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Adaptive rate scheduling for 3G networks with shared resourcesusing the generalized processor sharing performance modelSalman A. AlQahtani*King Fahd Security College, Riyadh, Saudi ArabiaReceived 25 September 2006; received in revised form 4 October 2007; accepted 8 October 2007Available online 13 October 2007AbstractIn current and next 3G and beyond wideband code-division with multiple access (WCDMA) cellular networks, sharing the radioaccess network has become an important issue for 3G mobile operators. 3G and beyond network rollout is a very costly and time con-suming process. Therefore, sharing of network infrastructure among operators offers an alternative solution to reducing the investmentin the coverage phase of WCDMA. In radio access network (RAN) sharing method, which is our focus in this study, each operator hasits own core network and only the RAN is shared. It implies that multiple operators fully share the same RAN. Without an efficientRRM, one operator can exhausts the capacity of others. This study tackles an efficient scheduling to provide maximum system through-put and proportional fairness in accordance with operator capacity share through adaptive resource allocation scheme. We refer to thisnew scheme as Multi-operators Code Division Generalized Processor sharing scheme (M-CDGPS). It employs both adaptive rate allo-cation to maximize the resource utilization and GPS techniques to provide fair services for each operator. The performance analysis interms of bounded delay and queue size are obtained.? 2007 Elsevier B.V. All rights reserved.Keywords: Adaptive rate allocation; Mobile wireless; Multi-operator; Utilization; WCDMA1. IntroductionIn current and next 3G and beyond wideband code-divi-sion with multiple access (WCDMA) cellular networks,sharing the radio access network has become an importantissue for 3G mobile operators. 3G and beyond networkrollout is a very costly and time consuming process. There-fore, sharing of network infrastructure among operatorsoffers an alternative solution to reducing the investmentin the coverage phase of WCDMA. Another advantageof the deployment of shared networks is the increased cov-erage, since operators can cooperate on coverage and sitesas a more cost-effective way to cover large geographicalareas. All together, this will result in reduced time to mar-ket and earlier user acceptance for WCDMA and itsrelated services. The sharing methods available for 3G net-work operators are proposed in many literatures 13.These sharing methods include, site sharing, radio accessnetwork (RAN) sharing, common network sharing, andgeographical network. The previous proposals and studiesof WCDMA wireless sharing methods present the problemfrom architectural and technical point of view withoutinvestigating how the shared radio resources are going tobe managed and controlled through RRM. The RANbased sharing method is of special importance as it reflectsthe most recent and critical sharing option where morethan one operator shares the same RAN. In RAN sharingmethod, which is our focus in this study, each operator hasits own core network and only the RAN is shared (seeFig. 1). It implies that multiple operators fully share thesame RAN. Without an efficient RRM, one operator canexhausts the capacity of others. Therefore, there is a criticalneed for radio resource control between the multiple oper-ators to prevent one operator from exhausting the capacityof others.0140-3664/$ - see front matter ? 2007 Elsevier B.V. All rights reserved.doi:10.1016/com.2007.10.011*Tel.: +966 505225172.E-mail address: salman.sa/locate/comcomAvailable online at Computer Communications 31 (2008) 103111Service level agreements (SLA) specify the usage of theradio network capacity for each operator under the RANbased sharing agreement 16. Each operator receives theagreed upon QoS level by following the specified operationrules in the SLA. More about SLA and service manage-ment are described in 16. In order to secure the fair accessto the network capacity resources and to optimize theusage of the allotted capacity, it is very important to enablethe RRM to separately control each operator and guaran-tee