PERFORMANCE ANALYSIS FOR BANDWIDTH ALLOCATION IN IEEE BROADBAND WIRELESS NETWORKS USING BMAP QUEUEING

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1 PERFORMANCE ANALYSIS FOR BANDWIDTH ALLOCATION IN IEEE BROADBAND WIRELESS NETWORKS USING BMAP QUEUEING Sid EL KAFHALI Abdelli EL BOUCHTI Mohmed HANINI nd Abdelkrim HAQIQ Computer, Networks, Mobility nd Modeling lbortory e-ngn reserch group, Afric nd Middle Est FST, Hssn st University, Settt, Morocco {kfhlisid,.elbouchti, hninimohmed, ABSTRACT This pper presents performnce nlysis for the bndwidth lloction in IEEE brodbnd wireless ccess (BWA) networks considering the pcket-level qulity-of-service (QoS) constrints. Adptive Modultion nd Coding (AMC) rte bsed on IEEE stndrd is used to djust the trnsmission rte dptively in ech frme time ccording to chnnel qulity in order to obtin multiuser diversity gin. To model the rrivl process nd the trffic source we use the Btch Mrkov Arrivl Process (BMAP), which enbles more relistic nd more ccurte trffic modelling. We determine nlyticlly different performnce prmeters, such s verge queue length, pcket dropping probbility, queue throughput nd verge pcket dely. Finlly, the nlyticl results re vlidted numericlly. KEYWORDS IEEE 802.6; Qulity of Service; Bndwidth Alloction; Performnce Prmeters; BMAP Process; OFDMA; Queueing Theory; Adptive Modultion nd Coding.. INTRODUCTION.. Reference system IEEE stndrd networks ccommodte the incresing user demnd to enble pervsive, high-speed mobile internet ccess to very lrge coverge re. Worldwide Interoperbility for Microwve Access (WiMAX), first stndrdised in 2004 [] known s IEEE 802.6, cn provide brodbnd communictions over wireless for vrious types of multimedi trffic, such s video streming, VoIP, FTP etc. WiMAX presents very chllenging multiuser communiction problem [2] mny users in the sme geogrphic re will require high on-demnd dt rtes in finite bndwidth, with low ltency. Multiple ccess techniques llow different users to shre the vilble bndwidth by llotting ech user some frction of the totl system resources. Due to the diverse nture of nticipted WiMAX trffic, nd the chllenging spects of the system deployment (mobility, neighboring cells, nd high required bndwidth efficiency), the multiple ccess problems re quite complicted in WiMAX. The IEEE stndrd defines two types of operting mode for shring the wireless medium: Point-to-Multipoint (PMP) nd Mesh. The PMP mode dopts cellulr rchitecture, in this mode subscriber sttions re scttered in the cellule round centrl bse sttion. There re two directions: Downlink (from BS to SS) nd Uplink (from SS to BS). Trnsmissions from DOI : 0.52/ijwmn

