Capacity optimization in multiservice mobile wireless networks with multiple fractional channel...

$: Capacity optimization in multiservice mobile wireless networks with multiple fractional channel reservation$
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 52, NO. 6, NOVEMBER 2003 1519

Capacity Optimization in Multiservice MobileWireless Networks With Multiple

Fractional Channel ReservationHeraclio Heredia-Ureta, Student Member, IEEE,, Felipe A. Cruz-Pérez, Member, IEEE, and Lauro Ortigoza-Guerrero

Abstract—In this paper, the multiple fractional channelreservation (MFCR) strategy for service differentiation is pro-posed. MFCR overcomes the “integer nature” of traditionalchannel reservation schemes (also referred as guard channel,trunk reservation, or cutoff priority) that precludes them toachieve maximum system capacity in single- and multiserviceenvironments. Contrary to the rest of channel reservation schemespreviously proposed in the literature on the topic, MFCR re-serves, on average, real numbers of channels to prioritize newand/or handoff calls in multiple service environments. Given aset of requirements on new call blocking and forced terminationprobabilities for each service type, MFCR maximizes systemcapacity while meeting the Quality of Service (QoS) constraintsin multiservice mobile cellular networks. It finely controls thecommunication service quality, by varying the average numbersof reserved channels by a fraction of one. Determining the rightamount of resources (cutoff threshold or number of reservedchannels) to prioritize each call type and to satisfy all QoS con-straints in multiservice environments, however, is a difficult task.Selecting the optimal prioritization order is not an easy processeither, as it is affected by QoS constraints, system characteristics,and resource sharing. Thus, an heuristic algorithm to determinethe optimum numbers of reserved (resources) channels to achievemaximum system capacity when using the MFCR is also proposed.To our knowledge, the capacity optimization problem consideringindividual QoS constraints had only been addressed in singleservice environments. Also, a comprehensive survey on channelreservation strategies proposed in the literature has been included.

Index Terms—Capacity optimization, channel reservation,integrated services, radio resource management, service differen-tiation.

I. INTRODUCTION

T O guarantee acceptable Quality of Service (QoS) in mul-tiservice mobile environments, network planners need to

consider certain constraints that provide upper limits for the

Manuscript received February 7, 2003; revised July 25, 2003. This work wassupported in part by the CONACYT under Project I39348-A.

H. Heredia-Ureta was with the Communication Section, Center for Researchand Advanced Studies—IPN (CINVESTAV-IPN), Mexico City, CP 07360,Mexico. He is now with Universidad de Occidente, Campus Culiacán,Carretera a Culicancito Km 1.5, Culiacán, Sinaloa, CP 80020, Mexico (e-mail:[email protected]).

F. A. Cruz-Pérez is with the Communication Section, Center for Researchand Advanced Studies—IPN (CINVESTAV-IPN), Col. San Pedro Zacatenco,Mexico City, CP 07360 Mexico (e-mail: [email protected]).

L. Ortigoza-Guerrero is with WFI, 4810, San Diego, CA 92122 USA (e-mail:[email protected]).

Digital Object Identifier 10.1109/TVT.2003.819617

blocking probability of different service types.1 An admissioncontrol policy, based on certain criteria, i.e., ensuring fair accessamong services, is also necessary (in this frame maximum fair-ness is referred to as the situation where the difference betweenblocking probability for calls belonging to any two different ser-vice types is minimum). However, it may also be necessary toprotect some delicate calls, such as handoff calls, to further en-sure acceptable QoS. Additionally, calls of different servicesmay need different amount of system resources depending ontheir data rate requirements [1] which cause unfairness since itis harder to find a greater amount of available resources for ser-vices with high bandwidth2 requirement. Thus, different servicetypes may have different prioritization level requirements. Asnoticed in [2], the level of relative prioritization provided to dif-ferent service types is specified by relative blocking/droppingprobabilities. Hence, in a multiservice mobile environment it isnecessary to provide multiple prioritization levels to efficientlysatisfy the QoS of the different traffic classes.

