Performance Analysis of A Burs-Frame-Based MAC Proocol for Ulra-Wideband Ad Hoc Neworks Kejie Lu, Dapeng Wu, Yuguang Fang Deparmen of Elecrical and Compuer Engineering Universiy Of Florida Gainesville, FL 32611, USA Email: {lukejie,wu,fang}@ece.ufl.edu. Rober C. Qiu Deparmen of Elecrical and Compuer Engineering Tennessee Technological Universiy Box 5077, Cookeville, TN 38505 Email: rqiu@nech.edu. Absrac Ulra-wideband (UWB) communicaion is becoming an imporan echnology for fuure Wireless Personal Area Neworks (WPANs). A criical challenge in high daa rae UWB sysem design is ha a receiver usually needs ens of micro-seconds or even ens of milliseconds o synchronize wih ransmied signals, known as he iming acquisiion problem. Such a long synchronizaion ime will cause significan overhead, since he daa rae of UWB sysems is expeced o be very high. To address he overhead problem, we previously proposed a general framework for MAC proocols in high daa rae UWB neworks. In his framework, a node can aggregae muliple upper-layer packes ino a larger burs frame a he MAC layer. In his paper, we analyze he unsauraed hroughpu performance of a bursframe-based MAC proocol wihin he framework. Numerical resuls from he analyical mehod give excellen agreemen wih he simulaion resuls, indicaing he accuracy of our analyical mehod. I. INTRODUCTION In he pas few years, UWB communicaion has received considerable aenion in boh academia and indusry. Compared o radiional narrow band sysems, UWB can provide high daa rae (> 100 Mb/s) wih very low-power emission (less han 41 dbm/mhz) in a shor range. These feaures make UWB paricularly suiable for wireless personal area nework (WPAN) applicaions. Currenly, IEEE 802.15.3 working group is sudying he use of UWB as an alernaive physical layer echnique 1]. To successfully implemen a UWB sysem, a number of challenges mus be addressed 2]. One of he criical issues is iming acquisiion, which is a process of synchronizing he receiver s clock wih he ransmier s clock so ha he receiver can deermine he boundary beween wo ransmied symbols. Depending on he receiver design, he acquisiion ime varies from ens of micro-seconds o ens of milliseconds. Evidenly, for high daa rae applicaions, he overhead of preambles will significanly reduce he efficiency of UWB neworks 2]. Exising works ha consider he iming synchronizaion issue in UWB MAC layer design include 3], 4]. In 3], he auhors assumed ha he UWB nework can provide muliple channels hrough differen ime-hopping (TH) codes. To reduce he iming synchronizaion overhead, 3] proposed a link mainenance scheme in which he daa channel is mainained by ransmiing low-rae conrol packes when here is no daa packe o ransmi. Alhough he link mainenance scheme achieves good performance in he simulaion, here are sill some criical issues unclear in 3]. For insance, i is no clear how a node selecs a TH code for is daa channel in a disribued manner so as o avoid using he same TH code as ha used by anoher node. Anoher poenial problem is ha he link mainenance scheme will increase he ransmission ime of he ransmier, hereby reducing he baery life and inroducing exra inerference. In 4], he auhors sudied he impac of long synchronizaion ime on he performance of CSMA/CA and TDMA schemes used in UWB neworks. However, he paper did no provide soluions o miigae he iming acquisiion problem. To address he overhead problem, we proposed a general framework for MAC proocols in high daa rae UWB neworks 5]. In his framework, he MAC proocol is based on he well-known IEEE 802.11 CSMA/CA proocol. The main idea of he scheme is o assemble muliple upper-layer packes ino one burs frame a he MAC layer. In conras o he radiional approach, under which each upper-layer packe is delivered individually, ransmiing