Access Delay Analysis of IEEE DCF in the Presence of Hidden Stations

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1 Access Delay Analyss of IEEE 82. DCF n the Presence of Hdden tatons Fu-Y Hung and Ivan Marsc CAIP Center, ECE Deartent, Rutgers Unversty Pscataway, NJ {fuyhung, arsc}@ca.rutgers.edu Abstract In ths aer, we resent an analytcal odel to evaluate the hdden staton effect on the access delay of the IEEE 82. Dstrbuted Coordnaton Functon (DCF n both non-saturaton and saturaton condton. DCF s a rando channel-access schee based on Carrer ense Multle Access wth Collson Avodance (CMA/CA ethod and the exonental backoff rocedure to reduce acket collsons. However, hdden statons stll cause any collsons under CMA/CA ethod because statons cannot sense each other s transsson and often send ackets concurrently, resultng n sgnfcant erforance degradaton. Pror research has bult accurate access delay odel for 82. DCF. However, the hdden staton effect on the erforance has not been adeuately studed. Our odel generalzes the exstng work on access delay odelng of 82. DCF for both non-saturaton and saturaton condtons, under the hdden-staton effect. The erforance of our odel s evaluated by coarson wth ns-2 sulatons and they are found to agree. I. INTRODUCTION IEEE 82. [] s the ost oular standard used n reless Local Area Networks (LANs. The IEEE 82. Medu Access Control (MAC defnes two access ethods: the Dstrbuted Coordnaton Functon (DCF and the Pont Coordnaton Functon (PCF. The ollng-based PCF uses a vrtual carrer-sense echans aded by an access rorty echans to control the channel access. On the other hand, the contenton-based DCF uses a rando access schee where each staton has the rght to ntate ts transsson wthout nfrastructure suort. o, ths schee s useable not only n nfrastructure network confguratons but also n dstrbuted and self-organzed wreless networks. The suort for varous wreless networks has ade the DCF very oular. The basc access echans s a two-way handshakng ethod where the sender transts a data frae and the recever reles wth an acknowledgeent ( frae to confr a successful transsson. However, t unavodably suffers fro the hdden staton roble [2 4] because of ultle sultaneous transssons on the sae channel wthout any coordnator. In order to revent the nterference fro hdden statons, DCF ntroduces Reuest-To-end/ Clear-To-end (RT/CT access echans. RT/CT, whch s a four-way handshakng ethod, reserves the edu before transttng a data frae by transttng a RT frae and relyng a CT frae. The odelng of IEEE 82. has attracted a nuber of studes. Ref. [5] was the frst to derve a odel that ncororates the exonental backoff rocess nherent to 82. as a two densonal Markov chan. Ref. [6] follows the sae Markov chan odel and consders frae retry lts to avod overestatng the throughut of 82. as n [5]. Ref. [7] extends ths odel to evaluate the saturated throughut under the hdden staton effect. Refs. [8, 9] odfed ths odel to reresent the non-saturaton and saturaton condtons. On the other hand, an average servce te and jtter analyss n the saturated condton s derved n [] based on ths Markov chan odel. Ref. [] consders the data length and the nuber of backoff slot as rando varables. It rooses a robablty generatng functon (PGF for the access delay and nverts ths PGF to obtan an aroxate dstrbuton of the access delay. Refs. [2, 3] extend ths PGF work by consderng ore araeters as rando varables to derve ther PGFs and dstrbutons for the access delay. Pror research has atteted to buld an accurate access delay odel for 82. DCF. However, the hdden staton effect on the backoff schee has not been gven adeuate attenton. As wll be shown below, ths effect sgnfcantly ncreases the access delay, esecally for the basc access ethod n the saturated condton. In ths aer, we study the access delay of 82. DCF under non-saturaton and saturaton condtons n the resence of hdden statons for both basc and RT/CT access ethods based on the Markov chan odel and the PGF analyss. The rest of ths aer s organzed as follows. In secton II, we ntroduce the concet of vulnerable erod to study the effectveness of both basc and RT/CT access ethods n the resence of hdden statons. In secton III, we use a two-densonal Markov chan odel to calculate the acket transsson robablty n the vulnerable erod and the access delay n both non-saturaton and saturaton condton. In secton IV, we valdate the analytcal odel by coarng the nuercal results wth ns-2 sulaton [4]. Fnally, conclusons are resented n secton V. II. THE HIDDEN TATION EFFECT ON 82. DCF The DCF s the fundaental access ethod of the IEEE 82.. It s based on the CMA/CA and a backoff rocedure to reduce the collson robablty between ultle statons accessng the channel. The CMA/CA echans defnes two channel states: dle and busy. If a staton senses no transsson on the channel, t consders the channel state as dle; otherwse t consders the channel state as busy. hen a staton tres to access the channel, t enters the backoff rocedure that randoly chooses a backoff te n a range (, C wth a unfor robablty. The C s known as the nu contenton wndow sze. Durng the backoff rocedure, f the staton senses channel as dle ts ter decreents one backoff slot. If the channel s sensed as busy, /7/$ IEEE Ths full text aer was eer revewed at the drecton of IEEE Councatons ocety subject atter exerts for ublcaton n the IEEE GLOBECOM 27 roceedngs. Authorzed lcensed use lted to: Rutgers Unversty. Downloaded on Arl, 29 at 5:26 fro IEEE lore. Restrctons aly.