The Channel Reservation3 (CR) scheme is a classical topicin cellular systems related literature. It has widely been usedas a prioritization technique in cellular systems for morethan 20 years [3]–[15]. CR reserves4 an amount of resources(bandwidth/number of channels/transmission power) for theexclusive use of a call type (i.e., new, handoff, etc.), but it hasmainly been utilized to reduce the handoff failure probabilityin mobile cellular networks [4]–[12]. Reducing the blockingprobability of calls with high bandwidth requirements in mul-tiservice networks has recently become another of its commonapplications [13]–[15]. However, due to the fact that an integernumber of channels5 or bandwidth basic units (BBUs) is re-served in conventional CR the blocking probabilities of the calltypes involved vary greatly in form as the number of reserved

1We limit the QoS discussion to the issues of call acceptance and droppingin order to minimize the dimensionality of the problem. Thus, we restrict ourdiscussion to issues concerning efficient bandwidth allocation and handoff man-agement for all the different traffic classes.

2We use a very general term, bandwidth (not necessarily meaning a frequencyband in Hz), to describe the different resource requirements between two servicetypes.

3Also referred as guard channel, trunk reservation, or cutoff priority strategy.4In the terminology of the cutoff priority strategy, this is described as follows:

when a predetermined channel utilization threshold is reached, new calls aresimply blocked (cutoff), and only handoff call requests are attended.

5The entire spectrum allocated to a cell is divided into a number of channelsbased on a multiple access scheme (FDMA, TDMA, or CDMA). Each servicemay require a different number of resources to carry a call based on its QoSrequirements, and/or data rate [1].

0018-9545/03$17.00 © 2003 IEEE

1520 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 52, NO. 6, NOVEMBER 2003

channels or BBUs changes. Although CR effectively reducesthe blocking probability of the prioritized calls, it does so at thecost of increasing the blocking probability of the nonprioritizedones. Therefore, increasing the number of reserved channelsor BBUs by one could result in significant system capacityreduction.

With the intention of overcoming the aforementionedproblem, the fractional channel reservation (FCR) scheme wasproposed in [9]–[11]. FCR finely controls the communicationservice quality, by varying the average number of reservedchannels by a fraction of one. In other words, FCR allows thereservation of a real, rather than an integer, number of channels[11]. This allows the system to reach its maximum capacitywhile meeting the QoS constraints [9]–[11]. FCR is a particularcase of the new call thinning schemes in which, for each cellstate, a new call is admitted with certain probability [9], [16].Ramjeeet al. proved that the FCR scheme is optimal forthe problem of minimizing the new call blocking probabilitysubject to a hard constraint on the handoff blocking probabilityfor a given number of channels. They also proved that theFCR scheme is also optimal, in addition, for the problem ofminimizing the number of channels subject to hard constraintson the new and handoff call blocking probabilities [9].

Also with the fundamental idea of overcoming the “integernature” of conventional CR schemes, the unequally shared chan-nels (USC) strategy was proposed in [12]. In this strategy, re-served channels are shared between new and handoff calls withdifferent priority. This priority is controlled by a sharing prob-ability. In [17] and [18], adaptive algorithms for call admissioncontrol in wireless networks based on the CR were proposed.Both algorithms use an adaptation mechanism to search auto-matically the optimal number of reserved channels at each basestation ensuring that the handoff failure probability is met. Thealgorithm of [17] adjusts the number of reserved channels forhandoff adaptively according to the dropping rate during a timeperiod, which is normally long in order to avoid fluctuations.The approach of [18] is based on reinforcement learning wherethe goal is to minimize the new call blocking probability whilekeeping the handoff failure probability close to a targeted ob-jective. As in the previous cases, a single-service scenario wasused to evaluate the strategies. Even though the authors in [17]and [18] did not realize it, they used a form of FCR scheme.References [9], [10], [12], [17], and [18] proposed CR strate-gies that overcome the “integer nature” problem while simulta-neously presenting studies regarding the optimum cell capacityin a single-service mobile cellular environment.

Although the FCR and the USC eliminate the integer natureof traditional CR schemes in single service environments, rela-tively few studies have addressed the multipriority reservationproblem (i.e., reserving several groups of resources for differentcall types). To our knowledge, a limited number of papers havestudied the capacity optimization problem in multiservice mo-bile wireless environments to date (i.e., [46]). This statement issupported by [19], where the authors affirmed that as far as theyknew, there was only one paper addressing handoff schemes forthe case of mixed media (voice, data) cellular systems ([20]).