2 SSs re directed to nd coordinted by the BS. On the other hnd, in Mesh mode, the nodes re orgnized d hoc nd scheduling is distributed mong them. The WiMAX stndrd [] defines the physicl lyer specifictions nd the Medium Access Control (MAC) signling mechnisms. IEEE uses two types of the modultion systems: OFDM (Orthogonl Frequency Division Multiple) nd OFDMA (Orthogonl Frequency Division Multiple Access). OFDMA [2], extended OFDM, to ccommodte mny users in the sme chnnel t the sme time, nd it hs been dopted s the physicl lyer trnsmission technology for IEEE bsed brodbnd wireless networks..2. Relted works In order to promise the qulity of rel-time trffic nd llow more trnsmission opportunity for other trffic types, n Adptive Bndwidth Alloction model (ABA) for multiple trffic clsses in IEEE worldwide interoperbility for microwve ccess networks ws studied in [7]. The im of work in [28] is to show how to exploit dptive bndwidth lloction to increse system utiliztion (for the system dministrtor) with controlled QoS degrdtion (for the users). Insted of only focusing on bndwidth utiliztion or blocking/dropping probbility, two new user-perceived QoS metrics, degrdtion rtio nd upgrde/degrde frequency, re proposed. A Mrkov model is then provided to derive these QoS metrics. Using this model, uthors evlute the effects of dptive bndwidth lloction on user-perceived QoS nd show the existence of trde-offs between system performnce nd user-perceived QoS. Mthemticl tools were used in [7, 8 nd 9] to study performnces prmeters of both the connection-level nd the pcket-level for model using two Connection Admission Control (CAC) schemes considered t subscriber sttion in single-cell IEEE environment in which the bse sttion lloctes sub-chnnels to the subscriber sttions in its coverge re. For wireless mobile networks, the problem of providing pcket-level QoS ws studied quite extensively in the literture. A scheduling mechnism for downlink trnsmission ws proposed in [32] to provide dely gurntee. In [5], uthors proposed two credits bsed scheduling schemes which cn efficiently serve rel time burst trffic with reduced ltency. The effect of the proposed schemes on ltency, bndwidth utiliztion nd throughput for rel time burst flows is compred with Round Robin scheduling scheme. In [4], the proposed intergrded model cn be pplied to IEEE.6e. This model supports qulity of service for request mechnism nd dt trnsmission in the uplink phse in the presence of chnnel noise; the uthors clculte the performnce prmeters for single nd multichnnel wireless networks, like the requests throughput, dt throughput nd the requests cceptnce probbility nd dt cceptnce probbility. In [33], dynmic fir resource lloction scheme ws proposed to support reltime nd non-rel-time trffic in cellulr CDMA networks. In [34], uthors considered dt trnsmission system over wireless chnnel, where pckets re queued t the trnsmitter. Using A Mrkov pproximtion, they studied the sttistics of the pcket dropping process due to buffer overflow under utomtic repet request (ARQ) bsed error control scheme. In [27], the uthors consider point-to-point wireless trnsmission where link lyer ARQ is used to counterct chnnel impirments. They presented n nlyticl model frmework to compute link-lyer pcket delivery dely sttistics s function of the pcket error rte. An dptive cross-lyer scheduler ws proposed in [4] for multiclss dt services in wireless networks. The proposed scheduler uses the queuing informtion s well s it tkes the physicl lyer prmeters into ccount so tht the required QoS performnces cn be chieved. The cpcity of TDMA nd CDMA-bsed brodbnd cellulr wireless systems ws derived in [30] under constrined pcket-level QoS. In [3], n nlyticl model is proposed to study the impcts of the chnnel ccess prmeters, bndwidth configurtion nd piggybck policy on the performnce. The impcts of physicl burst profile nd non-sturted trffic hve lso been tken into ccount. It is observed by 40

3 simultions tht the bndwidth utiliztion cn be improved if the bndwidth for rndom chnnel ccess cn be properly configured ccording to the chnnel ccess prmeters, piggybck policy nd network trffic. Besides, there isn t single set of configurtions tht is lwys the best for ll the network scenrios. The uthors in [5] present pipeline pproch to grnt bndwidth t the BS of n IEEE FDD network with hlf-duplex SSs. Bsed on this, they proposed grnt lloction lgorithm, nmely, the Hlf-Duplex Alloction (HDA) lgorithm, which lwys produces fesible grnt lloction provided tht the sufficient conditions re met. Although there hve been severl proposls for QoS scheduling frmeworks nd lgorithms in IEEE BWA networks in the literture [24, 3], they minly focus on the QoS rchitecture nd scheduling lgorithm in bse sttion to stisfy diverse QoS requirements, rther thn bndwidth request lgorithm in subscriber sttion. A previous resercher in n ttempt to ddress bndwidth lloction in IEEE ws reported by the uthors in [0]. They considered similr model in OFDMA bsed-wimax but they modeled pcket-level by MMPP process nd they compred vrious QoS mesures. Since the introduction of Btch Mrkovin Arrivl Process (BMAP) by Lucntoni [], the reserchers [6, 2, nd 29] prove tht BMAP enbles more relistic nd more ccurte trffic modeling; it cn lso cpture dependency in trffic processes nd outperforms MMPP nd Poisson trffic models. Since the incoming trffic in IEEE hs self-similrity nd bursting nture cusing correltion in inter-rrivl times -which influences the performnce of the system- we re motivted for using BMAP which cn model such trffic correltion..3. Aims of the pper In this pper, we present performnce nlysis for bndwidth lloction in IEEE brodbnd wireless ccess networks considering the pcket-level qulity-of-service (QoS). Adptive modultion nd coding (AMC) rte bsed on IEEE stndrd is used to djust the trnsmission rte dptively in ech frme time ccording to chnnel qulity in order to obtin multi-user diversity gin. A queueing nlyticl model is developed bsed on Discrete- Time Mrkov Chin (DTMC) which cptures the system dynmics in terms of the number of pckets in the queue. We ssume tht the rrivl process is modelled by the Btch Mrkov Arrivl Process (BMAP) s the trffic source. Bsed on this model, vrious performnce prmeters such s verge queue length, pcket dropping probbility due to lck of buffer spce, the queue throughput, nd the verge queueing dely re obtined. Finlly, the nlyticl results re vlidted by numericl results..4. Orgnistion of the pper The rest of the pper is orgnized s follows: In Section 2, we briefly introduce QoS rchitecture of IEEE networks. Section 3 presents Modultion nd Coding Schemes for IEEE Section 4 describes the system model. The formultion of the nlyticl model is presented in Section 5. In section 6, different performnce prmeters re nlyticlly determined. Section 7 sttes numericl results. Finlly, section 8 gives conclusion of this pper. 2. QOS ARCHITECTURE OF IEEE NETWORKS In this pper, we consider point-to-point wireless mode (PMP) of IEEE 802.6, where bse sttion (BS) serves set of subscriber sttions (SSs). The Uplink nd the downlink re served in the seprte region of physicl lyer (OFDMA/TDD) frme.the downlink chnnel is in brodcst mode, but n SS is only required to process dt which re ddressed to itself. In the 4

