Performance Evaluation of IEEE e based on ON-OFF Traffic Model I. Papapanagiotou PhD. Student

Transcription

1 erformance Evaluaton of IEEE 82.e based on ON-OFF Traffc Model I. apapanagotou hd. Student Wreless Telecommuncaton Laboratory Unversty of atras atras Greece papapanag@upnet.gr J.S. Vardakas hd. Student Wre Communcatons Laboratory Unversty of atras atras Greece jvardakas@wcl.ee.upatras.gr G.S. aschos Researcher VTT Dgtalo o Box 244 VTT Fnland gpasxos@gmal.com M.D. Logothets Assocate rofessor Wre Communcatons Laboratory Unversty of atras atras Greece m-logo@wcl.ee.upatras.gr S.A. Kotsopoulos rofessor Wreless Telecommuncaton Laboratory Unversty of atras atras Greece kotsop@ece.upatras.gr ABSTRACT We nvestgate the performance of the IEEE 82.e whle emphaszng on the end-to-end delay performance. In our MAC delay analyss we are based on elementary condtonal probabltes avodng the complex Markov Chans method. For a thoroughly study of the MAC delay we take the Z- transform of the backoff duraton n order to provde hgher moments of the MAC delay dstrbuton. The frst moment corresponds to the mean MAC delay whle the second moment to the Standard Devaton of the MAC delay whch depcts the jtter. We also estmate the robablty Mass Functon (MF) of the MAC delay through the Lattce osson Algorthm. For the queung delay we consder a queue for each Access Category (AC) wth one common server and an nput process whch s descrbed by an O -OFF model depctng the bursty nature of traffc. The servce tme follows the MAC delay dstrbuton. Analyzng ths queue we provde results both for saturated and non-saturated channel condton. The end-toend delay s estmated by the sum of queung and MAC delay. The analytcal results are valdated through smulaton. Keywords IEEE 82.e QoS MAC delay queung delay end-to-end delay.. I TRODUCTIO Nowadays WLANs have become very popular and meet a broad range of applcatons based on the man protocol standard for Wreless Local Area Communcatons IEEE 82. [] whch has turned out to be a major factor of growth n the network ndustry. Due to heterogeneous applcatons n the Internet wth dverse end-to-end delay requrements the IEEE has certfed a newer IEEE 82. verson the IEEE 82.e for provdng QoS (Qualty of Servce) [2]. In the IEEE 82.e a Hydrd Coordnaton Functon (HCF) s ntroduced to control the medum access. Two dfferent access methods are defned based on whether the medum access s centrally or dstrbuted controlled. The central MAC procedure s called HCCA (HCF Controlled Channel Access) whle the dstrbuted s called EDCA (Enhanced Dstrbuted Channel Access). The performance analyss of these standards s wdely spread n the research communty not only for the legacy 82. [3] [4] but also for the 82.e [5][6]. Most of the analyses tend to provde analytcal results based on mean values and saturaton condtons of the channel by formulatng large Markov Chans. Some few works exst whch provde analyss for non-saturaton condtons by studyng the queues of the statons [7] and others wth addtonal enhancements [8]. In ths paper we analyzed both the MAC and the queung delay for the IEEE 82.e. Startng wth the MAC delay the proposed performance analyss s avant-garde due to the fact that we do not use complex solutons of Markov Chans but we base the analyss on elementary condtonal probabltes [9] [] whch are defned for each Access Category (AC) separately. Moreover n order to thoroughly study the MAC delay we do not provde only mean values but we take the Z-transform of the backoff duraton n order to provde hgher moments of the MAC delay dstrbuton. The use of the Z-transform s done due to the fact that the standard [2] s based on tme slots rather than contnuous tme. More precsely from the frst and second dervatves of the Z-transform of the backoff duraton the mean and the Standard Devaton (SD) of the MAC delay s provded respectvely. It s readly seen that the Varance depcts the jtter that a multmeda applcaton faces n the MAC layer. Afterwards we am at estmatng the robablty Mass Functon (MF) of the MAC delay. To ths end we need the nverse transform of the Z-transform of the backoff duraton []. Ths s acheved approxmately through the Lattce osson Algorthm [2]. The MF of the MAC delay depcts the exact performance of the Backoff Exponental Algorthm of IEEE 82. n correlaton wth the QoS features of the IEEE 82.e.