In this paper, the capacity maximization in multiservicemobile cellular networks by making use of the Multiple

FCR strategy is investigated. The multiple fractional channelreservation (MFCR) strategy is proposed and mathematicallyanalyzed. An algorithm to determine the maximum cell ca-pacity and the optimum amounts of reserved resources (cutoffthresholds, number of reserved channels, or reserved BBUs)is carefully addressed. We consider that the different servicetypes have arbitrary bandwidth requirements with potentiallydifferent QoS requirements (in terms of the new call blockingand forced termination6 probabilities) each. The rest of thispaper is organized as follows. Section II describes multilevelprioritization related works previously published in the litera-ture. The proposed MFCR strategy description and its teletrafficanalysis are presented in Sections III and IV, respectively. Theproposed algorithm to determine the maximum cell capacityand the optimum numbers of reserved channels in MFCRis described in Section V. In Section VI, guidelines on theselection of the optimal prioritization order are given. Finally,numerical results and conclusions are presented in Sections VIIand VIII, respectively.

II. WORKSRELATED TO MULTILEVEL PRIORITIZATION

A first approach to provide multilevel prioritization withmultiple channel reservation (MCR) in cellular communicationsystems was discussed in [21], where the types of trafficwere correlated to the speed of the mobile users. Users wereclassified based on their speed into two categories: high andlow mobility (or vehicular and portable), hence, two types oftraffic were considered. The call admission policy in [21] givespriority to handoff attempts over vehicular call attempts andthe vehicular call attempts over new portable call attempts.Later on, this strategy was generalized in [22] for the case of amixed traffic load environment. Several numbers of channelsare reserved to prioritize different call types. In [8] a calladmission control policy with prioritized handoff requests ina single service environment was proposed. Users are dividedinto two mobility platforms: high and low speed users. Inaddition, a queue is considered for handoff calls in combinationwith a two-level channel reservation. In this policy, high-speedhandoff requests have priority over low-speed ones and allhandoff requests have priority over new calls. Then, in [23]a queueing strategy for multiple priority calls in multiservicepersonal communications services was proposed. The strategyis based on the partial buffer sharing (PBS) control method [24]which allows a call to access a queue if the queue space is largerthan a predefined threshold value. The access control schemetakes into account the call class. Calls with the highest priorityhave access to the entire queue. This simple method guaranteestraffic order [24]. The authors in [23] did not consider mobility(and therefore did not consider handoff calls). In [25], BoLi et al.proposed a bandwidth allocation scheme for voice/dataintegrated mobile wireless networks. The scheme is a naturalextension of the Guard Channel scheme and it is called dualthreshold reservation (DTR). DTR’s basic idea is to use twothresholds, one for reserving channels for voice handoffs, while

6The forced termination probability is the probability that an accepted callis forced to terminate due to an unsuccessful hand-off because of the lack ofresources in the target cell.

HEREDIA-URETA et al.: CAPACITY OPTIMIZATION IN MULTISERVICE MOBILE WIRELESS NETWORKS 1521

the other is used to block data traffic into the network in order topreserve voice performance in terms of handoff dropping andcall blocking probabilities. The performance between handoffand new arrivals of data are not distinguished. In [19] and[26], Agrawal et al. proposed a handoff scheme in integratedvoice and data mobile cellular systems with prioritized voicehandoff requests. The suggested strategy reserves a numberof channels for voice and data handoff requests. The voicehandoff requests have priority over data handoff requests andall the handoff requests have priority over new calls. Thereare only two integer numbers of reserved channels and thereis no distinction between new calls of the different servicetypes. Also, an arbitrary priority order is assumed rather thandetermined.

All the above schemes deal only with homogeneous traffic(systems in which each type of traffic has the same bandwidthrequirements). Furthermore, all the schemes were limited by theinteger nature of their admission control policies that precludesystems from achieving maximum capacity. In all the works, thetopic of capacity optimization was not addressed either.

