Performance of the IEEE e Sleep Mode Mechanism in the Presence of Bidirectional Traffic

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1 Performance of the EEE e Sleep Mode Mechansm n the Presence of Bdrectonal Traffc Koen De Turck, Sergey Andreev 1, Stjn De Vuyst, Deter Fems, Sabne Wttevrongel and Herwg Bruneel Ghent Unversty, Department of Telecommuncatons and nformaton Processng Abstract We refne exstng performance studes of the WMAX sleep mode operaton to take nto account uplnk as well as downlnk traffc. Ths as opposed to prevous studes whch neglected the nfluence of uplnk traffc. We obtan numercally effcent procedures to compute both delay and energy effcency characterstcs. A test scenaro wth an ndvdual Subscrber nternet traffc model n both drectons shows that even a small amount of uplnk traffc has a profound effect on the system performance.. NTRODUTON The EEE e standard (WMAX) [1] s an emergng standard that has the potental to become the major standard for wreless communcaton n the near future. t regulates the communcaton between moble statons (MS) and base statons () n a metropoltan area wreless network. Energysavng mechansms n wreless communcatons are currently a hot topc. Short battery lfe s one of the man mpedments to a more wdespread use of wreless devces. Hence, understandably, a lot of research s drected at solvng or at least lessenng ths problem. n the frst place, ths can be done by makng more effcent batteres, but lately there s also a lot of nterest n ncludng energy-savng measures n the communcaton protocols themselves. On that account, t s no wonder that the WMAX commttee has opted to ncorporate varous energy-savng elements whch are commonly referred to as sleep mode and dle mode. Power savng s generally acheved by turnng off parts of the MS n a controlled manner when there s nether traffc from the MS (uplnk traffc) nor to the MS (downlnk traffc). Whereas a MS n sleep mode s stll regstered to a and stll performs hand-off procedures, dle mode operaton (whch s optonal n current WMAX standards) goes further and allows the MS to be completely swtched off and unregstered wth any, whle stll recevng broadcast traffc. n ths paper, we consder manly the sleep mode mechansm, n whch the MS turns tself off for predetermned perods of tme whch are negotated wth the. These perods are often referred to as sleep wndows. Three sleep mode classes are defned by the WMAX standard. When n Sleep Mode lass, the sleep wndow s progressvely doubled n sze from a prenegotated mnmum to a prenegotated 1 Sergey Andreev was on a research vst at Ghent Unversty durng the realzaton of ths work. He s afflated wth the Sant-Petersburg State Unversty of Aerospace nstrumentaton. maxmum value. Havng reached the maxmum sleep wndow length, ths sleep wndow s repeated ncessantly, untl traffc arrves. Ths class s consdered to be sutable for best-effort and non-real-tme traffc. lass features fxed-length sleep wndows, that s the same sleep wndow sze s repeated contnuously untl there s uplnk or downlnk traffc to be transmtted. Ths class s typcally employed for UGS (unsollcted grant servces) traffc. Fnally, class negotates only a one-tme sleep perod. Ths s typcally used for management traffc, when the MS knows when the next traffc s to be expected. Although class s the most nterestng from a modelng pont of vew (and wll as such get the most attenton), the analyss n ths paper s general enough to encompass all three classes. That s, n our model we assume that a general sequence of sleep wndow szes t, 1, has been negotated between MS and. We furthermore assume that ths sequence s kept fxed durng the entre operaton of the system, nstead of beng negotated. Sleep mode operaton has receved qute a lot of nterest lately from the performance modelng communty. n [2], the average energy consumpton of the MS s obtaned n case of downlnk traffc only, as well as an approxmate expresson for the mean packet delay. The energy consumpton of the MS n case of both downlnk and uplnk traffc s