4 uplink sub-frme, on the other hnd, the SSs trnsmit dt to the BS in Time Division Multiple Access (TDMA) mnner. Downlink nd uplink sub-frmes re duplexed using one of the following techniques: (Frequency Division Duplex FDD), where downlink nd uplink subfrmes occur simultneously on seprte frequencies, nd Time Division Duplex (TDD), where downlink nd uplink sub-frmes occur t different times nd usully shre the sme frequency. SSs cn be either full duplex or hlf-duplex. IEEE 802.6e uses connection-oriented medium ccess control (MAC) protocol which provides mechnism for the SSs to request bndwidth to the BS. IEEE 802.6e MAC supports two clsses of SS: grnt per connection (GPC) nd grnt per SS (GPSS). In the cse of GPC, bndwidth is grnted to connection individully. In contrst, for GPSS, portion of the vilble bndwidth is grnted to ech of the SSs nd ech SS is responsible for llocting bndwidth mong the corresponding connections. The lengths of the downlink nd uplink sub-frmes for ech SS re determined by the BS nd brodcst to the SSs through downlink nd uplink mp messges (UL-MAP nd DL-MAP) t the beginning of ech frme. Therefore, ech SS knows when nd how long to receive from nd trnsmit dt to the BS. In the uplink direction, ech SS cn request bndwidth to the BS by using BW-request pckets. WiMAX is ssocited with the IEEE stndrd [, 2, nd 3], which defines five clsses of trffic flows representing different types of services in the following order: Unsolicited Grnt Service (UGS), Extended Rel Time Polling Service (ertps), Rel Time Polling Service (rtps), Non-Rel Time Polling Service (nrtps), nd Best Effort Service (BE). Ech clss hs its QoS mechnisms t the Medi Access Control (MAC) lyer to support the vrious pplictions. UGS is designed to support rel-time service flows tht generte fixed-size dt pckets on periodic bsis, such s VoIP without silence suppression. ertps supports rel-time pplictions which generte vrible-sized dt pckets periodiclly tht require gurnteed dt rte nd dely with silence suppression. rtps supports rel-time service flows tht generte vrible dt pckets size on periodic bsis. nrtps supports dely-tolernt dt strems which re more bursty in nture, such s FTP, in generl, the nrtps cn tolerte longer delys nd is insensitive to dely jitter, but requires minimum throughput. BE supports trffic with no QoS requirements, such s emil, nd therefore my be hndled on resource-vilble bsis. 3. MODULATION AND CODING SCHEMES FOR IEEE Adptive modultion nd coding scheme (AMC) is supported in the WiMAX networks. The bsic ide of AMC is to mximize the dt rtes by djusting the trnsmission prmeters ccording to the fluctutions in the chnnel. The chnnel qulity is determined by the instntneous received Signl-to-Noise Rtio (SNR) γ in ech time slot. We ssume tht the chnnel is sttionry over the trnsmission frme time. Lower dt rtes re chieved by using Modultion Level nd rte error correcting corresponding to Rte ID = 0 (BPSK nd /2). The higher dt rtes re chieved by using Modultion Level nd rte error correcting corresponding to Rte ID = 6 (64QAM nd 3/4). In ll, there re 52 different possible configurtions of modultion order nd coding types nd rtes [2], lthough most implementtions of WiMAX will offer only frction of these. Tble lists these schemes represented by different rte IDs for IEEE WiMAX Networks. In n OFDMA system [2], ech user will be llocted block of subcrriers, ech of which will hve different set of SNR. Therefore, cre needs to be pid to which constelltion/coding set is chosen bsed on the vrying SNR cross the subcrriers. To determine the mode of trnsmission (i.e., modultion level nd coding rte), n estimted vlue of SNR t the receiver is used. In this cse, the SNR t the receiver is divided into N + 42

