Cross-Layer Performance of a Distributed Real-Time MAC Protocol Supporting Variable Bit Rate Multiclass Services in WPANs

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1 Cross-Layer Performace of a Distributed Real-Time MAC Protocol Supportig Variable Bit Rate Multiclass Services i WPANs David Tug Chog Wog, Jo W. Ma, ad ee Chaig Chua 3 Istitute for Ifocomm Research, Heg Mui eg Terrace, Sigapore 963, Sigapore wogtc@ir.a-star.edu.sg Ceter for Wireless Commuicatios, Uiversity of Waterloo, Waterloo, Otario, Caada NL 3G jwma@bbcr.uwaterloo.ca 3 Electrical ad Computer Egieerig, Natioal Uiversity of Sigapore, et Ridge Crescet, Sigapore 96, Sigapore chuakc@us.edu.sg Abstract. A cross-layer optimizatio problem to maximize utilizatio for a distributed real-time medium access cotrol (MAC protocol supportig variable bit rate (VBR multiclass services is formulated. A complete sharig (CS scheme is used as the admissio cotrol policy at the coectio level to relate the maximum umber of devices that ca be admitted i the wireless persoal area etwo (WPAN to the grade of service (GoS of blockig probability at the coectio level, the quality of service (QoS of packet loss probability at the packet level ad the effective data trasmissio slots efficiecy at the MAC layer. With this cross-layer aalytical framewo, the maximum umber of devices that ca be admitted ito the system to achieve maximum utilizatio while maitaiig prescribed GoS/QoS requiremets uder differet total device mea coectio arrival rate ca be determied. Numerical results are preseted to demostrate the effectiveess of the proposed cross-layer couplig strategy. Itroductio Cross-layer desig, a hot research area [], aims to optimize performace across differet layers of the layered-commuicatios model. By cosiderig cross-layer desig, the desig system performace ca be optimized. I this paper, we cosider a basic distributed real-time medium access cotrol (MAC protocol like the multibad OFDM Alliace (MBOA MAC [] without the o-real-time cotetio MAC protocol for Ultra-Widebad (UWB systems. A wireless mobile multimedia UWB etwo has to provide a reasoable user-trasparet grade of service (GoS/quality of service (QoS for differet service classes. To our kowledge, there is o cross-layer performace aalysis amog utilizatio, maximum umber of devices, blockig probability, packet loss probability, effective data trasmissio slots efficiecy ad total device arrival rate i such a distributed real-time MAC protocol to date. The blockig probability is at the coectio level i the etwo layer, while the packet loss probability is at the packet level i the etwo layer. The effective data trasmissio slots efficiecy is at the MAC sublayer i the lik layer. The goal is to fid the maximum umber of devices that ca be supported such that utilizatio is maximized uder reaso-

2 able GoS/QoS specificatios. The mai cotributio of this paper is the aalytical formulatio ad evaluatio of the cross-layer optimizatio problem for the support of variable bit rate multiclass services. The cross-layer optimizatio here is show to have some system utilizatio improvemet exceedig % compared with a simple admissio scheme. Distributed Real-Time MAC Protocol The distributed real-time MAC protocol, e.g., [], uses a frame format, as show i Fig.. Each frame cosists of two parts: a beaco subframe ad a data trasmissio subframe. The former cosists of beaco slots for existig devices i the system, which are packed at the begiig of the beaco period subframe, while N BC beaco slots are available for ew devices to get ito the system through cotetio usig, e.g., the slotted ALOHA protocol. After successful etry ito the system, the ew devices are packed together at the begiig of the beaco period. The umber of cotetio beaco slots is assumed costat. Whe devices leave the system, a packig protocol is used to pack the remaiig devices beaco slots together at the begiig of the beaco slots period. Thus the beaco period is ot fixed but varies accordig to the umber of devices i the system. The beaco period subframe is assumed to be a iteger umber of packet slots. The data trasmissio period is used to trasmit data packets whose data reservatios are aouced i its device beaco slot. This is called the data reservatio protocol (DRP []. Trasmissio eed ot be i the same order as the devices i the beaco slots ad the DRP packets for each device also eed ot be trasmitted immediately after other DRP packets. The umber of trasmissio data packets for each device is ot fixed but ca vary. Note that all devices aouce their data reservatios ad each device beaco slot cotais iformatio o all other devices [4]. Sice the beaco period varies, the available umber of data packet slots, C, also varies, depedig o the umber of devices i the system ad the umber of cotetio beaco slots: C C(,,..., N SF k N BC N BS, k N D, + ( k where is the umber of traffic classes, N SF is the umber of packet slots i a superframe, k is the umber of class k devices i the system ad N BS is the umber of beaco slots equivalet to oe packet slot. x is the earest upper iteger value of x. Existig devices DEV Beaco Period DEV 3 DEV Cotetio beaco slots, N BC Variable boudary Variable available badwidth C Data Trasmissio Period DRP 3 DRP DRP Fig.. Frame format of a distributed real-time MAC protocol