Traffic performance analysis in cellular systems with hetero-geneous traffic sources has been addressed in recent years. Aninitial approach to address the problem of capacity optimiza-tion by providing multilevel prioritization in multimedia orheterogeneous traffic environments in cellular communicationnetworks (systems supporting multiple service types trafficwith arbitrary bandwidth requirements each) was presented in[27]. The problem of capacity optimization through channelrestriction for certain classes is mentioned in [27]. However,handoffs are not included in the model and then the new callblocking probability is the only performance measure. In [2],Schwartz and Epstein compared different reservation and re-source sharing strategies considering only two types of traffic:narrowband (NB) voice calls and wideband (WB) images. In[2] it is assumed that the NB traffic occupies a single basicbandwidth unit (BBU) and the WB traffic BBUs; and thatthere were not WB handoff attempts. Thus, three classes oftraffic were considered. In [28], a rather general approach totraffic performance evaluation was provided. It accounted forthe presence of different platforms (i.e., different mobility pa-rameters) and different service types (with different resourcerequirements) in cellular mobile networks with uniform spatialtraffic distribution. The model also included limits and quotason the availability and usage of resources. Two generic ex-amples were considered. One typified loss-type systems withresource cutoff priority for handoff calls. The other typifiedhybrid delay-loss systems in which queueing of handoff as wellas resource cutoff priority was used. Although the approachof [28] is good enough to permit modeling of many practicalsystems, it may face the problem of high dimensionality ofstate space. In [29], Rappaport’s model is extended to cellularmobile networks with nonuniform spatial traffic distributionand a fixed-point approximation is given which can avoid theproblem of high dimensionality. In addition to handoff pri-ority dealt with in [28], an access regulation strategy amongcalls with different bandwidth requirements is considered in[29]. Trunk reservation policy is applied to the model not onlyfor handoff priority but also for access regulation (multiplechannel reservation).

In [30], Chao and Chen studied a generic class of coordinatedadmission control policies for mobile multiple-class personalcommunications networks. They assumed that the network’sset-up for evaluation contains only two cells and that subscriberscan roam freely between the two cells. For the class of controlconsidered, admission decisions depend on the state the cellwould enter if the call request is admitted. For a given state, theadmission decision may be different for different classes and/ordifferent types (new callorhandoff)of call requests. It isassumedthere are classes of traffic, each with different bandwidthrequirements and mobility characteristics. Three examples ofadmission control policies are explained but only the trunkreservation policy is numerically evaluated. Another approachto provide multilevel prioritization with MCR in multimediawireless systems was presented in [13]. In [13], a system withtwo services was considered, where calls with service type 2require an integer number of basic channels, which in turn is amultiple of those channels required by calls with service type1. An arbitrary prioritization order of increasing importance,which does not contribute to achieve maximum capacity atall times, is assumed, rather than determined. Nevertheless,the integer nature of the admission control policy precludesthe system from achieving maximum capacity.

In [31], Li et al.proposed a new scheme referred as the hybridcutoff priority scheme (HCPS), in which each type of traffichas its own cutoff threshold (Multiple Channel Reservation).This scheme extends the simple cutoff priority scheme forsingle stream traffic into multiple classes of traffic. The maincharacteristic of this scheme is that it supports any numberof classes of traffic, each of which can have its own QoSrequirements in terms of number of channels needed, lengthof the connections, and cutoff priority employed. The HCPSuses also finite buffering for both new and handoff calls. Theauthors consider that each cell in the system can havetypesof new calls and types of handoff calls, where(some class of service could no experience handoffs). Eachnew or handoff call of class of servicerequires channels.In the HCPS, each class of calls may have a different cutoffthreshold, say for the new calls belonging to class. Whena class new call arrives, it can be attended only if the numberof channels in use is at most . Otherwise, the newcall arrival is placed in a queue or discarded due to bufferoverflow. HCPS does not differentiate handoff calls of thedifferent classes of service. Thus, handoff call attempts withhigher bandwidth requirements are dropped more frequentlydue to the fact that it is harder to find a greater amount offree resources. With numbers of reserved channels it is notpossible to differentiate (for ) call types.