5 nonoverlpping intervls (i.e., N = 7 in WiMAX) by thresholds Γ ( n n {0,,..., N }) where Γ < Γ < Γ =. The subchnnel is sid to be in stte n (i.e., rte ID = n will be used) 0... N + n γ n+ if Γ < Γ. To void possible trnsmission error, no pcket is trnsmitted when γ < Γ 0. Note tht, these thresholds correspond to the required SNR specified in the WiMAX stndrd, SNR, Signl-to-Noise Rtio [8, 23, nd 25]. Tht is, Γ 0 = 6.4, Γ = 9.4,..., Γ N = 24.4 (s shown in Tble ). Tble : IEEE Profiles. Rte ID Modultion Level Informtion Required (Coding) Bits/Symbol SNR (db) 0 BPSK (/2) QPSK (/2) QPSK (3/4) QAM (/2) QAM (3/4) QAM (2/3) QAM (3/4) MODEL DESCRIPTION 4.. Arrivl Process Trffic The BMAP hs received considerble interest during the lst few yers. It ws first introduced by Neuts [] s the verstile Mrkovin point Process. It generlizes Mrkovin Arrivl Process (MAP) introduced by Lucntoni et l. [20]. To cpture the rrivl process trffic, we use BMAP process [6]. The rrivls in the BMAP is directed by the irreducible continuous time Mrkov chin CTMC with finite stte spce {0,,, S}. Sojourn time of the CTMC in the stte s hs exponentil distribution with prmeter λ s. After time expires, with probbility p 0 ( s, s) the chin jumps into the stte s without genertion of pckets nd with probbility pk ( s, s) the chin jumps into the stte s nd btch consisting of k pckets is generted, k. The introduced probbilities stisfy conditions: p ( s, s ) = 0, the 0 sum of the probbilities of ll outgoing trnsitions hs to be equl to, S S pk ( s, s ) + pk ( s, s ) =, 0 s S. k = s = 0 s = 0 s s () The BMAP is two dimensionl Mrkov process { A( t), J ( t)} on the stte spce {( i, j) / i 0,0 j S} with infinitesiml genertor given by: D 0 D D 2 D 3 K 0 D 0 D D 2 K Ψ = 0 0 D 0 D K (2) D 0 K M M M M O where the mtrices D 0 = [ Dss ], 0 s S, 0 s S hs negtive digonl elements nd non negtive off digonl elements given by: 43

6 D ss λs, s = s = λs p( s, s ), s s The mtrices Dk, k > 0 re defined by: D = [ D ], 0 s S, 0 s S, k > 0 (4) k k, ss where: D, = λ p ( s, s ), 0 s S, 0 s S, k > 0. (5) The mtrix D defined by. k ss s k D = D k k = 0 (3), is n irreducible infinitesiml genertor. We lso ssume tht D k D0, which ensures tht rrivls will occur. The vrible A( t) counts the number of rrivls during [0, t[ nd the vrible J ( t) represents the phse of the rrivls process. The stedy-stte probbility vectorπ of the CTMC with genertor D cn be clculted s BMAP usul: π BMAP.D = 0, π. =. (6) BMAP e Where 0 nd e re row nd column vectors consisting of zeros nd units, respectively. The men stedy-stte rrivl rte generted by the BMAP is: λ = π kd e. (7) BMAP BMAP k k = More detil nd results concerning this Process cn be found in [9] for instnce. The probbility f ( λ, T ) of = 0,,..., A incoming pckets, with A denoting the mximum s pckets number, tht rrive with men rte λs within time slot intervl T is given by: λs e T ( λ ) st f( λs, T) = (8)! + λst e ( λst ) It is lso essentil for the condition < er s lwys to stnd, with er expressing = A! sufficiently smll number. Note tht the probbility tht Poison rrivls with verge rte λs occur during n intervl T is given by the S S digonl mtrix ξ which is defined s: 4.2. System Model f ξ = ( λ, T ) f ( λ, T ) 2 O f ( λs, T ) We consider n infrstructure-bsed wireless ccess network, where connections re estblished between bse sttion (BS) nd multiple subscribers sttions (SSs) through TDMA/TDD ccess mode using single crrier ir-interfce (s shown in Figure ). Ech subscriber sttion serves multiple connections. For ech connection seprte queue in SS with size X pckets is used for buffering the pckets from higher lyers. In prticulr, for one connection, there is queue for uplink nd nother queue for downlink trnsmissions from the SS nd the BS, (9) 44

7 respectively. We consider n SS of type GPC. Therefore, through the SS certin mount of bndwidth is reserved for ech connection during bndwidth lloction. Figure : System model 5. FORMULATION OF THE ANALYTICAL MODEL 5.. Stte Spce The stte of the queue is observed t the beginning of ech frme. We ssume tht connection i is llocted with bi units of bndwidth nd pckets rriving during frme period f will not be trnsmitted until frme period f + t the erliest. The stte spce of the queue cn be defined s follows: E = {( x, s);0 x X, s S}, (0) where x, s represent, the number of pckets in the queue, the stte (phse) of n irreducible continuous time Mrkov chin of BMAP rrivl process respectively Trnsition Mtrix for the Queue The trnsition mtrix M for the queue cn be expressed s follows: m0,0 m0,l m0, A M M O O md,0 md, L md, D L L m D, D+ A M = O O O O O O mx A, X A D L L m X A, X O O O O M mx, X D L L mx, X () The rows of mtrix M represent the number of pckets in the queue nd element inside this mtrix denotes the trnsition probbility for the cse when the number of pckets in the queue chnges from x in the current frme to x in the next frme. Also, the mximum number of pckets tht cn enter into or deprt from the queue within frme time is represented with A nd D respectively. x, x 45