consdered n [3]. Both [2] and [3] model the ncomng (and outgong) traffc as a Posson process. An accurate assessment of the delay experenced at the buffer however, requres a queueng model. For EEE e, n [4] the buffer s modeled as a contnuous-tme fnte-capacty queue wth a Posson arrval process and determnstc servce tmes. A sem-markov chan analyss leads to expressons for the mean packet delay and the mean energy consumpton by the MS. The analyss n [5] s based on an M/G/1/K queueng model wth multple vacatons and exhaustve servce, where the vacatons represent the sleep perods. Smlar work can also be found n [6], where the length of a vacaton s assumed to depend on the prevous vacaton length. n [7], the sleep mode operaton n ellular Dgtal Packet Data (DPD) servces s evaluated. The dfference wth EEE e s that the subsequent sleep perods do not ncrease n length. The system can thus be modeled as a queueng system wth multple vacatons and exceptonal frst vacaton. The loss probablty n both [5] and [7] s obtaned as well. A smulaton study of DPD

2 sleep mode performance s found n [8]. An alternatve to the exponental ncrease of the sleep perod lengths s evaluated by smulaton n [9]. Fnally, n our prevous work on the sleep mode mechansm [11], we consdered a general D-BMAP arrval process, and we found that traffc correlaton, whch was htherto neglected n almost every study, has an mportant nfluence on the sleep mode performance. n the present paper, we nvestgate how the presence of uplnk traffc affects the performance of the sleep mode operaton, whch s another aspect that has receved lttle attenton n exstng studes. n fact, only n [3], uplnk traffc has thus far been gven attenton, although n that paper t was restrcted to Possonan traffc only. The nfluence of uplnk traffc s consderable, as the MS mmedately ceases the sleep mode operaton whenever there s uplnk traffc to be transmtted. Thus, durng uplnk transmsson, no extra sleep mode delay s experenced by ncomng downlnk traffc (but nether s there any power savng, as the antenna s already swtched on). We model the uplnk actvty by a fnte but otherwse general Markovan background process. The structure of ths paper s as follows. n Secton, we expound on the detals of the model. The analyss s spelled out n Secton. We show how to employ our analyss for a realstc WMAX scenaro n Secton V together wth some numercal results. Fnally, we draw some conclusons n Secton V.. MODEL We model the buffer n the base staton (from now on denoted as smply the buffer ) as a dscrete-tme queue wth nfnte capacty and a frst-come-frst-served (FFS) server dscplne. Ths buffer models the traffc n the downlnk drecton (.e. from the base staton to the moble staton). A sample evoluton of the system s shown n Fgure 1. B A A A M B A A S 3 B A A A A MS B B A A A S 3 MS Fg. 1. The bdrectonal sleep mode model at work over 90 slots. The sleep perod lengths are t 1 = 2, t 2 = 4, t 3 = 6, t 4 = t max = 8. The specal sets of nstants A, B,,, and S n are ndcated. Durng each slot, packets arrve n the buffer n batches accordng to an arrval process that s detaled later on. The servce tmes of the packets (.e. the tmes needed to transmt a packet to the MS) are consdered to be ndependent and have probablty generatng functon (pgf) S(z). = Pr[s = ]z. Durng the course of our analyss we refer to slots durng whch there s uplnk traffc as actve ; the rest of the slots are called passve. Both the uplnk traffc and the downlnk traffc are modulated by the same (background) Markov chan wth M phases, characterzed by transton matrx P, wth entres as follows: [P] j. = Pr[ϕk = j ϕ k 1 = ], (1) where ϕ k s the random varable that denotes the phase (or background state) at tme nstant k. The probablty that a slot s actve s phase dependent; durng phase, ths probablty s q. The dstrbuton of the number of arrvals s also modulated by the background Markov chan. The pgf of the batch sze durng phase s gven by A (z). For convenence, we defne three dagonal matrces wth entres as follows: [Q] j j