In [32] a threshold-type call admission control (CAC) al-gorithm is proposed for quality of service provisioning and anonlinear programming model is formulated for determiningthe optimal threshold values. It is supposed that there areclasses of adaptive multimedia services and they are sortedaccording to their priority. The bandwidth of each class calltakes its discrete value from a set. The bandwidth of callswith lower priority is always preferably reduced/increased. Anewly arriving call of a given class is blocked if the cur-rent number of ongoing calls with the class of the arriving


Fig. 1. Architecture of cells for MFCR where� represents the arrival rate of the calls of typej (for j = 1; . . . ; 2n).

call is equal to or greater than a predefined threshold. Anincoming handoff call of a given class is accepted regardlessof the number of ongoing calls of this class; if the availablebandwidth is insufficient, bandwidth adaptation is performedto accommodate the handoff call. The threshold CAC algo-rithm was chosen because the steady state probability is easilytractable via product form. The optimal thresholds (decisionvariables) for each class for which the revenue is maximizedare determined by solving a nonlinear programming problem.Contrary to this strategy, in this work we consider completeresource sharing (CRS) and nonadaptive multimedia services.As our proposed strategy employs CRS, it achieves higherbandwidth utilization.

Finally, in [46] an heuristic approach is used to determinean optimal channel allocation plan. Several channel access con-trol policies (notable among these are Complete Sharing, Com-plete Partitioning, and Partial Sharing) are evaluated for eachcell site, and the policy that improves the overall network rev-enue while ensuring an acceptable level of service availability isselected. In the capacity optimization procedure, depending onboth the call blocking and call dropping probabilities require-ments of a service, a particular channel allocation policy could

be deduced, or the existing one could be fine tuned. A heuristicbased procedure is used by the system for such purposes. Smalladjustments in capacity allocations over the entire network areevaluated and the one that improves revenue by the maximumamount is selected for implementation. This intensive processis repeated until an optimal channel allocation plan is achieved.Both, the redistribution of channel allocations within the cell,as well as, borrowing of channels from the neighboring cellsare considered.

The channel allocation strategies for heterogeneous multiser-vice environments described earlier ([2], [27]–[32], [46]) cannotfinely tune capacity allocations because of the integer nature ofthe numbers of allocated and reserved channels used in the dif-ferent strategies. Then, it is not possible to achieve optimumsystem capacity with any of the strategies previously described.To date, the integer nature problem of current call admissionpolicies has only been solved for single systems environmentsand has not been solved for multiple services. As such, cur-rent call admission policies preclude systems with multiple ser-vices or different user types to reach maximum capacity. To ourknowledge, to the problem of capacity maximization in multi-service mobile cellular systems has not been solved.


Fig. 2. Call admission policy for the MFCR strategy.

III. T HE MFCR

The proposed MFCR scheme is suitable for multiservice en-vironments and aims at eliminating the integer nature problemof previous call admission policies. It assumes that the prior-itization level assigned to a call type is directly proportionalto the amount of resources it has access to. Thus, the higherpriority a call type has the more resources it can use. Thisguarantees traffic order as in PBS [24]. The MFCR strategyeffectively reserves real numbers of channels or BBUs in orderto provide a certain protection level to each of the diversecall types. In multiservice mobile cellular networks withdifferent services and individual QoS constraints ( fornew call types for handoff call types), MFCR reserves

different real numbers of channels. This is because todifferentiate call types, independent control variablesare needed.7 For example, to prioritize one call type over theother in a two-call type system, only one control parameter isnecessary (i.e., a single number of reserved channels). Thus,calls with the lowest priority (called type 1 calls) cannot use

channels (cutoff threshold), calls with the second lowestpriority (called type 2 calls) cannot use channels, , andcalls with the second highest priority (called type calls)cannot use channels. There is no access restriction tocalls with the highest priority (called calls type ). Noticethat can also be seen as the number of channels reservedto prioritize calls types , and over callstype , , and 1. The cell architecture for the MFCR

7Every service type has two call types (new and handoff calls). Hence,there aren service types and2n call types.

admission policy is shown in Fig. 1 where represents thearrival rate of the call type , for and rep-resents the total number of channels available in the cell.