muliple upper-layer packes in one frame will significanly reduce he synchronizaion overhead. Since performance analysis is imporan for MAC proocol design, his paper focuses on unsauraed performance analysis for he burs-frame-based MAC proocol, which has no been addressed previously. Performance of CSMA/CA proocols, paricularly IEEE 802.11, has been sudied exensively in he lieraure 6] 8]. However, unil recenly, mos heoreical sudies are focusing on sauraion performance 6], 7], where a node in he nework always has packes ready o be ransmied. Recenly, an unsauraed analysis for IEEE 802.11 is provided in 8], where he sysem under sudy is decomposed ino a queueing subsysem and a service ime subsysem. In his model, he MAC layer queue is modelled as M/G/1/K; he service ime is characerized by a ransfer funcion. However, his model is no direcly applicable o he unsauraed performance analysis of our burs-frame-based MAC proocol due o he complicaed queueing behavior caused by burs frames. In his work, we ake he same ransfer-funcion approach used in 8] o analyze he unsauraed performance of our burs-frame-based MAC proocol. The major conribuion of our work is ha our analyical mehod can no only handle complicaed queueing behavior bu also provide accurae resuls, which have no been achieved previously. Our numerical resuls from he analyical mehod give good agreemen wih he simulaion resuls, validaing he accuracy of our analyical 0-7803-8938-7/05/$20.00 (C) 2005 IEEE 2937
mehod. The res of he paper is organized as follows. In Secion II, we briefly describe our MAC proocol for UWB neworks. In Secion III, we analyze he unsauraed performance of he MAC proocol. Simulaion and numerical resuls will be shown in Secion IV. Finally, Secion V concludes he paper. II. A BURST-FRAME-BASED MAC PROTOCOL FOR UWB NETWORKS In his secion, we briefly describe a burs-frame-based MAC proocol which is a special case wihin he framework proposed in 5]. In his proocol, we consider only one qualiyof-service (QoS) class of raffic for each desinaion, i.e., all packes for he same desinaion have he same QoS requiremens. Incoming packes are firs classified based on is desinaion, and hen pu ino a corresponding packe queue. Suppose here are N nodes in a UWB nework; hen we can implemen N packe queues in each node, among which N 1 queues are used for buffering packes desined o oher N 1 nodes, and one queue is used for buffering broadcas packes. For each queue, we use ail-dropping when here is a buffer overflow. A burs frame will be generaed if he oal number of packes in he queue exceeds a hreshold B min and he server is idle (i.e., here is no oher burs waiing for ransmission). In addiion, we assume ha he oal number of packes in a burs mus be smaller han or equal o a prese value B max.in his proocol, we require ha all he packes in a burs frame have he same desinaion so ha mos exising funcions of IEEE 802.11 can be re-used. To achieve he fairness among desinaions, a simple round-robin scheme will be employed. When a burs assembly is finished, he burs frame will be sored in a buffer and waiing for ransmission. If a burs frame is correcly received, he receiver will send one ACK frame o he ransmier. III. UNSATURATED PERFORMANCE ANALYSIS In his secion, we presen an analyical model for evaluaing our burs-frame-based MAC proocol under differen incoming raffic load. Similar o 8], we also decompose he sysem ino a queueing subsysem and a service ime subsysem. For he queueing subsysem, we exend he model for general bulk service queues 9]. Paricularly, we consider ha a burs can be assembled only when he oal number of packes in he queueing subsysem is greaer han or equal o B min ;wealso consider he fac ha he service ime depends on he number of packes