8 The mximum number of trnsmitted pckets within time slot is given by D = min( x, D). Hence, if k represents the number of the successfully trnsmitted pckets. The probbility tht k pckets will be trnsmitted in timeslot is obtined by the mtrix T which is defined s k follows: x k x k ( θ ) θ, k < D k Tk = (2) x x j x j ( θ ) θ, k = D j= U j where θ is the probbility tht pckets is successfully trnsmitted. The elements in the mtrix M cn be obtined s follows: mx, x u = Ψ ξ Tk (3) m m k = u = Ψ ξ T (4) x, x+ v k k = v = Ψ ξ T (5) x, x k k = for u =, 2,..., D nd v =,2,..., Awhere, k {0,,..., D } nd {0,,..., A} represent the number of deprted pckets nd the number of pckets rrivls, respectively. With x, x u m, m x, x + nd v m we represent the probbility tht the number of pckets in the queue x, x increses by u, decreses by v, nd does not chnge, respectively. The remining rows { x = X A+, X A+ 2,..., X} of the mtrix M, include the occurrence where some pckets would be dropped due to lck of queue spce. We clculte the probbilities s follows: A x, x+ v x, x+ for = v m = m x + v X (6) Which express tht no pcket hs been dropped nd occur when more incoming pckets to n lredy fully queue re dropped. Additionlly, the lst element of the min digonl of M is given by: A x, x x, x x, x+ = m = m + m for x = X (7) where m is obtined for the cse without ny pckets dropping. x, x Equtions (6) nd (7) indicte the cse tht the queue will be full if the number of incoming pckets is greter thn the vilble spce in the queue. In other words, the trnsition probbility to the stte tht the queue is full cn be clculted s the sum of ll the probbilities tht mke the number of pckets in queue equl to or lrger thn the queue size X. 6. PERFORMANCE PARAMETERS The performnce prmeters re nlyticlly clculted using the stedy stte probbility of the system. The vector π of these probbilities is obtined by solving the system π.m = π nd π. =, where is column mtrix of ones. 46

9 The stedy-stte probbilities, denoted by π ( x, s) for the stte tht there re x {0,,..., X} pckets in the queue, cn be extrcted from mtrix π s follows: [ ] π( x, s) = π, s,..., S X = (8) S The mtrix π contins the stedy stte probbilities corresponding to the number of pckets in the queue nd the stte (phse) of n irreducible continuous time Mrkov chin of BMAP rrivl process. Using the stedy stte probbilities, the vrious performnce mesures cn be obtined. 6.. Averge Queue Length The verge number of pckets in the trnsmission queue is obtined s follows: 6.2. Pcket Dropping Probbility X X E ( x) x π ( x, s) S = = (9) x = 0 s = In order to compute the pcket dropping probbility ( p drop ), we firstly obtin the number of dropped pckets per time slot, obtined using the verge number of dropped pckets per frme. If x is the number of pckets in the queue nd this number increses by n, the number of dropped pckets X drop is: X drop = n ( X x). ], [( x) where X n + if x A A( x) = (20) 0 otherwise The verge number of dropped pckets per frme is obtined s follows: X drop = E( X ) drop X S A S (2) = [ mx, x+ n] s, l.( n ( X x)). π( x, s) x= 0 s= n= X x+ l= S where the term [ m x, x + n] s, l in Eqution (2) indictes the totl probbility tht the number l= of pckets in the queue increses by n t every rrivl phse. The probbility m x, x + nis used rther thn the probbility of pcket rrivl, becuse the pcket trnsmission in the sme frme is considered. After clculting the verge number of dropped pckets per frme, we cn obtin the probbility tht n incoming pcket is dropped s follows: p drop X λ drop = (22) BMAP where λ BMAP is the men stedy stte rrivl rte generted by the BMAP (s obtined from (7)). 6.3.Queue throughput It mesures the number of pckets trnsmitted in one frme nd cn be obtined from: ϕ = λ ( p ) (23) BMAP drop 47