2 DIF IF DIF ource Backoff-ndow DATA - Destnaton Hdden taton Backoff-ndow Freeze Backoff Ter - -, (- - -, - -, , , - Vulnerable Perod Fg..The vulnerable erod for the hdden statons: Basc access ethod -, /, /, 2 /, -2, - DIF IF IF IF ource Backoff-ndow RT DATA - ', /ax ', ', 2 /ax ', ax -2 ', ax - Destnaton CT /ax /ax /ax Hdden taton Backoff-ndow Freeze Backoff Ter Vulnerable Perod Fg. 2.The vulnerable erod for the hdden statons: RT/CT access ethod /ax /ax,,, 2, ax -2 Fg. 3. Markov chan odel for backoff rocedure, ax- the ter s frozen. After the channel becoes dle agan, the ter resues fro the frozen slot and counts down the reanng backoff slots. After the ter fnshes the countdown, the staton accesses the channel agan. If the transsson fals, the staton reeats the backoff rocedure and doubles the contenton wndow sze. After every faled transsson, the exonental backoff echans doubles the contenton wndow sze u to a redefned axu range. However, f soe statons are hdden to each other so they cannot sense each other s transsson, they ay stakenly deterne the channel as dle and transt concurrently. The erod fro the end of the revous transsson untl an ongong transsson s detected s called the vulnerable erod. A. Hdden taton Effect on the Basc Access Method The basc access ethod s shown n Fg.. Any staton that can sense the transsson fro the source, called covered staton, wll deterne the channel as busy and defer ts own transssons for the duraton of the Network Allocaton Vector (NAV. The only ossble acket collson between the source and a covered staton haens f they fnsh ther backoff countdown sultaneously. The vulnerable erod for covered statons s one backoff slot long. However, the hdden statons do not sense the transsson fro the source untl they receve an, so they sense the channel as dle untl sensng the. If any one of these hdden statons coletes ts backoff rocedure before sensng the, t wll send another data frae to the destnaton, whch wll collde wth the data frae fro the exstng source. The vulnerable erod for hdden statons euals the length of a data frae. B. Hdden taton Effect on the RT/CT Access Method The RT/CT access ethod s shown n Fg. 2. As n the basc access ethod, the vulnerable erod for the covered statons s also one backoff slot long. The hdden statons wll set ther NAV after recevng the CT frae fro the destnaton, so the vulnerable erod for the hdden statons euals the length of the RT frae lus a IF erod. Unlke the basc access ethod, the vulnerable erod for hdden statons n RT/CT access ethod s a fxed length erod and s not related to the length of the data frae fro the source. III. THE ACCE DELAY MODEL The key contrbuton of ths aer s the cobned analytcal evaluaton of the access delay for both non-saturated and saturated condtons n the resence of hdden statons. A. Markov Chan Model of taton Transssons In the analyss, we assue the followng condtons: (a deal channel condton,.e., no cature effect; (b constant and ndeendent collson robablty of a acket transtted by each staton, regardless of the nuber of collsons already suffered; and (c fxed nuber of contendng statons. Let n denote the nuber of contendng statons. Let b(t be the stochastc rocess reresentng the backoff ter for a gven slot. As n [5], the key aroxaton n ths odel s that the robablty of a transtted acket colldng wth another acket s ndeendent of the staton s backoff stage s(t. o, the two-densonal rocess {s(t, b(t} can be odeled as a dscrete-te Markov chan, shown n Fg. 3, where s the axu backoff stage and s the backoff stage at whch the contenton wndow sze reaches the axu value, C ax, and reans at C ax after ths stage. (C n and (C ax. The C n s the nu contenton wndow sze. e set 5 n ths aer. Based on the 82. standard [], the contenton wndow, also called backoff wndow, ncreases exonentally fro C n to C ax. It can be reresented as 2 2 > The backoff states (, k for k (, n Fg. 3 reresent the ost-backoff stage. After a successful ( /7/$ IEEE Ths full text aer was eer revewed at the drecton of IEEE Councatons ocety subject atter exerts for ublcaton n the IEEE GLOBECOM 27 roceedngs. Authorzed lcensed use lted to: Rutgers Unversty. Downloaded on Arl, 29 at 5:26 fro IEEE lore. Restrctons aly.