in he burs, which is no considered in 9]. For he service ime subsysem, we analyze he impac of burs assembly on he probabiliy ha a server is idle, and on he service ime disribuion. To faciliae our discussion, we make he following assumpions: There are N idenical nodes in he nework, and any wo nodes in he nework can direcly communicae wih each oher. A each node, packe arrivals are Poisson wih rae λ (packes/sec), and he packes have a common desinaion. The size of all packes are fixed a P (bis). The burs service ime is an ineger muliple of a prese ime uni τ (sec). Here he burs service ime is defined as he ime inerval from he ime epoch ha a burs is assembled o he ime epoch ha he burs is removed from he ransmission buffer. 1 A ransmission buffer is locaed in he service ime subsysem. Packes being sored in a ransmission buffer means ha he packes are in service. There is no ransmission failure due o bi errors. The probabiliy ha a burs ransmission aemp fails, denoed as p, does no depend on he backoff sage of he node. The propagaion delay in UWB neworks is negligible. A. The Bulk Service Queueing Sysem Based on he assumpions above, we can model he queueing sysem in any node as an M/G Bmin,Bmax] /1/K queue, where K is he capaciy of he queue and he superscripion B min,b max ] means ha he oal number of packes in a burs is an ineger in he range of B min,b max ]. Noe ha here K is he oal number of packes ha can be sored in he queue, which does no include packes in he ransmission buffer. To analyze his queueing sysem, we firs define he sae space of he queueing sysem according o he saus of server and he number of packes in he queue. Paricularly, sae I k means ha he server is idle and here are k cusomers waiing in he queue; while sae A k means ha he server is busy and here are k cusomers waiing in he queue. Wih he packe assembly policy described in he previous secion, we noe ha if he server is idle, hen he maximum number of packes in he queue mus be smaller han B min. Therefore, he sae space is S = {I 0,I 1,,I Bmin 1,A 0,A 1,,A K }. Le ξ() ( 0) be he sae of he queueing sysem a ime ; leδ n be he epoch of he n-h burs deparure. We now consider he embedded Markov process ξ n, where ξ n is he sae of he queueing sysem jus before δ n, which is ξ n = ξ(δ n ). An embedded Markov chain can hen be formulaed, where he sae space is {A 0,A 1,,A K }.Lep d k (0 k K) be he seady-sae probabiliy ha ξ n = A k ;lep ij be he seady-sae ransiion probabiliy from sae A i o sae A j for all i, j, where 0 i K and 0 j K: p ij = n Prξ n+1 = A j ξ n = A i ]. Consequenly, p d k can be obained by solving he embedded Markov chain wih all p ij. To calculae p ij, we define α(k, b) as he probabiliy ha k packes arrive during one burs service ime, given ha he 1 A burs will be removed from he ransmission buffer if he burs is successfully received by he desinaion, or if he number of burs ransmission failures exceeds a pre-defined rery i. 2938
burs conains b packes. Le B() be he number of packes in he firs burs afer. Define B k = B(δ n ) given ha ξ n = k. Here we noe ha B k depends only on he assembly policy, B min 0 k B min B k = k B min <k B max (1) B max B max k K. Since B k packes will be assembled ino he firs burs afer δ n if ξ n = k, we can see ha he number of packes remaining in he queue immediaely afer he burs is creaed, denoed by K k,is K k = max(0,k B k ). (2) Therefore, we can calculae all p ij hrough 0 0 j<k i α(j K i,b i ) K i j<k p ij = K 1. (3) 1 α(k K i,b i ) j = K k=k i Le q bi be he seady sae probabiliy ha he burs service ime is iτ, given ha here are b packes in he burs. Since he packe arrival is a Poisson process wih rae λ, α(k, b) can be calculaed by α(k, b) = i q bi (λiτ)k e λiτ k! In summary, we noe ha p d k can be calculaed if all