-saturated Condtons IEEE/ACM Transactons on Networkng (TON) Vol (February 007) []L. Klenrock: Queung SystemsVol. : Theory Wley Interscence 976. []. Chatzmsos V. Vtsas A. C. Boucouvalas: Throughut and delay analyss of IEEE 80. rotocol n roceedngs of 00 IEEE 5th Internatonal Worksho on Networked Alances (00). [3].E. Engelstad O.N. Osterbo: Delay and Throughut Analyss of IEEE 80.e EDCA wth Starvaton redcton In roceedngs of the The IEEE Conference on Local Comuter Networks LCN 05 (005). [4].E. Engelstad O.N. Osterbo: Queueng Delay Analyss of 80.e EDCA roceedngs of The Thrd Annual Conference on Wreless On demand Network Systems and Servces (WONS 006) France (January 006). [5].E. Engelstad O.N. Osterbo: The Delay Dstrbuton of IEEE 80.e EDCA and 80. DCF n the roceedng of 5th IEEE Internatonal erformance Comutng and Communcatons Conference (ICCC 06) (Arl 006) USA. [6]The network smulator ns- htt:// [7]Y. Xao: erformance analyss of IEEE 80.e EDCF under saturaton condtons roceedngs of ICC ars France (June 004). [8]V. Kanoda C. L: Dstrbted rorty Schedulng and Medum Access n Ad-hoc Networks ACM Wreless Networks Volume 8 (November 00). Ubqutous Comutng - and Communcaton Journal - 6 -