3 (2 ( (, b 2 2 (2 2 (4 τ 2 V b, k k V V ( ( ( ( V ( ( 2 2 ( V V( ( V V ( ( ( ( V ( 2 (2 (2 2 (2P V V (2 ( ( 2 b, V ( ( ( b, < V,, (6, V > transsson, the staton resets ts C value to and erfors a rando backoff rocedure even f there are no endng ackets n the ueue. Ths ost backoff ensures that there s at least one backoff nterval between two consecutve transssons of a staton. e assue that each staton can buffer one acket and reresents the robablty that at least one acket wats for transsson durng a slot te. If, then the staton s n the saturaton condton and does not go to ost-backoff stage. In ths Markov chan, the transton robabltes are P(,, P (,, ( P (, k, k P(, k, k P (, k, k k ( ( P (, k, k, P(, k, k ( P(, k, k, P (, k, k k, P (, k, P (, k, k k, Let b,k l t P{s(t, b(t k}, (,, k (, be the statonary dstrbuton of the Markov chan. By usng the noralzaton condton for a statonary dstrbuton, we have (2 b, k b, k k k (3 Based on the chan regulartes, we can obtan b, n (4. The statonary robablty τ (that a staton transts a acket n a randoly chosen te slot, can be reresented as: τ b, b, (5 The statonary robablty τ 2 (that a staton transts a acket n a vulnerable erod, can be reresented as E. (6 where V s the vulnerable erod length n the unts of backoff slots. s the nu backoff stage at whch the backoff wndow sze s greater than V. For exale, f < V 2, then use 2 n E. (6. As already noted, τ s a secal case of τ 2 because τ can be consdered as the vulnerable erod wth the duraton of one slot te. e can verfy ths usng V and n the frst case of E. (6. In the statonary state, the collson robablty s the robablty that at least one covered staton transts n the sae backoff slot as the source, or at least one hdden staton transts n the vulnerable erod. Thus can be exressed as: n C n ( τ ( H τ 2 (7 where n C s nuber of the covered statons that ncludes the transttng staton tself, and n H s the nuber of the hdden statons. The total nuber of contendng statons, n, euals n n C n H. e solve the nonlnear Es. (4 (7 by nuercal ethod to obtan τ and τ 2. B. The Access Delay Analyss Let P tr be the robablty that there s at least one transsson n the consdered slot te. n P tr ( τ (8 The robablty of a successful transsson n the resence of hdden statons, P s, s the robablty that exactly one of n backlogged statons transts and none of ts covered staton /7/$ IEEE Ths full text aer was eer revewed at the drecton of IEEE Councatons ocety subject atter exerts for ublcaton n the IEEE GLOBECOM 27 roceedngs. Authorzed lcensed use lted to: Rutgers Unversty. Downloaded on Arl, 29 at 5:26 fro IEEE lore. Restrctons aly.