10 6.4. Averge Pcket Dely The verge pcket dely is defined s the number of frmes tht pcket wits in the queue since its rrivl before it is trnsmitted. We use Little s formul [22] to obtin verge pckets dely s follows: X D = = ϕ λ BMAP whereϕ is the throughput nd X is the verge queue length. 7. NUMERICAL RESULTS X ( P ) In the next, performnce prmeters re numericlly evluted, using Mtlb softwre. 7.. Prmeter Setting We consider the system model depicted in section 4. Adptive Modultion nd Coding (AMC) is used in which the modultion level nd the coding rte re incresed if the chnnel qulity permits. Tble lists these schemes represented by different rte IDs for IEEE The mximum number of pckets tht cn be trnsmitted in one frme period is 50 pckets per frme. The queue size is ssumed to be 50 pckets (i.e. X = 50 ). For simplicity of computtion we ssume the mximum size of the btch to be 2, nd the mtrices governing the stte trnsitions of the BMAP re giving s follows: drop D0 =, D =, D2 = Its sojourn times t ech stte re ssumed to be exponentilly distributed with rtes λ 0 = 2.0, λ =.0 respectively. The performnce prmeters re mesured respectively under different mount of llocted bndwidthb, under different chnnel qulities with constnt trffic intensity, nd under different trffic intensities with chnnel SNR in the rnge of rte IDn = 0. In this work, bndwidth b is defined (s in [0]) s the number of pckets tht cn be trnsmitted in one frme using rte IDn = Results nd Discussion We first exmine the impct of trffic intensity on bndwidth lloction. Vritions in throughput with trffic intensity re shown in Figure 2. When the trffic intensity increses, the throughput increses until it becomes sturted. At this point (e.g., 3.0 ), the rriving pckets cnnot be trnsmitted fster thn the trnsmission rte tht the chnnel qulity llows. (24) 48

11 Figure 2: Throughput under trffic intensity. Figure 3: Averge queue length under trffic intensity. Figure 4: Averge dely under trffic intensity.. 49

12 Figure 5: pckets dropping probbility under trffic intensity. Averge queue length, verge dely nd pckets dropping probbility increse s the trffic intensity increses (Figures 3, 4 nd 5). Therefore, we cn sy tht the increse of the prmeters previously mentioned is linked with the trffic intensity. On the other hnd, those prmeters decrese s the chnnel qulity improves (Figures 6, 7 nd 8). Figure 6: Averge queue length under different chnnel qulities. Figure 7: Averge dely under different chnnel qulities. 50

13 Figure 8: Pcket dropping probbility under different chnnel qulities. Figure 9: Throughput under different chnnel qulities. When the chnnel qulity improves, the trnsmitter cn utilize higher modultion level nd code rte to increse throughput (Figure 9). Note tht if trnsmission rte is high enough to ccommodte most of the rrivl trffic, incresed mount of llocted bndwidth or better chnnel qulity will not impct the queue throughput since ll the pckets cn be trnsmitted within few frmes. Moreover, different mount of llocted bndwidth results in different throughput. 8. CONCLUSION In this pper, queuing nlyticl model bsed on Discrete-Time Mrkov Chin (DTMC) hs been presented to nlyze the pcket-level performnce in IEEE brodbnd wireless ccess networks considering dptive modultion nd coding t the OFDMA physicl lyer. In the considered WiMAX system model, bse sttion serves multiple subscriber sttions, nd the bse sttion lloctes certin number of sub-chnnels for ech subscriber sttion. To model the rrivl process nd the trffic sources we use the Btch Mrkov Arrivl Process (BMAP), which enbles more relistic nd more ccurte trffic modelling. Using this queuing model, the impct of different trffic sources nd the impct of chnnel qulity on QoS prmeters, such s verge queue length, pcket dropping probbility, queue throughput nd verge pcket dely, re nlyticlly studied. Finlly, the nlyticl results re vlidted numericlly. 5