The sorted list of call types based on their relative priorities isknown as “prioritization order” in MFCR. The MFCR strategydoes not have a mechanism to determine the prioritization order.Hence during the system design stage, a prioritization order isselected to be tested. If it does not provide capacity maximiza-tion another prioritization order can be tried. As noticed in [31],choosing the cutoff threshold for each class of traffic is a non-trivial problem, since the threshold chosen for one type of trafficclearly affects the performance of other(s) type(s) of traffic dueto resource sharing. Notice that this issue was not considered in[31]. The details of the MFCR strategy are given below.

When a call arrival request (new or handoff) of any servicetype occurs, one of the following steps is carried out:

1) When a call with the highest priority arrives to thesystem and there are enough available resources toattend it, the call is accepted. Otherwise, the call isblocked or dropped.

2) When a call with the second highest priority arrivesto the system, a uniformly distributed random number

is generated, and

a) If : If the number ofchannels available after the call was accepted isat least equal to , then the call isaccepted; otherwise, it is blocked or dropped.

b) Else, if : Then if thenumber of channels available after the call wasaccepted is at least equal to , then


Fig. 3. Architecture of cells for MFCR forn service types and the prioritization orderN1�H1�N2�H2� . . .�Nn�Hn.

the call is accepted; otherwise, it is blocked ordropped.

2n) When a call with the lowest priority arrives to thesystem: a uniformly distributed random number

is generated, and

a) If : If the number of channelsavailable after the call was accepted is at leastequal to , then the call is accepted;otherwise, it is blocked or dropped.

b) Else, if : Then if the number ofchannels available after the call was accepted isat least equal to , then the call is accepted;otherwise, it is blocked or dropped.

is the integer part of . The admission control policy,shown in the flow diagram of Fig. 2 with , is executedupon a new call arrival or handoff attempt of any priority.For each case there are, effectively, different real numbers ofreserved channels. The FCR is achieved because sometimes

channels are reserved with probability whileat other times channels are reserved with probability

[11].

We define the optimal prioritization order (the one thatachieves maximum capacity) as the one that simulta-neously satisfies all individual QoS constraints with

. Moreover, with the optimalprioritization order, all the new call blocking and forcedtermination probabilities of each service type simultaneouslyequals their respective maximum acceptable QoS constraints.As stated before, MFCR does not have means to select theoptimal prioritization order, hence one must be assumed. If,after evaluating the performance of the MFCR strategy withthe assumed prioritization order, all the individual QoS con-straints are not satisfied or the blocking and forced terminationprobabilities are not equal to their maximum acceptable values,another prioritization order can be assumed. This order can thenbe tested and accepted or rejected. As noticed above, selectingthe optimal prioritization order is a complicated task, as itdepends on both QoS constraints and system characteristics.It is also affected by resource sharing. Due to the traffic order[24], only one prioritization order achieves maximum capacity.Priorities must be assigned to call types based on their offeredload, bandwidth requirements, and QoS constraints. Otherwise,resource efficiency decreases. A delicate balance between all


of these parameters exists and must be found to efficientlyuse the resources. The algorithm described in Section V helpsto determine and calculate the optimum numbers of reservedchannels to achieve the maximum capacity.

IV. TELETRAFFIC ANALYSIS

The study presented here focuses on single-cell behavior be-cause we assume a homogeneous system with fixed cell capacitywhere the behavior of neighboring cells is statistically identical.In the following analysis, different service types with arbi-trary bandwidth requirements ( different call types) are con-sidered as follows: new calls of service 1, , hand-off callsof service 1, , new calls of service 2, , hand-off calls ofservice 2, , , new calls of service , , and hand-offcalls of service , . In the next teletraffic analysis, a par-ticular prioritization order in terms of increasing importance isassumed without loss of generality. The prioritization order is

. The cell architec-ture for this prioritization order is shown in Fig. 3. The systemmodel considered in this paper is described below.