2 To analyze the queung delay we consder a queue for each AC wth one common server and an nput process that s descrbed by an ON-OFF model. The choce for such an nput was made n order to express the bursty character of multmeda traffc. As far as the servce-tme s concerned t follows the MAC delay dstrbuton wth mean value the mean MAC delay. Wth the ad of ths queue we can provde results both for saturated and nonsaturated channel condton as a unfed model. It s readly seen that when λ/µ< the model s transformed to a non-saturaton analyss and n any other case to a saturaton analyss. Havng determned the queung delay the total mean end-to-end delay s estmated by the sum of mean queung and mean MAC delay. The rest of the paper s organzed n the followng way: Secton 2 provdes a bref overvew of EDCA access method. Secton 3 presents the proposed erformance Analyss of the IEEE 82.e both n terms of throughput and delay (wth emphass to the latter). Secton 4 valdates the accuracy of the analytcal results through smulatons made by Opnet Modeler 2 [3]. Fnally concludng remarks are gven n Secton OVERVIEW OF EDCA The IEEE 82.e has been certfed as a QoS extenson of the IEEE 82.. In the followng paper we nvestgate the case of the Enhanced Dstrbuted Coordnaton Access (EDCA) mechansm n whch there s not any central coordnator and the network s n ad-hoc mode. The QoS provsonng s done va the use of four Access Categores ts one havng dfferent EDCA parameters; Arbtraton Inter Frame Space (AIFS) Contenton Wndow (CW) and Transmsson Opportunty (TxO) lmts. In our case TxO s not studed explctly. In 82.e standard f there s a packet ready to be transmtted EDCA must sense the channel dle and complete an AIFS nterval pror to startng the transmsson. In order to determne a dfferentaton of access probabltes between ACs the AIFS[] nterval has dfferent values for each Access Category (AC) where 3. Smlarly to the legacy of 82. CW[] stands for the backoff delay that the packet encounters. In 82.e the CW mn [] and CW max [] values are dfferently set so as to have lower probablty of delay n delay-prone AC s for example those that serve VoI/Vdeo. In EDCA each AC functons ts backoff counter ndependently from the other AC s of the same staton but ts access probablty has a correlaton. An nternal collson handler s run by grantng access to the AC wth the hghest prorty. All these are analysed n detal n [2] and [7]. 3. erformance Analyss of the IEEE 82.e In the followng we suppose n statons n each AC separately tryng to contend for the channel access. The channel s consdered perfect and there are not any hdden node problems. 3. Transmsson robablty The performance analyss s verfed by supposng smple probabltes than dffcult soluton of Markov Chans. We can envson the Bnary Exponental Backoff (BEB) Algorthm as a functon of two coordnates (xy) as shown n Fg. where x represents the backoff stage (m s the AC s retry [ ] m count) and y [ CW x ] represents the value of the backoff counter at the backoff stage x. In order for an AC to be n a Fgure : Depcton of Backoff States specfc x f poston a number of collsons have happened n the prevous x f j where j [ f ] and x f. Thus the event that the staton s n poston x s gven by the geometrc seres whch s the number of collson n a geometrc progresson: ( p ) x ( ) p x () m + p The probablty that a staton transmts whle beng n the backoff stage x s obtaned from the mean value of the unform dstrbuton that each y s chosen plus a tme slot that t s needed to leave the specfc y coordnate and go to another y of a dfferent x or transmt. ( y) where x. Backoff counter y (2) + E [ BD] y E[ BD] x s the average value of the backoff counter at stage In order to fnd the transmsson probablty the above equatons should be dvded and summed over a regon x : of [ ] m τ m (3) ( x) ( ) x y 3.2 Accurate MAC Delay Dstrbuton To fnd the accurate MAC delay dstrbuton we need to know the mean value the varance and the robablty Mass Functon (MF). The frst two can be easly found from the frst and second moments of the dscrete Z-transform of the Backoff Duraton snce the BEB Algorthm s slotted whereas the thrd one can be found by the Lattce-osson algorthm. The nterrupton of the backoff perod of the tagged staton can occur by two dfferent events and s analyzed as follows. The frst