14 REFERENCES [] IEEE WG, IEEE stndrd for locl nd metropolitn re networks prt 6: Air interfce for fixed brodbnd wireless ccess systems, IEEE Stndrd, June [2] IEEE WG, IEEE stndrd for locl nd metropolitn re networks prt 6: Air interfce for fixed nd mobile brodbnd wireless ccess systems, Amendment 2, IEEE Stndrd, December [3] Mobile WiMAX Prt I: A Technicl Overview nd Performnce Evlution, August, [4] Abdelslm Amer nd Fyez Gebli, Generl Model for Single nd Multiple Chnnels WLANs with Qulity of Service Support, Interntionl Journl of Wireless & Mobile Networks (IJWMN), Vol, No 2, November [5] Andre Bcioccol, Cludio Cicconetti, Alessndro Ert, Lucino Lenzini, nd Enzo Mingozzi, Alessndro Ert, Lucino Lenzini, nd Enzo Mingozzi, Bndwidth Alloction with Hlf-Duplex Sttions in IEEE Wireless Networks, IEEE trnsctions on mobile computing, vol. 6, no. 2, december [6] B. Bynt, S. Doirieux, G. Nogueir, M. Mqbool, nd M. Coupechoux, An efficient nlyticl model for wimx networks with multiple trffic profiles, in Proc. of ACM/IET/ICST IWPAWN, September [7] Abdelli EL BOUCHTI, Abdelkrim HAQIQ nd Sid EL KAFHALI, Anlysis of Qulity of Service Performnces of Connection Admission Control Mechnisms in OFDMA IEEE Network using BMAP Queuing, Interntionl Journl of Computer Science Issues (IJCSI), Vol. 9, Issue, No 2, ISSN (Online): , pp , Jnury 202. [8] Abdelli EL BOUCHTI, Sid EL KAFHALI, nd Abdelkrim HAQIQ Performnce Modeling nd Anlysis of Connection Admission Control in OFDMA bsed WiMAX System with MMPP Queueing World of Computer Science nd Informtion Technology Journl (WCSIT), Vol., No. 4, pp , 20. [9] Abdelli EL BOUCHTI, Sid EL KAFHALI, nd Abdelkrim HAQIQ Performnce Anlysis of Connection Admission Control Scheme in IEEE OFDMA Networks Interntionl Journl of Computer Science nd Informtion Security (IJCSIS), Vol. 9, No. 3, pp Mrch 20. [0] M. Fthi, H. Theri, Queuing nlysis for dynmic bndwidth lloction in IEEE stndrd, 3rd IEEE Interntionl symposium on wireless pervsive computing, 7-9 My [] M.F.Neuts, Averstile Mrkovin Point Process, J.Appl.Prob, 6: , 979. [2] Jeffrey G. Andrews, Orthogonl Frequency Division Multiple Access (OFDMA), book chpter, July 29, [3] Jinhu He, Kun Yng, Ken Guild, nd Hsio-Hw Chen, On Bndwidth Request Mechnism with Piggybck in Fixed IEEE Networks, IEEE trnsctions on wireless communictions, vol. 7, no. 2, december [4] K.B. Johnsson nd D.C. Cox, An Adptive Cross-Lyer Scheduler for Improved QoS Support of Multiclss Dt Services on Wireless Systems, IEEE J. Selected Ares in Comm., vol. 23, no. 2, pp , Feb [5] C.Klyn Chkrvrthy nd Prof. P.V.G.D. Prsd Reddy, Selfless Distributed Credit Bsed Scheduling For Improved QoS In IEEE WBA Networks, Interntionl Journl of Wireless & Mobile Networks (IJWMN), Vol, No 2, pp. 8-25, November [6] A. Klemm, C. Lindemnn, nd M. Lohmnn, "Trffic Modeling of IP Networks Using the Btch Mrkovin Arrivl Process", in Proc. Computer Performnce Evlution / TOOLS, 2002, pp [7] T.-L. Sheu K.-C. Hung, Adptive bndwidth lloction model for multiple trffic clsses in IEEE worldwide interoperbility for microwve ccess networks, The Institution of Engineering nd Technology, Vol. 5, Iss., pp , 20. [8] Q.Liu, S. Zhou, nd G. B. Ginnkis, Queuing with dptive modultion nd coding over wireless links: cross-lyer nlysis nd design, IEEE Trnsctions on Wireless Communictions, vol. 4, no. 2, pp , My [9] D.M. Lucntoni, The BMAP/G/ queue : A tutoril, In L.Dontiello nd R.Nelson, editors, Performnce Evlution of Computer nd Communictions Systems, pges , lectures Notes in Computer Science 729, Springer Verlg, 993. [20] D.M.Lucntoni, K.S.Meier-Hellstern, nd M.F.Neuts, A single server queue with server vctions nd clss of non-renewl rrivl processes, Adv.Appl.Prob,22: ,990. [2] D. M. Lucntoni, New Results on the Single Server Queue with Btch Mrkovin Arrivl Process, Comm. in Sttistics: Stochstic Models 7, -46,