its minimum required capacity. In other word, RRMguarantees that the maximum traffic per operator asdefined by SLA is not exceeded unless it is wanted orallowed. RRM can allow an operators traffic to exceedits limit in an adaptive way if there are unused resourcesrelated to other unbacklogged operator in order to increasethe system utilization. Hence, the shared radio resourcesmust be controlled in a fair and efficient way between oper-ators. The call admission control (CAC) is key element ofRRM and used to control the admission of the connectionrequest of an operator. However, after the admission of theconnection request, the packets of this operator connectionare transmitted based on the scheduling scheme used.Scheduling scheme, as part of RRM, controls the packetstransmissions during the connection time. This studyfocuses on designing an efficient and fair scheduling schemefor multi-operator WCDMA system.1.1. Related Works and MotivationAn ideal fair scheduling discipline is the well known gen-eralized processor sharing (GPS), and also known asweighted fair queuing (WFQ) 4,5.The GPS was intro-duced in 4,5 and then extensively studied under varioustraffic conditions 6. Several GPS-based fair schedulingschemes have been proposed for wireline packet network46. Also, these GPS-based scheduling have been adaptedto wireless networks. The works in, 79, extend fair sched-uling schemes developed for wireline networks to time divi-sion multiple access (TDMA)-based and hybrid time-division/code-division multiple access (TD/CDMA) basedwireless networks. These schemes are implemented usinga conventional time-scheduling approach, requiring highcomplexity due to the intensive computation for the virtualtime of each packet 10.However, The radio resources in CDMA-based net-works are mainly related to the spreading bandwidth,transmission power and channel rates and hence, the timescheduling approach is not fully suited to CDMA-basedwireless networks 8,11,12. One issue with GPS techniqueis that it is based on a fluid-flow model 4. Ideally, itassumes that multiple sessions can be served simulta-neously and at variable rates. Hence, the significant featureof GPS is that it treats different traffic types differentlyaccording to their QoS requirements. Unlike TDMA, par-allel service is natural to DS-CDMA systems where multi-ple sessions (i.e., traffic flows) can be served simultaneouslyand using different direct sequence codes (i.e., differentrates). Moreover, the share of each session from CDMAchannel resources can be varied theoretically by varyingits spreading factor and/or its power level. Due to the sim-ilarity existence between WCDMA system and GPS fluid-flow model, GPS service discipline seems to be a logicalcandidate for CDMA systems 8,12. This motivation wasused to study the GPS-scheduling in WCDMA systemsand it will be used as our motivation to study GPS-sched-uling for WCDMA system with multi-operator sharing thesame RAN.In order to improve radio resource utilization andachieve fairness with low complexity in such WCDMA-based wireless networks, number of recent works relatedto GPS-based uplink scheduling for WCDMA environ-ments are studied and adapted in 1115. In 11, a rate-scheduling approach based on GPS is applied to theCDMA downlinks. Given the limit of the total downlinkNode BNode BNode BRNCRNCOperator 1Core NetworkOperator nCore NetworkOperator 2Core NetworkShared RANPSTN/IPPSTN/IPPSTN/IPFig. 1. RAN sharing.104S.A. AlQahtani / Computer Communications 31 (2008) 103111transmission power, the rate-scheduling scheme dynami-cally allocates the downlink power and rates according toweights assigned to the users. The user weights are opti-mized for each scheduling period to guarantee the requiredminimum channel rates, adapting to the time-varying chan-nel condition, at the cost of high complexity. In 12,13, alow-complexity code-division GPS (CDGPS) scheme fordynamic fair scheduling in the uplink of a WCDMA cellu-lar network is proposed. The scheme makes use of theadaptive feature in the wideband CDMA physical layerto efficiently support QoS for multimedia traffic and usesa fixed weight assignment to guarantee GPS fairness. TheCDGPS scheduler makes use of both the traffic