3 one s the collson of two or more AC s and the second s the transmsson of a sngle AC other than the tagged one. In both of them we take nto account. The probablty of a slot of the tagged staton to be nterrupted from the transmsson of any other staton (one or more) s gven by: p n ( ) ( π ) τ ( τ ) n (4) z> where π s the probablty that the AC s queue s empty. The case where π refers to saturated condtons of the channel whereas n any other case wth < π < refers to non-saturated condtons. The probablty p that the tagged staton s nterrupted by the transmsson of a sngle staton (one exactly) s gven by: n ( ) 2 ( π ) τ ( τ ) n n p ' τ (5) z> Moreover the probablty that the channel s busy s defned as pb n ( τ ) (6) The probabltes that the slot s nterrupted by a successful transmsson or a collson of another staton/s are respectvely gven by: ( successful transmsson slot s nterrupted) p s p p p p ( collson AC slot s nterrupted) pc (8) p Accordng to [9] there s a probablty that the staton wll defntely transmt another packet after a successful transmsson. Ths occurs when n the second transmsson chooses a backoff value equals to zero. Hence the Z-transform of the transmsson perod and the collson perod are respectvely gven by: T Z s S (9) T Z c C () The values of T s and T c can be found from [5]. In order to decrease the backoff process the channel must not be nterrupted and multpled by the respectve tme of the dle slot whereas the probablty to stay at the same state s the sum of two multplcatons where the staton stays at the same state. Thus the robablty Generatng Functon (GF) of each state s gven by: Dx y p σ ( p) Z S + p C ( p ) s c (7) () However the backoff duraton s not doubled after m tmes and stays at the same value for the remanng backoff stages: Dx CWx Dx y CW y x Dm x m m < x m Thus for each x the backoff duraton s gven by: BD + ( ) ( ) ( ) x Z p S Z ( p C ) D m + ( ( )) p C Z D ( z) m f m x f f x f. + (2) (3) The frst term of the second part of (3) sgnfes the transmsson delay multpled by the delay encountered n the prevous x and y stages whereas the second term s the delay of the droppng packet whch has encountered n all x collsons. The mean value E[M ] and the varance Var[M ] of the MAC delay can be derved by takng the dervatve of (3) wth respect to Z: E [ M ] BD Z (4) ( BD ) 2 2 Var ( M ) BD Z + BD Z Z (5) where the prme ndcates the dervatve. In order to calculate the GF (robablty Generatng Functon) of the MAC delay the Z-transform of the delay can also be expressed as: k BD d k Z (6) k The goal s to calculate d k whch expresses the MF of the backoff duraton of each AC. A method that gves the nverse Z- transform wth a predefned error bound s the Lattce-osson Algorthm [2] whch s vald for d k. However n the stuaton of BD (Z) d k s a MF and thus valdates the above method. Thus the MF s: 2k ( ) h ( ) j h / k Re BD ( re π d k ) k 2kr h (7) where Re(BD (Z)) stands for the real part of the complex BD (Z). Eq. (7) s derved by ntegraton of BD (Z) over a crcle wth radus r where <r<. For practcal reasons we suppose that the predefned approxmaton error s γ / 2k we let r γ [2]. k r 2 therefore to have accuracy

4 3.3 Queung Delay End-to-End Delay The average end-to-end packet delay can be calculated as the sum of the mean MAC delay E[M ] and the queung delay E[Q ]. Such a sum s possble due to the lnear characterstcs of the mean values. We consder that each AC s a dscrete-tme queung system wth the wreless channel as the sngle server and nfnte buffer capacty. In order to descrbe the arrval procedure we consder a two-state Markov chan; the arrvals are modeled by an ON-OFF source shown n Fg.2. The parameters q and q 2 are the probabltes that the Markov chan remans n states ON and OFF respectvely. Calls arrve n the queue for each tme slot the system s n state ON; the arrval rate s denoted λ. Every transton of the queue s done n a tme slot as defned n the MAC layer. The probablty of two consecutve