q, [Q] j j (1 q ), [A(z)] j j A (z), (2) where the notaton δj denotes Kronecker s delta. Note that ths scheme s very versatle and permts the uplnk traffc to be correlated to the downlnk traffc. The load ρ s defned as the average number E[a] of packet arrvals per slot tmes the average servce duraton E[s]. The system s stable f the condton ρ < 1 s fulflled. When the queue s empty and the system s actve, the operaton s not dfferent from usual queueng models: the server resumes work n the slot mmedately after the frst packet arrval. However, when the buffer becomes empty and the system s passve, t enters sleep mode: an nternal tmer s then started and the server awakes to check the queue content after a sleep perod of t 1 tme slots. When upon awakng the server fnds that there are stll no packets, t goes to sleep agan, ths tme for a sleep perod of t 2 slots. The next sleep perod would be of length t 3, and so on. n general, t n, n 1, denotes the length (expressed n slots) of the nth sleep perod after the queue has become empty. f after a sleep perod, the server fnds a non-empty queue, t serves all packets present at that pont and also all new packets that arrve whle the server s workng, untl the queue becomes empty agan and the whole procedure s repeated. When the system becomes actve durng a sleep perod, sleep mode s mmedately abandoned, and the system s ready to serve ncomng packets mmedately. Note that, when the system becomes passve agan whle the buffer s stll empty, sleep mode s resumed, but startng agan wth a sleep perod of length t 1, and so on. Let us agree upon some termnology: the system alternates busy perods (durng whch the downlnk traffc s beng processed) wth dle perods. dle perods consst of sleep perods and dle but actve perods. Note that some of our termnology s standard n queueng theory, but may have another meanng n the EEE communty. For example, the term

3 dle perod s farly standard queueng theory termnology but should not be confounded wth the dle-mode mechansm of EEE WMAX. Secondly, we have opted for the neutral term slots but wll explan n Secton V that the most natural translaton nto a WMAX context s a WMAX frame. Lastly, the sleep perods we consder nclude the lstenng ntervals at the end. Hence, sleep perods n ths paper, are WMAX sleep ntervals plus the correspondng lstenng nterval.. ANALYSS We am to determne the vector generatng functon U(z) of the buffer content durng random slots. We do so by ntroducng event tags at specal tme nstants, and subsequently fndng relatonshps of the statonary dstrbuton of the buffer content at such tagged slots. For our frst set of specal tme nstants we look nsde dle perods. We mark the begnnng of an dle perod wth tag, the begnnng of the nth sleep perod by S n, n > 0, and actve but dle tme nstants by event tag A. Note that, necessarly, the buffer at such tme nstants s empty, and hence, the equlbrum state durng such tme nstants conssts only of the phase varable. The probablty vectors u, u A and u Sn have entres defned as follows: [u ] j. = Pr[ϕ = j, ]. (3) The other vectors are defned analogously. We state three relatonshps that lead to formulas nvolvng these probablty vectors. A. A tme nstant s marked by tag (.e. frst slot of the frst sleep perod) f one of two (mutually exclusve) condtons are fulflled: (1) the tme nstant s marked wth tag and t s a passve tme nstant as well; (2) the prevous tme nstant s actve but dle, no arrvals occur n the slot, and the current tme nstant s passve. Ths leads to the followng formula: u S1 = u Q + u A PQA(0). (4) B. A tme nstant s marked by tag S n+1 f the tme nstant t n slots earler s marked by tag S n, and the system has remaned passve and wthout arrvals durng those t n slots, u Sn+1 = u Sn (PQA(0)) tn. (5). The thrd formula clarfes the occurrence of actve but dle tme nstants. They occur f one of three mutually exclusve condtons s fulflled: (1) the tme nstant s marked wth tag and t s an actve tme nstant; (2) the prevous tme nstant s marked by A, no arrvals occur