A. System Model

As in the vast majority of the references cited, the proposedMFCR strategy has been evaluated using circuit switched com-munication or virtual circuits. Furthermore, the performanceof our proposed strategies is obtained by utilising the mostcommon assumptions made in the literature [28]–[33], [46].In particular, the assumption of Poisson arrivals, exponentialunencumbered service times, and exponential dwell times aremade to keep the analysis tractable. This set of assumptionshas been found to be reasonable and has been widely used inliterature. Each cell has a maximum number of channels.8

Calls of service require channels or BBUs (where isconsidered integer).9 New call arrival processes offered to agiven cell are Poisson processes for theservices. The meannew call arrival rates for each type of service are ,and , respectively. The handoff call arrival processes is alsoconsidered to be Poisson processes with mean handoff arrivalrates , and for each service (which valuesare determined by using an iterative procedure as in [34]).Calls have an unencumbered duration according to a negativeexponential distribution with parameters , and foreach service. The cell dwell time (the time spent by a mobilestation in a cell independent of being engaged in a session) is

8As noticed in [33], in a DS/CDMA-based system, since the number of chan-nels in a cell is dependent on the interference level in the system, it is not fixed.As in [33], to simplify the problem, we assume thatN is the average number ofCDMA channels in a cell and, therefore, the performance of a CDMA systemshould also treated as an average performance. However, this is valid only inCDMA systems that utilize fixed spreading factors and homogeneous QoS re-quirements in terms of bit error probability. In that case, the number of channelsshould be chosen so that outage probability due to admission control failures iskept low enough. In system utilizing variable spreading factors and or servicedependent bit error rate targets, the number of channels depends heavily on theused service mix and therefore the average number of channels cannot be deter-mined beforehand.

9If there is a contiguousness requirement, packing is assumed (idle channelsare consecutive). A channel, then, refers to a basic unit of resource.

a negative exponential distributed random variable with meanfor service type users (for ). At first glance,

it may seem that this assumption is highly inadequate. Indeed,it is known that cell dwell time tends to behave more like agamma distribution [35]. Consequently a general distributionshould be used in the model. However, in that case analyticalsolutions are neither readily available nor easy to obtain.The exponential assumption remains as it represents a goodperformance approximation. Essentially, only the average celldwell time matters. When the average cell dwell time is smallcompared to the call duration, there is no expected differencebetween the exponential assumption and the gamma one.When cell dwell times are large, the difference becomes morenoticeable, but the exponential assumption indicates generalperformance trends. This is the reason why the study can stillbe conducted with the exponential assumption [36].

B. Mathematical Analysis

This section develops an analytical model to find the perfor-mance of MFCR by means of a teletraffic analysis. We start themodel by observing that the new call arrival rate produced bycalls requesting the service type(for ), , is afraction, , of the total new call arrival rate . That is,

(1)

Where, the total new call arrival rate, , is given by thesum of all the individual new call arrival processes of the dif-ferent service types:

(2)

To satisfy individual QoS constraints (one for each calltype) it is necessary to reserve different numbers ofchannels (cutoff thresholds). Hence, for the prioritization orderassumed, it is necessary to reserve channels or BBUs toprioritize , and calls over calls.From these channels, channels are reserved to priori-tize , and calls over and callsFinally, from the reserved channels used to prioritize

, and calls over , andcalls; channels are reserved for exclusive use

of calls. Thus, . In order to ob-tain compact expressions in the teletraffic analysis, we use theauxiliary variables (with ) and (with

). represents arrival rate of calls of type(either new or handoff arrival process) and represents thenumber of resources used by a call of type. Let us assume that

, , , , ,, , , , ,

, , and . (for), as previously defined, represents the number of

resources that are used by calls of service. Let us denote thestate of the system as , where representthe number of users of service 1 toin a given cell, respec-tively. Describing the multidimensional birth and death by “rate


out equals rate in” equations [37], the equilibrium state equa-tions are given by:

(3)

for , and .is the probability that the system is in the state .The call birth rate for the call type (for

) is given by:

(4)

for (for ); otherwise, it iszero.