3 3 Aalytical Model At the coectio level, the GoS is the blockig probability. I geeral, this GoS decreases with icrease i the maximum umber of devices, N D. At the packet level, the QoS is the packet loss probability. I geeral, this QoS is zero as log as the maximum total packet trasmissios do ot exceed the available umber of data trasmissios i a frame. However, whe it starts to icrease with the icrease i the maximum umber of devices, N D, its iitial icrease ca be at a very sharp rate. This is the limitig costrait i the umerical example i Sectio 4. At the MAC layer, the QoS is the effective data slots trasmissio efficiecy. It decreases with the icrease i the maximum umber of devices, N D. The cross-layer optimizatio here is show to have some system utilizatio improvemet exceedig % compared with a simple admissio criterio i Sectio 4. The complete sharig (CS scheme is used as the resource admissio policy. Fig. shows the CS admissio Maov chai for classes of devices. λ k is the class k device mea coectio arrival rate, while μ k is the class k device mea departure rate. /μ k is the class k mea coectio holdig time. These parameters determie the blockig probability GoS. μ N D μ,, λ λ, μ N D μ λ μ λ λ λ μ, N D,, N D Fig.. Complete sharig resource allocatio scheme for two classes The steady state probability of a complete sharig resource allocatio scheme for classes is give by P(, where,..., ( λ μ ( λ μ ( λ μ...!! N N N...!! k i, k, i N k N D,..., ( λ μ ( λ μ ( λ μ...!!, (. The N k s together with the summatios determie the state space of the -dimesioal Maov chai. The blockig probability, P B, is give by

4 N N N P B... P(,,...,, if k N D. (3 k A class k variable bit rate source ca be modeled by a cotiuous-time Maov chai with fiite states [3] i Fig. 3. M kα k ( M k α α k k M k β k β k M k β k Fig. 3. Cotiuous-time Maov chai for a sigle variable bit rate source Each state represets the discrete level of bit rate geerated by a sigle source. State requires r k umber of packet slots for trasmissio. The highest state is state M k. This state requires M k r k umber of packet slots for trasmissio. Thus the packet slots variatios are i the set of {,r k,r k,3r k,,m k r k }. α k is the icrease rate of oe twostate mii-source, while β k is the decrease rate of oe two-state mii-source. The steady-state probability of beig i state m k, deoted by P m k, is give by M k P ( mk ( Mk mk m pk pk, mk,,,..., M k, k m (4 k where pk α k ( α k + β k. The probability that l k levels of bit rate for class k traffic give that there are k sources, deoted by Pr[l k k ], is give by k M k Pr[ l ] ( lk ( k Mk lk k k pk pk, lk,,,..., k M k, l (5 k Assumig real-time traffic with o storig of packets for retrasmissio, the packet loss probability, P L, is give by N N N M M M... P(,,...,... Pr( l l l l + Pr( l...pr( l lk C(,,..., k PL, (6 N N N M M M... P(,,...,... Pr( l l l l Pr( l l...pr( lk k + where [ x ] max[, x]. The utilizatio, N u, is give by where N u N Pr( l... P(,,...,... Pr( l l l, (7 N N...Pr( l U, M M M l