durng the prevous slot and the current slot s actve; (3) the system becomes actve durng a sleep perod, that s there exsts a tme nstant marked wth, no arrvals have occurred n the nterval up untl the current tme nstant, and all but the current tme nstant n the enclosed nterval are passve. Ths gves u A = u Q + u A PQA(0) + u S1 ( PQA(0)) 1 PQA(0). (6) Now we focus our attenton to sets of specal tme nstants nsde busy perods. We dscern three types: the frst slot of a busy perod (marked by tag B); the tme nstants at whch a new servce s started (marked by tag b); and the tme nstants at whch a servce s completed (marked by tag ). They are characterzed by vector generatng functons of the buffer content U B (z), U b (z) and U (z) respectvely, wth entres defned as follows: [U B (z)] j = Pr[u = k, ϕ = j, B]z k. (7) k=0 Ther behavor s captured n the followng three relatons: D. The system has three dstnct possbltes of enterng a busy perod at a tme nstant: (1) the prevous nstant s actve but dle, and there was at least one arrval durng the prevous slot; (2) the system has become actve durng a sleep perod n whch at least one arrval occurred; (3) at the end of a sleep perod, n whch the system has remaned passve but durng whch arrvals have occurred. Each of the possbltes corresponds to a term n the followng equaton: U B (z) = u A P (A(z) A(0)) t n 1 + u Sn (PQ) PQ(A(z) +1 A(0) +1 ) + =0 u Sn (PQ) tn (A(z) tn A(0) tn ). (8) E. The evoluton of the buffer content from the begnnng to the completon of a servce s as follows. n a sngle server FFS system, from the start to the completon of a servce, only one packet leaves the buffer. The number of arrvng packets durng a servce tme depends on the length of a servce. When the servce length s k, the pgf of the number of arrvals s A(z) k, and the transton of the background phase s gven by transton matrx P k. Therefore, we have U (z) = U b (z) 1 Pr[S = k](pa(z)) k z k=1 = U b (z) S(PA(z)). (9) z F. The set of tme nstants that s marked as but not as, s equal to the set of tme nstants that s marked as b but not as B. Hence, the dstrbuton of the buffer content at such a subset of tme nstants must be equal as well: U (z) u = U b (z) U B (z). (10) There are two fnal relatons that gve the dstrbutons durng a random slot and a random busy slot. G. We can prove that U(z) = U(z)PA(z) + (1 z)u (z). (11)

4 H. The vector generatng functon of the buffer content durng a random busy slot s gven by U β (z)( PA(z)) = U b (z)( S(PA(z))). (12) We can solve each of the occurrng functons and varables n terms of the constant vector u, whch can subsequently be found by standard technques to compute the boundary vector of an M/G/1-type queueng model [12]. We can then get such performance measures as the moments of the buffer content at varous tme nstants, as well as probabltes that slots of a certan type occur. As we wll see, ths s crucal for the computaton of power consumpton measures. By Lttle s law, we can get from the mean buffer content also the mean packet delay. V. APPLATON TO A WMAX SENARO n order to provde a numercal example to the analytcal approach of ths paper we conduct a smplfed but representatve power consumpton nvestgaton of an EEE e moble staton. We restrct further dervatons to the Tme Dvson Duplex (TDD) scheme together wth the Orthogonal Frequency Dvson Multplexng (OFDM) physcal layer. Followng many works on the performance analyss of EEE networks (see, for example [13] and [14]) we set the necessary operaton parameters as follows: TABLE EEE PARAMETERS Parameter Value Descrpton T f µs Frame duraton T h 400 µs Header duraton DL:UL 50:50 Downlnk-uplnk rato T RTG 22.9 µs Receve transton gap M6-QAM 1 2 Modulaton and codng scheme We denote T d = T f 2 and T u = T f 2 to be the duratons of the DownLnk (DL) and UpLnk (UL) sub-frames, respectvely. As we focus on the Best Effort (BE) and Non Real-Tme Pollng Servce (nrtps) traffc classes only, we select packet arrval model for the downlnk traffc accordng to EEE recommendatons [15]. n the