4 transts n the sae te slot and none of the hdden statons transts n the vulnerable erod nc n H nτ ( τ ( τ 2 P (9 Ptr The length of a slot te E can be reresented as E ( Ptr σ P Ptr T ( P Ptr T C ( where σ s the duraton of an ety backoff slot. The T and T C are the erod of te that the channel s sensed busy because of a successful transsson or a collson, resectvely. They are dfferent n the basc and RT/CT access ethods: T bas DATA δ IF δ DIF T bas C DATA δ _ Teout ( where DATA s the data frae length and δ s the roagaton delay. The _Teout IF DIF. For RT/CT access ethod, T and T C can be exressed as: RT δ IF CT δ IF DATA δ IF δ DIF (2 T C rts RT δ CT _ Teout where CT_Teout IF CT (2 σ. Let U be a rando varable wth a dscrete unfor dstrbuton Pr{ U k } k,,...(,,... (3 The accuulated backoff te B before a staton transts a acket successfully fro the th backoff stage or dscards t because of exceedng the retry lt can be reresented as U r TC,,... r B (4 U r TC r T rts The staton dscards the acket when the stage s reached. Hence, the robablty of a staton transttng a acket successfully at th stage or dscardng t at stage s (,,... (5 o the access delay D ncludng all backoff stages s D B T (6 In order to obtan the dstrbuton of the access delay, we derve the Probablty Generatng Functon (PGF of the access delay D(Z by z-transfor [ 3] T D ( Z B ( Z Z (7 where the B (Z can be reresented as ( Z U r ( Z Z B ( Z r ( Z U r ( Z Z r and E(Z can be reresented as TC TC,,... (8 tr tr T T ( P C Ptr Z σ (9 E ( Z ( P Z P P Z e nvert the PGF of the access delay nuercally to obtan ts dstrbuton. The aroxate dstrbuton of the access delay s valdated n next secton. IV. PERFORMANCE EVALUATION A. ulaton etu All the araeters used n the analytcal odel and the ns-2 sulaton are suarzed n Table I. Table I. yste araeters Transsson Rate Mbs Packet Payload 25 Bytes PHY header 92 bts RT 6 bts PHY header CT 2 bts PHY header 2 bts PHY header DIF 5 µs IF µs lot Te (σ 2 µs Proagaton Delay (δ µs C n 3 C ax 23 e use a rng toology that s coosed of one access ont located n the center of a rng and 6 statons unforly dstrbuted along the rng. The cature effect can be gnored n our toology because of eual dstance fro the access ont to all statons. The transsson range and carrer sensng ranges are set at 597 eters (. In ths study, we vary the rng daeter, defned as d, to obtan dfferent nuber of hdden statons n the 6-staton network: (a d 54 each staton can sense all the ackets fro the other 5 statons, so there s no hdden statons and there are 6 covered statons; (b d 6 hdden staton and 5 covered ones; (c d 63 3 hdden statons and 3 covered statons; (d d 68 5 hdden statons and covered ones. B. Model Valdaton and Access Delay Analyss Frst, we valdate the average access delay of our analytcal odel wth the ns-2 results for dfferent offered load n both basc and RT/CT access ethods, as shown n Fgs. 4 and 5. Based on the result, the access delay can be dvded nto three condtons: non-saturaton, transton and saturaton. In the non-saturaton condton, as the offered load ncreases, the access delay ncreases lnearly n both access ethods. Access delay values are alost the sae regardless of the nuber of hdden statons n the network. The hdden staton effect s nsgnfcant n ths condton. In the transton condton, the access delay jus fro ts non-saturated value to the saturated one. As the nuber of hdden staton ncreases, there s a hgher overshoot n the access delay curve. The analytcal access delay cannot cature the sulated result because we solve nonlnear Es. (4 (7 by nuercal ethod to get an aroxate analytcal result. In the saturaton condton, the access delay reans constant. Coarng ths value n both the basc and RT/CT access ethods, we can see that the basc access ethod s uch ore senstve to the hdden /7/$ IEEE Ths full text aer was eer revewed at the drecton of IEEE Councatons ocety subject atter exerts for ublcaton n the IEEE GLOBECOM 27 roceedngs. Authorzed lcensed use lted to: Rutgers Unversty. Downloaded on Arl, 29 at 5:26 fro IEEE lore. Restrctons aly.