character-istic in the link layer and the adaptability of the WCDMAphysical layer to perform fair scheduling on a time-slotbasis, by using a dynamic rate-scheduling approach ratherthan the conventional time scheduling approach as in GPS.Alow-complexityGPS-basedbandwidthschedulingscheme similar to the CDGPS is also proposed in 14,where a multi-carrier CDMA system is considered. Basedon the minimum power allocation algorithm, a WCDMAGPS scheduling scheme is proposed in 15. However, alltheses WCDMA-based scheduling schemes are designedfor single operator systems without considering how tocontrol and schedule the resources that are shared amongmore than one operator in an efficient and a unified way.1.2. Research contributionIn this study, the CDGPS and GPS discipline idea isadapted and extended in order to design a new high perfor-mance GPS-based scheduling scheme which can effectivelycontrol the shared resources among WCDMA multi-oper-ators in an efficient and fair manner. Efficient means highersystem utilization and fair means that each operatorguaranteed at least a capacity equals to its capacity sharespecified in SLA. Therefore, a multi-operator CDGPS(M-CDGPS)rateschedulingschemefortheuplinkWCDMA cellular network is investigated and analyzed,which employs both adaptive rate allocation to maximizethe resource utilization and M-CDGPS to provide fair ser-vices for each operator. The resource allocated to eachoperator session is proportional to an assigned weightingfactor brought from SLA specification. After allocatingeach operates its allotted capacity, M-CDGPS schemecan use the CDGPS service discipline to dynamically sche-dule the assigned channel rates of one operator among thetraffic classes within that operator independently.The rest of this paper is organized as follows. Section 2describes the system model and assumptions. Section 3explains the proposed scheme in details while Section 4 pre-sents the performance analysis.2. System model and assumptionsFrequency-divisionduplex(FDD)widebanddirectsequence code division multiple access (DS-WCDMA) cel-lular network with multi-operators sharing the same RANis considered. The study focuses on an uplink schedulerthat resides at each base station. The power control of eachoperator user is nearly perfect for maintaining the target biterror rate (BER). Since we are focusing on schedulingpackets of a connection after its admission, the uplinkcapacity of WCDMA cell is defined in term of the uplinkWCDMA channel rate (C = 5 Mbps).We assume that N operators can share the cell radioresource (channel rate). Each operator has number ofmobile stations (MS). The transmission rate of each oper-ators mobile station (MS) is scheduled on time-slot basis.For each slot, the scheduler allocates adequate service ratesto the N operators, using M-CDGPS scheduling proce-dures, to guarantee the capacity share requirements of allthe operators in a fair manner. After assigning each opera-tor j its fair service rate, its local scheduler allocates ade-quate service rates to its flows to guarantee the QoSrequirements of all the traffic classes within operator j ina fair manner. The scheduler within each operator can bedesigned independent of other operator scheduler. Eachoperator implements its own call admission control, whichattempts to control its own arrival traffic.The new RRM system model is shown in Fig. 2. When amobile terminal wants to connect, it needs to send a con-nection requests in the random access channel (RACH).When this request is received at the BS, the multi-operatorCAC scheme is firstly used to check the admission of theconnection request of an operator. If the answer is positive,the connection request of this operator is accepted andbecome ready to transmit the traffic. This is called theadmitted connections. When packets in a frame for anoperator are available for transmission, they need to bescheduled according to their QoS and BER requirementsas a second phase using the uplink scheduler. However,how the packets of this operators connections are trans-mitted in each frame is determined by our proposed M-CDGPS scheduling scheme. Therefore, the M-CDGPSscheme employs the dynamic rate allocation among opera-tors in order to