5 lk, if lk C(,,..., U. C(,,...,, if lk > C(,,..., (8 The probability of devices i the system, P, is give by N N N P Pr[ k ]... P(,,...,, if k,,,..., N D. (9 Thus the effective available capacity, C e, is give by N D Ce P C(,,...,, k k. ( The data slots trasmissio efficiecy, φ, is give by φ C (,,..., N SF, < φ <. ( Similarly, the effective data slots trasmissio efficiecy, φ e, is give by φ e Ce N SF, < φe <. ( The system utilizatio ca be maximized by solvig the followig costrait optimizatio problem of maximizig N u subject to the costraits of PB PB, PL PL, ad φe φe, where the superscript deotes the requiremet values of the correspodig parameters. The results here ca be exteded for the blockig ad loss probabilities of each traffic class. 4 Numerical Results I this sectio, we illustrate the system performace by presetig results for a twoclass traffic example. The parameter values used i the umerical examples are tabulated i Table. Table. Parameter Values Used Symbol Value Symbol Value N SF 64 / μ miute N BS 3 / μ miutes N BC 3 α.35 M β.65 M α.9 r β. r P B λ λ P L λ λ + λ φ e Due to lack of space, graphical results are ot show here but ca be obtaied usig the aalysis i sectio 3. From these graphical results, the data trasmissio efficiecy, φ, decreases as the maximum umber of devices icreases. It does ot deped o the total device mea coectio arrival rate but oly o the total umber of de

6 vices i the system. If we choose the data trasmissio efficiecy requiremet, φ, to be greater tha.8, the the maximum umber of devices, N D, that ca be supported is oly 33. The admissio criterio is simply limited to o more tha 33 devices. The utilizatio N u {.3,3.3,.6,.8,.} whe the total device mea coectio arrival rate, λ ( λ + λ, is {,,3,4,5} arrivals per miute. Similarly from the graphical results, the effective data trasmissio efficiecy, φ e, decreases at a slower rate compared to the data trasmissio efficiecy, φ, as the maximum umber of devices icreases. However, it decreases as the total device mea coectio arrival rate icreases. Solvig the cross-layer optimizatio i Sectio 3, we have the maximum utilizatio, N u {36.,46.,46.8,46.,45.3} packet trasmissio slots at the maximum umber of devices, N D {65,63,63,63,63} for the total device mea coectio arrival rate, λ{,,3,4,5} arrivals per miute. The improvemet i utilizatio are respectively {6%,98%,7%,%,6%}. Thus this optimized solutio results i much higher utilizatio compared to the case where the data trasmissio efficiecy requiremet, φ, is chose to be greater tha.8. The limitig costrait i this umerical example is caused by the packet loss probability requiremet, P L, at -3. Note that the maximum umber of devices, N D, to achieve maxi- mum utilizatio, N u, is quite isesitive to the total device mea coectio arrival rate. Thus, the maximum umber of devices, N D, ca be set at 63, for example, where the utilizatio is maximized for most of the total device mea coectio arrival rate uder cosideratio. This is a simple admissio criterio. I practical systems, measured average device arrival rates are eeded. 5 Cocludig Remas A cross-layer optimizatio problem has bee formulated to maximize utilizatio i a distributed real-time MAC protocol for WPANs. The GoS/QoSs performace metrics i the coectio level i the etwo layer, the packet level i the etwo layer ad the MAC layer have bee coupled together to optimize system performace. Numerical results show that this cross-layer optimizatio approach results i much higher utilizatio (6% to 6% tha the approach that simply cosiderig the data trasmissio efficiecy requiremet. The aalysis here ca be used to determie the optimal maximum umber of devices that ca be admitted ito the system such that the utilizatio is maximized uder differet total device mea coectio arrival rate i a distributed real-time MAC protocol for WPANs. Refereces. Wijtig, C., Prasad, R.: A Geeric Framewo for Cross-Layer Optimisatio i Wireless Persoal Area Netwos. Wireless Persoal Commuicatios, Vol 9, ( O Coor, J., Brow, R.: MBOA Techical Specificatio: Distributed Medium Access Cotrol (MAC for Wireless Netwos. MBOA Draft MAC stadard versio.95, ( April 5 3. Maglaris, B., Aastassiou, D., Se, P., arlsso, G., Robbis, J.D.: Performace Models of Statistical Multiplexig i Packet Video Commuicatios. IEEE Trasactios o Commuicatios, Vol. 36, No. 7, (July

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