arrvals s denoted by f q where f n s the nter-arrval tme dstrbuton. Smlarly followng an arrval the probablty that the system s n state OFF and jumps to the state ON s f 2 ( q)( q2). Subsequently the general expresson of the nter-arrval dstrbuton s ([4]): λ ( π ) λ µ π (24) µ By usng Lttle s theorem and (2) we calculate the mean queue sze and the mean watng tme whch are respectvely gven by: ξ λ [ ] E S lπ l (25) ρ µ ( ρ) l E[ S ] E[ Q ] (26) λ µ ( ρ) Fnally the average end-to-end packet delay E[D ] s gven by: [ D ] E[ M ] E[ Q ] E + (27) ( q ) ( ) n f n n 2 (8) q q2 q2 n> The probablty generatng functon (GF) s gven by ([4]): 2 z F ( z) qz+ ( q )( q2) (9) q2z and the mean nter-arrval tme can be calculated as: df ( z) dz 2 q q q z 2 2 λ The statonary queue sze dstrbuton (2) π m s n the form ([4]): ξ m π m m- (2) ξ (-ρ ) ρ m where ξ s a constant and ρ s the unque root of the equaton: z µ z+ (-µ )) (22) F ( where µ s the mean servce tme of the queue of the AC and equals to the mean MAC delay. Solvng equaton (2) we fnd that: µ ρ (23) µ µ ( q q2) + q2 Followng [4] by equatng the mean probablty of the arrval to the mean probablty of departure we fnd that Fgure 2: State transton dagram of the O -OFF arrval process. 3.4 Throughput Analyss In order to fnd the throughput of our analyss the followng formula s defned S dle σ + S [ ] 3 ι E L T S S + T c c where the transmsson probablty s (28) n S τ ( τ ) ( τ k (29) k ) The probablty that the channel s dle s defned as n dle ( τ ) (3) Smlarly the collson probablty s defned as the nverse probablty of the sum of the dle and successful probabltes. Addtonally E[L] s the mean packet length whch s equal to 24 bytes n our case n order to be lower from the TxO and fragmentaton threshold [2]. The rest are equally defned from [5]. 4. EVALUATIO The analytcal results are defned both under saturaton and nonsaturaton condtons of the channel. In order to valdate the mathematcal results Opnet Modeler 2 was used whch

5 mplements the exact model of the IEEE 82.e. The smulaton parameters ncluded error free channel a packet generator wth mean packet length of 24 bytes and basc bt rate (Mbps). Nodes are equally dstrbuted to every class. In the followng results are provded for the two upper classes named as AC and AC. The other two classes are omtted due to the unmportance of ther role. Background and Best Effort traffc whch are servced by these two lower classes are nether delay or prone nor requre specfc throughput. In Fg.3 throughput results are provded for saturaton condtons of channel and for both access mechansms (Basc and RTS/CTS). Smulaton results are smlar to the analytcal ones whch prove the accuracy of our analyss. Moreover t s readly seen that the throughput performance of the network s hgher when RTS/CTS type of traffc s used regardng both ACs. In Fg.4 the End-To-End to delay of the Backoff Exponental Algorthm s gven as the sum of the mean values of MAC delay and Queung delay. It s easly proven that such as a summaton s possble; although as metrcs they are correlated due to lnearty nature of the mean value operator. In order to fnd the mean value the frst dervatve of the Z-transform of the MAC delay s taken as shown n formula (4). Smlarly we show n Fg.5 that the varance of the MAC delay as second dervatve of the Z-transform s provded whch depcts the jtter nature of the MAC delay. Such a metrc s useful n order to prove that possble queues or admsson control s possble to the IEEE 82.e so as to overcome such an effect. In Fg. 6 the End-To-End delay s shown but for non-saturaton condton of the channel and for basc access method for both upper classes. For ths reason we have used varable traffc ntensty wth also varable number of nodes of each class. Thus the 3D graphcal representaton gves a vew of the performance of the End-To-End delay. From the fgures the End-To-End delay seems to be lnear to both traffc ntensty and Number of Nodes. Moreover the ncrease n hgher loads for varable number of statons s much hgher over that when there s small traffc load especally for AC. In Fg.7 the End-To-End s calculated for RTS/CTS access