ndvdual Subscrber nternet model from [15] the packet arrvals are assumed to conform to the nterrupted Posson Process (PP). Ths s a two-state Markov chan wth a Posson arrval process n the ON state, and no arrvals n the OFF state. The aforementoned source recommends an arrval rate of λ p = packets per tme unt n the ON state. The data packet length s L = 192 bytes. The resultng model represents a sngle user nteractng wth the nternet and gves the resultng data flow wth the average arrval rate of 15 Kbps. Snce the model approxmates the aggregaton of HTTP/TP and FTP traffc, t s subject to the lass 1 power savng mechansm. We follow the approach of [16] to obtan the data packet duraton for the 16-QAM 1 2 modulaton and codng scheme. The raw data rate n ths case s approxmately equal to R = Mbps. Therefore, packet duraton (T p ) s readly obtaned as: T p = 8 L R. (13) The above expresson allows us to calculate the number of packets per DL sub-frame (N d ) as: Td T h T RTG N d =. (14) As the derved analytcal model s dscrete wth a slot duraton beng equal to the frame duraton, t s convenent to rescale the packet arrval rate from packets per tme unt to blocks per tme unt. Here each block s exactly N d packets necessary to fll the DL sub-frame. The rescaled arrval rate s, therefore, λ b = λp N d blocks per tme unt n the ON state. Servce tmes of such blocks equal exactly one frame, and hence, S(z) = z. The uplnk traffc model s, agan followng the recommendatons of [15] a rescaled verson of the downlnk traffc model. That s, t carres 10 tmes less traffc (.e. 1.5 Kbps) and transton rates are 10 tmes smaller. As the uplnk traffc rate s very small compared to the maxmal capacty, we neglect the uplnk queueng effect. ombnng the two traffc models, we get a background process wth four states. n ths example, the two traffc streams are assumed to be ndependent, although our model can ncorporate such correlaton as well. To the best of our knowledge, no defntve real-world power consumpton values have been reported for EEE e MS. Therefore, we borrow the respectve values from the correspondng paper on EEE analyss [17] and summarze them n the followng table: T p TABLE POWER ONSUMPTON PARAMETERS Parameter Value Descrpton P s W Sleep mode power P l 1.15 W Lstenng mode power P r 1.40 W Receve mode power P t 1.65 W Transmt mode power Notce that there are fve types of frames (slots) n the consdered system: 1) Sleep frame: wreless nterface s nactve and consumes P s. 2) Lstenng frame: wreless nterface s actve and consumes P l, no packet receptons/transmssons. 3) Transmt frame: wreless nterface s actve (P l ) and there s a packet transmsson n the UL sub-frame (P t ). 4) Receve frame: wreless nterface s actve (P l ) and there s a recepton of N d packets n the DL sub-frame (P r ). 5) Receve-transmt frame: wreless nterface s actve (P l ), there s a recepton of N d packets n the DL sub-frame (P r ) and there s a packet transmsson n the UL subframe (P t ). The above frame types lead to the followng smple expressons for the energy costs per slot, whch are denoted by E s, E l, E t, E r and E rt for the sleep, lstenng, transmt, receve and receve-transmt frame type, respectvely:

5 Mean delay t mn Power consumpton (n W) t mn Fg. 2. Mean packet delay and power consumpton versus the ntal sleep nterval t mn, for downlnk traffc only (dashed lne), and bdrectonal traffc (full lne). E s = P s T f ; (15) E l = P l T f ; E t = P l T d + P t T p + P l (T u T p ); E r = P l T u + P r N d T p + P l (T d N d T p ); E rt = P r N d T p + P (T d N d T p ) + P t T p + P l (T u T p ). We set the lstenng nterval at the end of each sleep nterval to be equal to t (l) = 2 frames and we keep the fnal sleep nterval fxed at a value of t max = 256 frames. Usng the results from our analyss we can derve the followng expresson for the mean energy consumpton per frame: E = u Sn 1((t n t (l) )E s + t (l) E l ) + E rt ρu β (1)Q1 + E r ρu β (1)Q1 + E t u A 1, (16) where 1 s a column vector of length M, wth all entres equal to 