increase the overall system utilization anduse the GPS model in order to insure the fairness amongstoperator when allocating the shared resource. After allo-cating each operator its resource the CDGPS is then usedwithin each operator to schedule its traffic class.Two types of services are supported be each operatorMS. These two types are: (1) Real-time traffic (RT) suchas voice or video, (2) non-real-time traffic (NRT) such asdata traffic. The required QoS in terms of delay and BERare different according to RT and NRT traffic. In the nextsections, the detail descriptions of the proposed scheme arepresented.3. Proposed M-CDGPS schemesThe shared resources will be the WCDMA channel rate(C = 5 Mbps). We have N operators sharing the samechannel. In M-CDGPS scheduling schemes, the allocatedS.A. AlQahtani / Computer Communications 31 (2008) 103111105resources to an operator can be fixed or adaptive asfollows.3.1. Fixed rate M-CDGPSLet cjis the minimum assigned rate for operator j suchthatcj gjC;j 1;:;N1where gjis defined based on SLA, such thatPNj1gj 1andPNj1cj6 C. In this, at each time slot, an operator jis given cjif there is backlogged session. If no packet isready, and if the unutilized capacity of an operator is notallowed to be used by other backlogged operators, then thisscheduling called fixed rate M-CDGPS scheduling and thesystem can be viewed and multi-independent CDGPS sys-tems. The assigned rate for each operator is based on (1).3.2. Adaptive rate M-CDGPSIn case of adaptive rate M-CDGPS scheduling, eachtime slot, T, first operator j is given its minimum cjas in(1) and if there are unutilized resources such thatCr C ?XNj1cjP 02Then the excess resources are divided amongst the back-logged operator such thatcegjCrP8i such that operatorihas backloggi3Cjk cj ce43.3. Queuing model of the proposed M-CDGPS schemeThe queuing model of the proposed M-CDGPS schemeis shown in Fig. 3, where link capacity C is shared by Noperators. Each operator has its own assigned soft capacitydefined based on the (SLA) service level agreement. Theassigned weight for operator j is gj, where j = 1, 2,.,N.Therefore the total cell capacity in term of channel rate isdivided into N groups, each operator j group assigned min-imum service rate (Cj(t) with capacity gjC. Each operator jmaintains set of connections (two in our case) with link rateCj(k) during the kth MAC slot. The sum of Cj(k) over allthe operators should not exceed C in case of adaptive rateand should not exceed gjC in case of fixed rate allocation.The assigned capacity share to each operator j, Cj(k), isalso shared by K traffic classes (flows). Each traffic class iwithin each operator j has its arrival rate, queue, and main-tains a connection with link rate Rij(k) during the kth MACslot. The sum of Rij(k) over all classes (two in our case, RTand NRT) of one operator j should not exceed Cj(k).AdmissionControlResourceAllocationUplinkSchedulerConnectionRequestsPer Operator Existing(Admitted)ConnectionsAcceptRejectQueuedCallsQueueddequeuePer Operator BufferesBuffer1Buffer2BufferNBSFig. 2. RMM model for RAN sharing.106S.A. AlQahtani / Computer Communications 31 (2008) 1031113.4. Traffic source regulationsIt is assumed that the traffic characteristic of eachinput source (traffic stream) of M-CDGPS model isshaped by a Leaky-Bucket regulator 4 in order toachieve a bounded delay and bounded buffer size for traf-fic (user) (see Fig. 4). Leaky Bucket characterization of atraffic stream is based on specifying two parameters (rij,-qij) where rijand qijare token buffer size and token gen-erate rate, respectively of the leaky bucket. i.e., For eachsession i (i.e., traffic of class i) of operator j, tokens aregenerated at a fixed rate, qij, and packets can be releasedinto the network only after removing the required num-ber of tokens from the token bucket. There is no boundon the number of packets that can be buffered, but thetoken bucket contains at most rijbits worth of tokens.The traffic leaves the bucket at a maximum rate ofC qij.The constraint imposed by the leaky bucket is as fol-lows. If Aij(s,t) is the amount of session i of operator j flowthat leaves the leaky bucket and enters the network in timeinterval (s,t, then we haveAijs;t 6 