15 [22] R. Nelson, Probbility, stochstic process, nd queueing theory, Springer-Verlg, third printing, [23] D. Niyto nd E. Hossin, Dely-bsed dmission control using fuzzy logic for OFDMA brodbnd wireless networks, in Proc. IEEE ICC 06, June [24] D. Niyto, E. Hossin, Queue-Awre Uplink Bndwidth Alloction nd Rte Control for Polling Service in IEEE Brodbnd Wireless Networks, IEEE trns. on Mobile Computing, Vol. 5, No. 6, June [25] D. Niyto nd E. Hossin, "Connection dmission control in OFDMA-bsed WiMAX networks: Performnce modeling nd nlysis," invited chpter in WiMx/MobileFi: Advnced Reserch nd Technology, (Ed. Y. Xio), Auerbch Publictions, CRC Press, December [26] D. Niyto, E. Hossin, QoS-wre bndwidth lloction nd dmission control in IEEE brod bnd wireless ccess networks: A non-coopertive gme theoretic pproch, Comut. Netw. (2007), doi:0.06/jcomnet [27] M. Rossi nd M. Zorzi, Anlysis nd Heuristics for the Chrcteriztion of Selective Repet ARQ Dely Sttistics over Wireless Chnnels, IEEE Trns. Vehiculr Technology, vol. 52, no. 5, pp , Sept [28] C.T. Chou nd K.G. Shin, Anlysis of Adptive Bndwidth Alloction in Wireless Networks with Multilevel Degrdble Qulity of Service, IEEE Trns. Mobile Computing, vol. 3, no., pp. 5-7, Jn.-Mr [29] Tkine, T. nd Tkhshi, Y On the reltionship between queue lengths t rndom instnt nd t deprture in the sttionry queue with BMAP rrivls. Stoch. Mod [30] S.V. Krishnmurthy, A.S. Acmpor, nd M. Zorzi, On the Rdio Cpcity of TDMA nd CDMA for Brodbnd Wireless Pcket Communictions, IEEE Trns. Vehiculr Technology, vol. 52, no., pp , Jn [3] K. Wongthvrwt nd A. Gnz, Pcket scheduling for QoS support in IEEE brodbnd wireless ccess systems, Interntionl Journl of Communiction systems, vol. 6, pp. 8 96, [32] D. Wu nd R. Negi, Downlink Scheduling in Cellulr Network for Qulity-of-Service Assurnce, IEEE Trns. Vehiculr Technology, vol. 53, no. 5, pp , Sept [33] L. Xu, X. Shen, nd J.W. Mrk, Fir Resource Alloction with Gurnteed Sttisticl QoS for Multimedi Trffic in Widebnd CDMA Cellulr Network, IEEE Trns. Mobile Computing, vol. 4, no. 2, pp , Mr.-Apr [34] M. Zorzi, Pcket Dropping Sttistics of Dt-Link Protocol for Wireless Locl Communictions, IEEE Trns. Vehiculr Technology, vol. 52, no., pp. 7-79, Jn Authors Sid EL KAFHALI received the B.Sc. degree in Computer Sciences from the University of Sidi Mohmed Ben Abdellh, Fculty of Sciences Dhr El- Mhrz, Fez, Morocco, in 2005, nd M.Sc. degree in Mthemticl nd Computer engineering from Hssn st University, Fculty of Sciences nd Techniques (FSTS), Settt, Morocco, in He hs been working s professor of Computer Sciences in high school since 2006, Settt, Morocco. Currently, he is working towrd his Ph.D. t FSTS. His current reserch interests performnce evlution, nlysis nd simultion of Qulity of Service in mobile networks. Abdelli EL BOUCHTI received the B.Sc. degree in Applied Mthemtics from the University of Hssn 2 nd, Fculty of Sciences Ain chock, Csblnc, Morocco, in 2007, nd M.Sc. degree in Mthemticl nd Computer engineering from the Hssn st University, Fculty of Sciences nd Techniques (FSTS), Settt, Morocco, in Currently, he is working towrd his Ph.D. t FSTS. His current reserch interests include performnce evlution nd control of telecommuniction networks, stochstic control, networking gmes, relibility nd performnce ssessment of computer nd communiction systems. 53

16 Mohmed HANINI is currently pursuing his PhD. Degree in the Deprtment of Mthemtics nd Computer t Fculty of Sciences nd Techniques (FSTS), Settt, Morocco. He is member of e-ngn reserch group. His min reserch res re: Qulity of Service in mobile networks, network performnce evlution. Dr. Abdelkrim HAQIQ hs High Study Degree (DES) nd PhD (Doctort dett) both in Applied Mthemtics from the University of Mohmed V, Agdl, Fculty of Sciences, Rbt, Morocco. Since September 995 he hs been working s Professor t the deprtment of Mthemtics nd Computer t the fculty of Sciences nd Techniques, Settt, Morocco. He is the director of Computer, Networks, Mobility nd Modeling lbortory nd generl secretry of e-ngn reserch group, Moroccn section. He ws the chir of the second interntionl conference on Next Genertion Networks nd Services, held in Mrrkech, Morocco 8-0 July 200. He is lso TPC member nd reviewer for mny interntionl conferences. Professor Hqiq interests lie in the re of pplied stochstic processes, stochstic control, queueing theory nd their ppliction for modeling/simultion nd performnce nlysis of computer communiction networks. From Jnury 98 to December 98 he hd Post-Doctorl Reserch ppointment t the deprtment of systems nd computers engineering t Crleton University in Cnd. He lso hs held visiting positions t the High Ntionl School of Telecommunictions of Pris, the universities of Dijon nd Versilles St- Quentin-en-Yvelines in Frnce, the University of Ottw in Cnd nd the FUCAM in Belgium. 54