method. Except for the much smaller values of delay the varaton between saturaton and non-saturaton seems to be very small thus producng lower jtter when ON-OFF traffc s produced wth hgh probablty of transtons. Overall the performance of the standard under RTS/CTS although ncreases the load of the network but serves the packets much faster and wth lower values of delay and jtter. It s very nterestng to note the varablty of the delay when movng from non-saturaton to saturaton condtons. Such transtons can easly be solved wth RTS/CTS access method makes easer the access to the channel from the MAC layer. Fgure 3: Throughput for both access mechansms compared to smulaton results. Fgure 4: Mean End-To-End delay as the sum of the Mean MAC (frst dervatve of Z-transform) and Queung Delay Fgure 5: Varance of the MAC delay as a second dervatve of Z-transform for both access mechansms

6 supported by the research program ENED-23 Greek Mnstry of Development (GSRT). Fgure 6: End-To-End Delay for varable traffc ntensty ρ for AC AC and Basc Access Method Fgure 7: End-To-End Delay for varable traffc ntensty ρ for AC AC and RTS/CTS Access Method Table. EDCA parameters AC3 AC2 AC AC Applcaton VoI Vdeo Best-Effort Backround CW mn CW max AIFS SIFS+2 SIFS+2 SIFS+3 SIFS+7 5. CO CLUSIO The performance of the IEEE 82.e MAC layer s extensvely nvestgated regardng the analyss of the delay. We have used elementary condtonal probabltes n order to calculate the Mean MAC delay Jtter End-to-End delay and GF of the MAC delay of each AC. From the analyss the correlaton among ACs seems to affect the total delay. There s a great part of nformaton beng depcted by the MF of the delay regardng the general performance of the Backoff Exponental Algorthm wth dscrete applcatons. All these are combned wth an ON-OFF queue (ON/OFF traffc model s wdely used model for voce and telnet traffc) representng closely the varablty of the multmeda applcatons. Our analyss s valdated by smulaton results through Opnet Modeler. In fact some key ponts are left for future work regardng fnte queue length and separate types of queues n each AC. 6. ACK OWLEDGME TS The authors would lke to thank rofessor Dmtrs Toumpakars for hs valuable help n the calculaton of the Z-transform. Work 7. REFERE CES [] IEEE 82. WG. Internatonal standard for nformaton technology-local and metropoltan area networks part : Wreless LAN MAC and HY specfcatons 999 [2] IEEE 82.e WG Medum Access Control (MAC) Enhancements for Qualty of Servce (QoS) 82.e D.3 (Fnal) July 25 [3] Banch G. "erformance Analyss of the IEEE 82. Dstrbuted Coordnaton Functon" IEEE Journal on Selected Areas n Communcatons vol.8 No.3 (2) [4] Foh C. H. and Tantra J. W. "Comments on IEEE 82. Saturaton Throughput Analyss wth Freezng of Backoff Counters" IEEE Communcatons Letters Vol. 9 No. 2 (Feb. 25) pp [5] Y. Xao "erformance Analyss of the 82.e EDCF under Saturaton Condton" n roc. Of IEEE ICC 24 ars France 24. [6] J. Hu and M. Devetskots "A Unfed Model for the erformance Analyss of IEEE 82.e EDCA" IEEE Transactons on Communcatons Vol. 53 No.9 September 25. [7] Engelstad.E. and Osterbo O.N. "The Delay Dstrbuton of IEEE 82.e EDCA and 82. DCF" In roc. of the 25 th IEEE ICCC 26 Arzona USA Aprl [8] G. S. aschos I. apapanagotou S.A. Kotsopoulos and G. Karagannds "A new MAC protocol for supportng Qualty of Servce n 82. Wreless LA s" Eurasp Journal on Wreless Communcatons and Networkng Vol.6 Artcle ID [9] Banch G. and Tnnrello I. "Remarks on IEEE 82. DCF erformance Analyss" IEEE Communcatons Letters Vol. 9 No. 8(Aug. 25) [] J.S. Vardakas I. apapanagotou M.D. Logothets and S.A. Kotsopoulos "End-to-End Delay Analyss of the IEEE 82. Dstrbuted Coordnaton Functon" ICIM 27 Slcon Valley USA on July [] A. G. Ramm "Inverse roblems mathematcal and analytcal technques wth applcatons to engneerng" Sprnger Boston USA 25. [2] Abbate J. and Whtt W. " umercal nverson of probablty generatng functons" Operatons Research Letters 2 Oct [3] [4] I. Elhanany and D. Sadot "erformance analyss of a robust schedulng algorthm for scalable nput-queued swtches" n roc. Of IEEE ICC 23 Anchorage Alaska USA on May