rij qijt ? s;8t P s P 05Toexplainthis,wefirstweassumethatthesessionstartswithfull buckets of tokens rij. Then, the total number of tokensaccepted at the session i bucket of operator j in the interval(s,t is at most qij(t ? s) (it does not include rijand doesnot include arriving tokens that find the bucket full). Thatmeans the rate will be limited by the token arrival rate qijand in a very short interval of time, it is possible for a burstof up to rijbits to enter the queue of session i of operator j.Also, in the long term, the rate of arrivals into the queuecannotexceedqij.Therefore,eachsessioniofoperatorjhavethe following attributes: (1) Average rate (qij), (2) burstiness(rij), (3) allotted rate (rij), and (4) maximum (Peak) rate C.CDGPSA11(t)A21(t)w11w21RTQ11(t)Q21(t)NRTCDGPSA12(t)A22(t)w12w22RTQ12(t)Q22(t)NRTCDGPSA1N(t)A2N(t)w1Nw2NRTQ2N(t)NRTg1g2gNQ1N(t)Adaptive RateScheduling (M-CDGPS)OP1 : C1(t)OPN: CN(t)OP2: C2(t)R11(t)R21(t)R12(t)R22(t)R1N(t)R2N(t)VQ1(t)VQ2(t)VQN(t)Fig. 3. Queuing detail mode for M-CDGPS scheme.Incoming trafficsof session ijijijBufferRateijrTo the network),( tAijFig. 4. Leaky bucket idea 4.S.A. AlQahtani / Computer Communications 31 (2008) 1031111073.5. The M-CDGPS procedureThe M-CDGPS procedure is defined as follows. Con-sider a queuing system of WCDMA uplink channel ratewith link transmission rate of C. Let Wj(s,t) be theamount of operator j traffic served during interval of(s,t. Each operator j link is associated with a positivereal number (weight), gj, j = 1,.,N, which we call itthe relative service share of that operator. That is, thegjof each operator must be chosen based on its capacityshare defined by SLA.Let Sij(k) be the amount of session i traffic of operatorj served during the time slot k out of the Wj(s,t) that wasassigned to its operator. Each traffic i of operator j link isassociated with a positive real number (weight), wjj,i = 1,.,K selected based on QoS requirement of thistraffic class. Let the scheduling period of M-CDGPSscheme, i.e., the slot length, be T. The M-CDGPS serverwill allocate each Cj(k) and Rij(k) for each operator j andits individual traffic i, respectively using the followingsteps: Let OBj(k) be the total amount of backlogged traffic ofoperator j during time-slot k, and Bij(k), be the totalamount of backlogged traffic of class i of operator j dur-ing time-slot k, such thatOBjXKi1Bijk Based of OBj(k), the Wj(k) and Sij(k) which are theexpected amount of service received by operator j andthe expected amount of service received by traffic i ofthis operator, are determined as follows: If OBj(k) = 0, then Wj(k) = 0 and Sij(k) = 0 for all i; If OBj(k) 0, then Wj(k) = ciT and Sij(k) = rijT for allBij(k) 0, wherecigiCPNj1gj6is the minimum rate (capacity share) guaranteed tooperator j, andrijwijCjkPKi1wij7is the minimum rate guaranteed to traffic i form theassigned capacity share of its corresponding operatorj. The session i with Bij(k) = 0 will have Sij(k) = 0 andwij(k) = 0. After assigning each operator its Wj(k) then, in case ofadaptive rate scheduling ifPjWjk CT, then theremaining unused resource is distributed to the opera-tors who need more than their guaranteed service ciT.The distribution of the remaining unused resourceshould be in proportion to each operators weight gj,according to the M-CDGPS service discipline as shownin (4). When an operator j receives part of the unusedcapacity, it will be distributed to its traffic who needmore than their guaranteed service rijT in proportionto each traffics (session) weight wij. Finally the allocated channel rate to each operator j andto each backlogged operator traffic i can be determinedby Cj(k) = Wj(k)/T and Rij(k) = Sij(k)/T, respectively.3.6. Rational behind using GPS modelThere are several interesting features associated withGPS based techniques that make it an attractive scheme: As long as qij rij, the session can be guaranteed athroughput of qij, independent of the demands of othersessions. The delay of an arriving session i bit can be bounded asa function of the session i queue length, independent ofthe queues and arrivals of the other sessions. Schemessuch as FCFS, LCFS, and Strict Priority do not havethis property. By varying the gjand wijs we have the