q bi are known. B. Exponenial Backoff Scheme Using he Markov modelling echnique inroduced in 6], we can analyze he exponenial backoff scheme for he MAC proocol. Specifically, we can pariion he coninuous ime axis ino slos, where wo consecuive slos are deied by he even of a value change in he backoff couner. We can hen formulae a wo-dimensional discree ime embedded Markov chain as in 7], where he maximum number of reries for a packe is aken ino consideraion. By solving he Markov chain, a closed-form soluion for he probabiliy ha a node will ransmi a burs given ha he node is busy, denoed as p, can be achieved if he burs ransmission probabiliy p is known 2. Since a successful packe delivery means ha here is no collision, we can calculae p hrough (4) p =1 1 (1 p I )p ] N 1 (5) where p I denoes he probabiliy ha a node is idle (no burs pending for ransmission) in a slo. Wih 0 < p < 1 and 0 <p < 1, we can calculae p and p numerically. To calculae p I,weled k () (0 k K) be he oal number of burs deparures in ime (0,) such ha he number of packes in he queue is k jus before he deparure; le D() = k d k() be he oal number of burs deparures in (0,). Noe ha if here are k (k < B min ) packes in he queue jus before a deparure, hen he average ime from he 2 Please refer o 7] for deail discussion. deparure of he old burs o he epoch ha a new burs if formed is (B min k) 1 λ, since packe arrivals are Poisson wih rae λ. We can hen esimae p I as he fracion of ime ha he server is idle, which is Bmin 1 1 p I = ( d k () (B min k) 1 ) ] λ = 1 B min 1 λ Similar o 9], d k () d k () D() D() = p d k d k () (B min k) can be calculaed by ]. (6) ] 1. (7) D() Since D() is he oal number of served burss in, is he average burs deparure inerval. Therefore, D() we have B min 1 D() = T s + p d k (B min k) 1 ] (8) λ where T s denoes he average burs service ime, which is ] K T s = q Bk i (iτ). (9) p d k Finally, p I can be calculaed hrough p I = λt s + B min 1 i B min 1. (10) To summarize his subsecion, we noe ha p and p can be calculaed if all p d k are known. C. Service Time Disribuion Le Q b (z) be he probabiliy-generaing funcion (PGF) of q bi, which is Q b (z) = z i q bi. (11) i Due o he simpliciy of calculaion in he z-ransform domain and he one-o-one correspondence beween q bi and Q b (z), we compue Q b (z) insead of q bi. This approach is known as he ransfer-funcion approach 8]. To calculae Q b (z), we le X n be he lengh of slo n and le X n be he lengh of a period (wihin slo n), during which he server is busy. Noe ha for sauraed condiion, X n X n. However, for unsauraed cases, X n X n. We can hen apply he echnique used in 8]. In his model, he packe ransmission process is characerized by a linear sysem, where H(z) is he PGF of X n given ha he curren node is acive bu no ransmiing; C b (z) is he PGF of X n given ha a collision occurs and he curren node has ransmied a burs ha has b packes; and S b (z) is he PGF of X n given ha 2939
he curren node has successfully ransmied a burs wih b packes. Consequenly, he ransfer funcion of he linear sysem is equal o Q b (z). To simplify he noaion, we define H m (z) as follows H m (z) = 1 1+H(z)+H 2 (z)+ + H Wm 1 (z) ]. W m (12) Then Q b (z) can hen be calculaed hrough M m ] Q b (z) = (1 p)s b (z) (pc b (z)) m H i (z) m=0 M +(pc b (z)) M+1 H i (z) i=0 i=0 (13) We now consider he calculaion of S b (z), C b (z), and H(z). Due o ied space, here we only discuss he calculaion for he RTS/CTS access scheme. Since he packe size is fixed, S b (z) and C b (z) can be direcly derived as S b (z) = z (Tso+ bp R ) 1 τ C b (z) = z Tco τ (14) where R is he daa rae, T so is he ime overhead for a successful ransmission, and T co is he ime overhead for collision. According o IEEE 802.11 proocol, we have T so = 4T sync +3T SIFS + T DIFS + 1 R (4L PH + L RT S + L CTS + L ACK + L MH ) T co = 2T sync + T SIFS + T DIFS + 1 R (2L PH + L RT S + L CTS ) (15) where T sync denoes he synchronizaion ime, T SIFS denoes he ime duraion of SIFS, T DIFS denoes he ime duraion of DIFS, L PH denoes he lengh of physical frame header in bis (excluding he synchronizaion preamble), L MH denoes he lengh of MAC frame header in bis, L RT S denoes he lengh of ACK frame in bis, L CTS denoes he lengh of ACK frame in bis, and L ACK denoes he lengh of ACK frame in bis. To calculae H(z), we define he following parameers: q denoes he probabiliy ha here is a leas one packe ransmission in N 1 nodes in a slo, which is q =1 1 (1 p I )p ] N 1 (16) q s denoes he probabiliy ha here is only one packe ransmission in N 1 nodes in a slo, which is q s =(N 1)(1 p I )p 1 (1 p I )p ] N 2 (17) σ denoes he lengh of a prese fixed ime duraion for backoff. When here is no packe ransmission, we have X n = σ. In 802.11b direc sequence spread specrum mode, σ =20µs. Wih hese parameers, we have H(z) =(1 q )z σ τ + q s S(z)+(q q s )C(z) (18) where C(z) =C b (z) and TABLE I SETTING OF THE MAC PROTOCOL. Minimum conenion window size 8 Maximum conenion window size 256 σ 2 µs SIFS 1 µs DIFS 5 µs Rery i 4 Queue size 50 B max S(z) = p b S b (z) (19) b=b min where p b = k:b k =b pd k is he probabiliy mass funcion of he number of packes in a burs. To summarize his subsecion, we noe ha he service ime disribuion q bi can be calculaed if p, p, and all p d k are known. D. Throughpu Analysis Le S() be he oal number of successfully ransmied packes in 0,]. Then we have S() = K d k () B k ( 1 p M+1) + B(0) B(). (20) Now define hroughpu S as he oal amoun of daa (in bis) of MAC payload successfully received in a given ime (in sec). Based on Eqs. (20), (7), and (8), we have S() S = P = P EB] (1 p M+1 ) T s + 1 B min 1 λ (21) where EB] is he average number of packes in a burs EB] = B max b=b min b p b ]. E. Summary of he Algorihm In his analyical model, he performance is obained hrough a recursive algorihm. The algorihm can be summarized as follows 1) Iniialize p I and p b o sauraed condiion, i.e., le p I = 0, p Bmax =1, and p b =0for b B max. 2) Calculae p and p as shown in Secion III-B. 3) Calculae service ime disribuion q bi, using he ransferfuncion approach. 4) Calculae p d k by using he bulk service queueing model. 5) Calculae p I hrough Eq. (10). 6) Calculae S hrough Eq. (21) and sop if he resul converges, i.e., he difference beween he resuls of wo consecuive ieraions is less han a prese value; oherwise go o Sep 2. Alhough he convergence of he recursive algorihm has no been proved, he algorihm always achieves convergence in our numerical calculaions. 2940
Throughpu (Mb/s) 90 85 80 75 Analysis Simulaion Throughpu (Mb/s) 100 90 80 70 60 Bmin=1, Bmax=1] (Ana) Bmin=1, Bmax=1] (Sim) Bmin=1, Bmax=10] (Ana) Bmin=1, Bmax=10] (Sim) Bmin=10, Bmax=10] (Ana) Bmin=10, Bmax=10] (Sim) 50 70 0 2 4 6 8 10 12 14 16 18 20 Ieraion 40 50 60 70 80 90 100 Incoming raffic daa rae (Mb/s) Fig. 1. Analyical resuls vs. number of ieraions (B min =1,B max = 10,R i =90Mb/s). Fig. 2. Throughpu performance versus incoming raffic daa rae wih differen burs assembly policies. IV. SIMULATION AND NUMERICAL RESULTS In his secion, we evaluae he performance of he bursframe-based MAC proocol and compare he numerical resuls of he proposed analyical mehod in Secion III, o he simulaion resuls. Table I liss he values of he conrol parameers used in he simulaions and numerical analysis. Due o he space i, we only presen resuls under he following seing: N =10nodes are locaed in a4m 4 m area. All messages are ransmied wih channel daa rae R, which is 100 Mbis/s. The size of each packe is fixed a 1000 Byes. Packe arrivals o any