1. Fnally, we obtan the power consumpton of the rado nterface by dvdng E by the frame length T f. n Fgure 2, we compare a bdrectonal scenaro wth a scenaro n whch the uplnk traffc s neglected. The left subplot shows the mean delay of the uplnk traffc versus the length of the ntal sleep nterval. The delay s consderably lower for the bdrectonal scenaro. n the rght subplot, we see that a downlnk traffc-only model underestmates the power consumpton consderably. V. ONLUSON We analyzed the sleep mode mechansm of EEE e WMAX protocol, by means of a queueng model that takes nto account both downlnk and uplnk traffc. We are thus able to compute effcently such crucal performance measures as the mean packet delay and the expected power consumpton We appled our theoretcal model to a realstc scenaro and found that even a modest amount of uplnk traffc has a tremendous nfluence on the system performance. The versatlty of the chosen downlnk traffc model allows us to model a multtude of traffc stuatons, and to assess the nfluence on the delay and the power consumpton. AKNOWLEDGEMENTS The fourth author s a Postdoctoral Fellow wth the Research Foundaton Flanders (FWO Vlaanderen), Belgum. REFERENES [1] EEE e-2005, Part 16: Ar nterface for fxed and moble broadband wreless access systems Amendment 2: physcal and medum access control layers for combned fxed and moble operaton n lcensed bands orrgendum 1, February [2] Y. Xao, Energy savng mechansm n the EEE e wreless MAN, EEE ommuncatons Letters, Vol. 9, No. 7, 2005, pp [3] Y. Zhang and M. Fujse, Energy management n the EEE e MA, EEE ommuncatons Letters, Vol. 10, No. 4, 2006, pp [4] K. Han and S. ho, Performance analyss of sleep mode operaton n EEE e moble broadband wreless access systems, Proceedngs of the EEE 63rd Vehcular Technology onference, VT2006-Sprng (Melbourne, 7-10 May 2006), Vol. 3, pp [5] Y. Park and G.U. Hwang, Performance modellng and analyss of the sleep-mode n EEE e WMAN, Proceedngs of the EEE 65th Vehcular Technology onference, VT2007-Sprng (Dubln, Aprl 2007), pp [6] J.-B. Seo, S.-Q. Lee, N.-H. Park, H.-W. Lee, and.-h. ho, Performance analyss of sleep mode operaton n EEE e, Proceedngs of the 60th Vehcular Technology onference, VT2004-Fall (Los Angeles, September 2004), Vol. 2, pp [7] S.-J. Kwon, Y.W. hung, and D.K. Sung, Queueng model of sleepmode operaton n cellular dgtal packet data, EEE Transactons on Vehcular Technology, Vol. 52, No. 4, 2003, pp [8] Y.-B. Ln and Y.-M. huang, Modelng the sleep mode for cellular dgtal packet data, EEE ommuncatons Letters, Vol. 3, No. 3, 1999, pp [9] N.-H. Lee and S. Bahk, MA sleep mode control consderng downlnk traffc pattern and moblty, Proceedngs of the EEE 61st Vehcular Technology onference, VT2005-Sprng (Stockholm, 30 May 1 June 2005), Vol. 3, pp [10] K. De Turck, S. De Vuyst, D. Fems, and S. Wttevrongel, An analytc model of EEE e sleep mode operaton wth correlated traffc, Proceedngs of NEW2AN 2007, pp [11] K. De Turck, S. De Vuyst, D. Fems, and S. Wttevrongel, Performance analyss of the EEE e sleep mode for correlated downlnk traffc, Telecommuncaton Systems, Vol. 39, No 2, pp [12] H.R. Gal, S.L. Hantler, and B.A.Taylor, Spectral analyss of M/G/1 and G/M/1 type Markov chans, Advances n Appled Probablty, Vol. 28, No. 1, 1996, pp [13] L. Berlemann,. Hoymann, G.R. Hertz, and S. Mangold, oexstence and nterworkng of EEE and EEE (e), EEE 63rd Vehcular Technology onference (VT), 1:27 31, [14] S. Andreev, K. Dubkov and A. Turlkov. EEE and cooperaton wthn mult-rado statons, 11th nternatonal Symposum on Wreless Personal Multmeda ommuncatons (WPM), 1:avalable electroncally, [15].R. Baugh, J. Huang, R. Schwartz, and D. Trnkwon, Traffc model for tg3 mac/phy smulatons, Techncal report, EEE Broadband Wreless Access Workng Group, [16] D. Svchenko, B. Xu, V. Rakocevc and J. Habermann, nternet traffc performance n EEE networks, European Wreless, 1:avalable electroncally, [17] E.-S. Jung and N.H. Vadya, mprovng EEE power savng mechansm, Wreless Networks, Vol. 14 No. 3 pp , 2004.