flexibility of treat-ing the shared capacity fraction and the operators ses-sions in a variety of different ways. As long as thecombined average rate of the sessions is less than C,any assignment of positive wis yields a stable system. It is possible to make worst-case network queuing delayguarantees when the sources are constrained by leakybuckets.4. Performance analysisIn this subsection, we analyze the worst case perfor-mance of M-CDGPS systems with adaptive rate for opera-tors sessions that operate under Leaky Bucket constraint.Our next analysis of M-CDGPS follow the basic idea ofGPS analysis done in 4 as a main reference and extendedto cover the case of multi-operator with multi-traffic classin 3G WCDMA networks.Let Sij(s,t) be the amount of session ij (class i of opera-tor j) traffic served in the interval (s,t. From Fig. 5, Sij(0,t)is continuous and non-decreasing for all t. The session ijbacklog at time s is denoted by Qij(s) and defined asQijs Aij0;s ? Sij0;s8The session ij delay at time s is the amount of time thatwould take for the session ij backlog to clear if no session ijbits were to arrive after time s and is denoted by Dij(s).Thus,Dijs infft P s : Sij0;s Aij0;sg ? s9From Fig. 5, we see that Dij(s) is the horizontal distance be-tween curves Aij(0,t) and Sij(0,t) at the ordinate value ofAij(0,s).The problem we will analysis in the next subsection is:Given the rij, qij, and wijs of each session ij and gjs of eachoperator for a M-CDGPS system of rate 5 Mbps, what are108S.A. AlQahtani / Computer Communications 31 (2008) 103111the bounded delay and queue size for every traffic class i ofeach operator j (i.e., session ij)?4.1. Delay and queue sized boundsThe above assumptions and definitions are used here inorder to derive the QoS performance bounds for each traf-fic flow i of operator j in the M-CDGPS system in terms ofmaximum delay and queue size. Let Qij_Maxbe the maxi-mum of Qij(t) and Dij_Maxbe the maximum ofDij(t). Thedelay and backlog bound of the traffic flow i of operatorj can be derived using following two lemmas.Lemma 1. If rijP qij, where rijis given by Eq. (7) then themaximum queue size (backlog) isQij max6 rij qijTfor adaptive rate6 rij qijgjTfor fixed rate(10Proof. Assume that session i of operator j (i.e., session ij)start to backlog at time t1, such that sk?1 t16 skwheresk?1and skare starting instant of slot (k ? 1) and slot(k), respectively. Assume tmto be the time when session ijbacklog reaches the maximum Qij_Max. Now we are goingto define the amount of arrival traffic and the amount ofserved traffic during the interval t1,tm. Based on Eq. (5)the total amount of arrival Aij(t1,t) during the intervalt1,t can be defined asAijt1;tm 6 rij qijt1;tm11Notice that the arrive traffic are accepted to enter the net-work only during the interval t1,tm, where t1 tm. The to-tal amount of served traffic Sij(t1,t) during the intervalt1,t) is as defined in Eq. (8). According to M-CDGPS ser-vice discipline, a minimum service rate rijis assigned to ses-sion ij at time skas defined in (7) and rijP qij. Therefore,the amount of service for this session during the allowedinterval t1,tm can de written asSijt1;tm P max0;rijtm? sk12That is if sk tmthen the remaining traffic will be served atstarting of slot (k) at minimum rate of rij. If tm sk, the thatmeans all backlog traffic is already served during slot(k ? 1). Based on the Eq. (8) and having that rijP qijwehaveQij max Aijt1;tm ? Sijt1;tm13Using (11) and (12)Qij max6 rij qijtm? t1 ? max0;rijtm? sk14Wehavethatmax(qij(tm? t1) ? max(0,rij(tm? sk) =qij(tm? t1) and this is when tm6 sk. Also, we have thatqij(sk? t1) P qij(tm? t1) and therefore the Eq. (14) canbe written as Qij_max6 rij+ qij(sk? t1). Also we have thatsk?1 t16 skand sk? sk?1= T, hence the maximumbacklog can be written asQij max6 rij qijT?154.2. Queue sized boundUsing Lemma 1 the following lemma about delay boundof session ij can be obtained.Lemma 2. if rijP qij, where rijis given by Eq. (7) then thepacket delay bound of session ij isDij max6rijrij Tfor adaptive rate6rijrij gjTfor fixed rate(16Proof. Let Dij(t2) the delay experienced by traffic of sessionij arrived at time t2, where t2P t1. As stated before, the ses-sion ij starts backlog at time t1, such that sk?1 t16 sk.As shown in Fig. 6 and from the definition of delay in Eq.