node i are modelled by a Poisson process wih he same rae λ (packes/s). Consequenly, he incoming raffic daa rae is R i = NPλ (bis/s). We assume ha T sync = 10µs, which is a ypical assumpionin1]. We assume ha no packe ransmission failure occurs due o bi errors. We assume ha he RTS/CTS scheme is used. For he analyical model, we le ime uni τ = σ, le he maximum service ime be 30000 ime unis, and run he algorihm for 20 ieraions. Figure 1 shows he analyical resuls versus he number of ieraions, where we le B min =1, B max =10, and R i =90 Mb/s. We can observe ha, if he number of ieraions is larger han 15, he analyical resul converges, and is very close o he simulaion resul. Figure 2 compares he hroughpu performance versus incoming raffic rae for hree burs assembly policies: 1) B min = B max = 1 (benchmark), 2) B min = 1,B max = 10, 3) B min = B max = 10. We can see ha, compared o he bench mark case, he proposed MAC proocol can significanly improve he hroughpu performance. Paricularly, if R i = R, he bench mark hroughpu is only abou 52 Mb/s; while policy (2) and (3) can achieve as high as 88 Mb/s and 92 Mb/s, respecively. From Fig. 2 we can also observe ha our analyical model is highly accurae under differen incoming daa raes. Such accuracy has no been achieved by he previous analysis; hence our analysis represens a major conribuion. V. CONCLUSIONS In his paper, we developed an analyical model o evaluae he performance of a burs-frame-based MAC proocol, in which a node can aggregae muliple upper-layer packes ino a larger burs frame a he MAC layer. The proposed heoreical model can analyze he unsauraed hroughpu performance of he burs-frame-based MAC proocol, which has no been addressed previously. In addiion, he proposed mehod is general and hence applicable o unsauraed performance analysis for oher CSMA/CA based proocols. Numerical resuls from he analyical mehod give excellen agreemen wih he simulaion resuls, validaing he accuracy of our analyical model. REFERENCES 1] IEEE P802.15-04/0137r1, DS-UWB physical layer submission o 802.15 Task Group 3a, Mar. 2004, Projec: IEEE P802.15 Working Group for Wireless Personal Area Neworks (WPANs). 2] S. Roy, J. R. Foerser, V. S. Somayazulu, and D. G. Leeper, Ulrawideband radio design: The promise of high-speed, shor-range wireless conneciviy, Proc. IEEE, vol. 92, no. 2, pp. 295 311, Feb. 2004. 3] S. S. Kolenchery, J. K. Townsend, and J. A. Freebersyser, A novel impulse radio nework for acical miliary wireless communicaions, in Proc. IEEE MILCOM 1998, 1998, pp. 59 65. 4] J. Ding, L. Zhao, S. Medidi, and K. Sivalingam, MAC proocols for ulra wideband (UWB) wireless neworks: Impac of channel acquisiion ime, in Proc. SPIE ITCOM 2002, July 2002. 5] K. Lu, D. Wu, and Y. Fang, A novel framework for medium access conrol in ulra-wideband ad hoc neworks, Dynamics of Coninuous, Discree and Impulsive Sysems (Series B) Special Issue on Ulra-Wideband (UWB) Wireless Communicaions for Shor Range Communicaions, (o appear), 2005. Online]. Available: hp://www.wu.ece.ufl.edu/mypapers/uwb camera.pdf 6] G. Bianchi, Performance analysis of he ieee 802.11 disribued coordinaion funcion, IEEE J. Selec. Areas Commun., vol. 18, no. 3, pp. 535 547, Mar. 2000. 7] H. Wu, Y. Peng, K. Long, S. Cheng, and J. Ma, Performance of reliable ranspor proocol over IEEE 802.11 wireless LAN: analysis and enhancemen, in Proc. IEEE INFOCOM, June 2002, pp. 599 607. 8] H. Zhai, Y. Kwon, and Y. Fang, Performance analysis of IEEE 802.11 MAC proocol in wireless LAN, Wiley Journal of Wireless Communicaions and Moble Compuing (WCMC), pp. 917 931, Dec. 2004. 9] G. Hebuerne and C. Rosenberg, Arrival and deparure sae disribuions in he general bulk-service queue, Naval Research Logisics, vol. 46, pp. 107 118, 1999. 2941