5 Access delay (s hdden - odel 5 hdden - ns2 3 hdden - odel 3 hdden - ns2 hdden - odel hdden - ns2 hdden - odel hdden - ns2.5.5 Noralzed offered load Probablty No hdden - Model No Hdden - ns2 hdden - Model Hdden - ns2 3 hdden - Model 3 Hdden - ns2 5 hdden - Model 5 Hdden - ns No of Retranssson ( 7 dscard Probablty No hdden - Model No Hdden - ns2 hdden - Model Hdden - ns2 3 hdden - Model 3 Hdden - ns2 5 hdden - Model 5 Hdden - ns Aaccess Delay (s Fg. 4 Access delay versus noralzed offered load: Fg. 6 PMF of nuber of retry Fg. 8 PMF of the access delay Basc access ethod Basc access ethod Basc access ethod Access delay (s hdden - odel 5 hdden - ns2 3 hdden - odel 3 hdden - ns2 hdden - odel hdden - ns2 hdden - odel hdden - ns2.5.5 Noralzed offered load Probablty No hdden - odel No hdden - ns2 hdden - odel hdden - ns2 3 hdden - odel 3 hdden - ns2 5 hdden - odel 5 hdden - ns No of Retranssson ( 7 dscard Probablty.2 No hdden - odel. No hdden - ns2.2. hdden - odel hdden - ns2.2 3 hdden - odel. 3 hdden - ns hdden - odel 5 hdden - ns Aaccess Delay (s Fg. 5 Access delay versus noralzed offered load: Fg. 7 PMF of nuber of retry Fg. 9 PMF of the access delay RT/CT access ethod RT/CT access ethod RT/CT access ethod staton effect. As the nuber of hdden staton grows, the access delays n, 3 and 5 hdden staton cases are about 2.3, 5.5 and 3 tes of that n the case of no hdden statons, resectvely. nce the revous 82. DCF delay odels do not account for hdden statons, ther delays would corresond to the botto curves n Fgs. 4 and 5 (no hdden statons scenaro. Obvously, ths s nadeuate. e also study the Probablty Mass Functon (PMF of the nuber of retres before a successful transsson (Fg. 6 and 7 and access delay (Fgs. 8 and 9 n the saturaton condton. In the basc access ethod, as the nuber of hdden staton grows, fewer ackets can be transtted successfully n the frst attet and ore ackets wll be dscarded because of exceedng the retry lt (Fg. 6. The dstrbuton of the access delay (Fg.8 also shows ths tendency. The PMF s gettng flat and wdesread as the nuber of hdden statons ncreases. On the other hand, the RT/CT access ethod s ore robust to the hdden-staton effect. The PMF charts for dfferent network scenaros are slar (Fgs. 7 and 9. V. CONCLUION In ths aer, we derved an analytcal odel for the access delay of the basc and RT/CT access ethods n IEEE 82. DCF under both the non-saturaton and saturaton condton n the resence of hdden statons. The roosed odel s n good agreeent wth ns-2 sulatons and, thus, can be used to estate accurately the access delay. The revous work can be consdered as a secal case of our odel, wth zero hdden statons. REFERENCE [] IEEE tandard for reless LAN Medu Access Control (MAC and Physcal Layer (PHY secfcatons, IEEE 82.b, 999. [2] A.. Tanenbau, Couter Networks. 3rd Edton, Prentce Hall, Uer addle Rver, NJ, 996. [3] L. Klenrock and F. Tobag, Packet swtchng n rado channels, Part II The hdden ternal roble n carrer sense ultle access and the busy tone soluton, IEEE Trans. Co., vol. COM-23, no. 2, , Dec [4] H.. Chhaya and. Guta, Perforance odelng of asynchronous data transfer ethods of IEEE 82. MAC rotocol, reless Networks, vol. 3, , 997. [5] G. Banch, Perforance analyss of the IEEE 82. dstrbuted coordnaton functon, IEEE J. on elected Areas n Co., vol. 8, no. 3, , Mar. 2. [6] H. u, Y. Peng, K. Long,. Cheng, and J. Ma, Perforance of relable transort rotocol over IEEE 82. wreless LAN: Analyss and enhanceent, Proc. IEEE INFOCOM, vol. 2, , 22. [7] F. Hung, Pa and I. Marsc, Perforance Modelng and Analyss of the IEEE 82. Dstrbuton Coordnaton Functon n Presence of Hdden tatons, IEEE/AFCEA MILCOM, Oct. 26. [8] K. Duffy, D. Malone and D. Leth, Modelng the 82. Dstrbuted Coordnaton Functon n Non-saturated Condtons, IEEE Co. Letters. Vol. 9, No. 8, 75-77, Aug. 25. [9] P.E. Engelstad and O.N. Østerbø, Non-aturaton and aturaton Analyss of IEEE 82.e EDCA wth tarvaton Predcton, Proc. ACM MM 25, Oct. 25. [] M. Carvalho and J.J. Garca-Luna-Aceves, Delay Analyss of IEEE 82. n ngle-ho Networks, Proc. IEEE ICNP 3, Nov. 23. [] H. Zha, Y. Kwon, and Y. Fang, Perforance analyss of IEEE 82. MAC rotocols n wreless LANs, n Proc. reless Coun. And Moble Coutng 24, [2] O. Tckoo and B. kdar, Queueng analyss and delay tgaton n IEEE 82. rando access MAC based wreless networks, n Proc. IEEE INFOCOM 24, [3] H. Vu and T. akura, Accurate delay dstrbuton for IEEE 82. DCF, n IEEE Councatons Letters, Vol., NO. 4, Ar. 26. [4] The ns Manual, htt:// /7/$ IEEE Ths full text aer was eer revewed at the drecton of IEEE Councatons ocety subject atter exerts for ublcaton n the IEEE GLOBECOM 27 roceedngs. Authorzed lcensed use lted to: Rutgers Unversty. Downloaded on Arl, 29 at 5:26 fro IEEE lore. Restrctons aly.