(9) and since the session ij starts backlog at time t1, we haveAijt1;t2 Sijt1;t2 Dijt2Also since Qijt2Aijt1;t2?Sijt1;t2 and Sijt1;t2Dijt2Sijt1;t2Sijt2;t2Dijt2where Aij(t1,t2) ? Sij(t1,t2) = Sij(t2,t2+ Dij(t2). We have), 0(ijA), 0(tAij), 0(tSij()ijD)(ijQFig. 5. Aij(0,t), Sij(0,t), Qij(t) and Dij(t) similar to 4.1t),(21ttAij),(1ttAij),(1ttSij)(2tDij)(2tQij2t)(,(222tDttSijij+)(,(221tDttSijij+Fig. 6. Detailed Aij(0,t), Sij(0,t), Qij(t) and Dij(t).S.A. AlQahtani / Computer Communications 31 (2008) 103111109Qijt2 Sijt2;t2 Dijt217Now we have two cases for t.hCase 1: t2P skDuring the interval t2,t2+ D(t2), the M-CDGPS sched-uler can guarantee a minimum rate rijto session ij, hencewe haveSijt2;t2 Dijt2 P rijDijt218Using Eq. (17) and from Lemma 1 we know thatQij_max6 rij+ qijT. Thus we haverijDijt2 6 Qijt2 6 rij qijTDijt2 6rij qijTrijDijt2 6rijrijqijTrijAlso we have rij6 qij. HenceDijt2 6rijrijqijTrij6rijrij TDijt2 6rijrij T19Case 2: t2 skUsing the backlog definition in Lemma 1Qijt2 6 rij qijt2? t1Now (18) can be redefined asSijt2;t2 Dijt2 P rijDijt2 ? sk? t2?rijDijt ? sk? t? 6 rij qijt ? t1Dijt2 6rij qijt2? t1rij sk? t26rijrij sk? t26rijrij T20From (19) and (20), we can conclude that the maximumdelay is bounded byrijrij T.The proof of fixed rate is as derived in CDGPS withscheduling period equal to gjT.5. Simulation resultsInthissection,simulationresultsarepresentedtodemon-strate the performance of the proposed M-CDGPS schemein terms of delay and system throughput only due to paperlimitation. The scheduling period T is 10 ms. In simulation,the M-CDGPS scheme is compared in case of adaptive rateand fixed rate under heterogeneous traffic environments.ThetotalbandwidthisassumedtobeaconstantC = 5 Mbps. Three operators are considered each operatoris assigned different weight based on SLA. We assumed thateach operator is given (gj= 1/3) of the bandwidth as a min-imum. All operator follows are modeled by a Poisson pro-cess with average arrival rate k and packet length Lshaped by a leaky-bucket regulator for providing boundeddelay. In this simulation L = 512 bits, rij= 100L, qij= C/6, and k can be varied in order to change the system load.In the following experiments, the traffic loads of opera-tor 2 (OP2) and operator 3 (OP3) is fixed to 512 Kbps andthe traffic loads of operator 1 (OP1) is varied. The systemthroughputs and the average packet delay are depicted inFigs. 7 and 8.Fig. 7 shows the system throughputs comparison in caseof fixed rate (FR) and adaptive (AR) rate M-CDGPS. Thetraffic loads are the sum of average arrival rates of the 6data follows (two per operator). As expected the through-puts of adaptive rate M-CDGPS is higher in case of usingadaptive rate because of using the concept of utilizing theunused resources of other operators. Hence the systemthroughputs increase.Fig.8showstheaveragedelaywithdifferentsystemloads.In this figure it can be seen that the average delay perfor-manceofadaptiveM-CDGPSisbetterthanM-CDGPSwith02000400060008000010002000300040005000OfferdTraffic (Pkts/sec)Throughput (Pkts/sec) OP 1-FR MCDGPS OP 1-AR MCDGPSFig. 7. System throughputs.0100020003000400000.0050.010.015Offerd Traffic (Pkts/sec) Average Delay(sec) OP 1-FR MCDGPS OP 1-AR MCDGPSFig. 8. Average packets delay.110S.A. AlQahtani / Computer Communications 31 (2008) 103111a fixed capacity per operator. In adaptive M-CDGPS, theunusedresourcescanbedistributedamongstthebackloggedflows. Therefore, more packets can be served.6. ConclusionAn efficient adaptive rate M-CDGPS scheme has beenproposed for supporting Multiservices in the uplink ofWCDMA cellular networks with multi-operators. The per-formance bounds for the buffer size and delay are derived.The simulation results show that the proposed schemeimprove both system utilization and average delays. Theproposed scheme allows for a flexible trade-offbetweenthe GPS fairness and efficiency in resource allocation andis an effective way to maximize the radio resource utiliza-tion under the fairness and QoS constraints.References1 S. AlQahtani, U. Baroudi, An uplink performance evaluation forroaming-based multi-
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