And the call death rate for the service (for) calls is given by

; if

; otherwise(5)

for (for ); otherwise, it is zero.Together with the normalization condition

(6)

we calculate the corresponding steady state probabilities. Theblocking probability for call type (for ), , isgiven by:

(7)

Thus, for the prioritization order assumed, the service 1 newcall blocking probability is , the service 1 handoff

failure probability is , the service 2 new call blockingprobability is , the service 2 handoff failure proba-bility is , the service new call blocking prob-ability is , and the service handoff failureprobability is . Notice that the blocking proba-bility for call type (for ), , is a monotoni-cally increasing function of the number of channels that cannotbe used by calls of type, . That is, if , then

(8)

also depends on the other numbers of reserved channels,(for , and ). Then, should be

written as to indicate its dependence onthe different numbers of reserved channels. The forced termi-nation probability for the service(for ), , isgiven by [34]:

(9)

The forced termination probability of the service typeis alsoa monotonically increasing function of the number of channelsthat cannot be used by handoff calls of the service type. No-tice that the forced termination probability requirement can betranslated into a handoff failure probability requirement.

As in [38], we calculate the aggregated offered traffic loadper cell, , as:

(10)

Now, let us assume that there is a maximum aggregatedoffered traffic, , generated by all call types for whichequals its QoS constraint regardless of whether or not other

meet their QoS constraints. depends on thenew call arrival rate of the different service types. is thelargest aggregated offered traffic load for which equals itsmaximum acceptable value irrespective of the valueof (for , and ):

(11)

Therefore, for all the cases for whichregardless of the value of (for ,

and . The maximum aggregated offered traffic(for ) is calculated with (10). This calculation of

(for ) is made by varying the total new callarrival rate , given by (2), while keeping fix the traffic pro-portions (for ) of new call arrival generated byusers of the different service types, until achieves its max-imum acceptable value.

Notice that, strictly speaking, should be writtenas to indicate its dependence on thedifferent numbers of reserved channels. Also, (for

) depends on the different numbers of reserved chan-nels and on the QoS constraints .Then , for , should be written as

. How-ever, for the sake of space and clarity, we use the notation


or . Bear in mind that depending onthe prioritization order selected, may refer to the new callblocking or the handoff failure probability.

Now, let us define cell capacity, , as the maximum offeredload for which all the QoS constraints are still satisfied [12].That is, the maximum offered load for which the condition

is met for all . The cell capacity is,therefore, the minimum offered load for which all the QoSconstraints are met:

(12)

with

(13)That is, one QoS constraint can limit cell ca-

pacity. Notice that, strictly speaking, should be written asto denote its

dependence on the different system parameters. However forthe sake of space and to emphasize its dependence on the con-trol parameters, we use the notation . Theultimate aim of an efficient radio resource management schemeis to maximize cell capacity [12]. Nevertheless, determiningthe optimal configuration to achieve maximum capacity is adifficult task because of resource sharing. Complex relation-ships exist between the different system variables and a changeto any of them can result in system capacity variations. In thenext Section an heuristic algorithm to solve this problem isproposed.

In general, determining numbers of reserved channels to sat-isfy certain blocking probabilities and to maximize capacity isdifficult. However, if the objective is to offer the same blockingprobability for the new calls of the different service types theproblem is simplified. This is because relationships among somenumbers of reserved channels can be easily recognized. For ex-ample, let us suppose that there aredifferent service typeswith and that the optimal prioritizationorder is ; then bydoing , , and

, the same blocking condition forthe new calls of the different service types can be achieved. Thatis, . This is because with these cutoffthresholds the blocking condition for new calls of different ser-vice types is the same. Similar relationships can be establishedamong the different call types if other prioritization order is theoptimal one. However, the relationships with the rest of the num-bers of reserved channels can not be easily obtained.

To further explain the previous instance, let us assume that, , and that the optimal prioritization order is

(the new calls with service type 1 is the call typewith the lowest priority). Considering MFCR, three differentnumbers of reserved channels must be used:, , and(with ). Then, to achieve the same blockingprobability for the new calls of the two different service typesin MFCR, . In this way, a new call withservice type 1 (2) is blocked if the number of channels availableafter the call was accepted is less than . Notice that

because and are considered

integer. Then, new calls with service type 1 are blocked whenthe system is in states where there are less than

channels available. Also,new calls with service type 2 are blocked when the system is instates where there are less than channels available.Additionally, a new call with service type 1 (2) is blocked withprobability if the number of channelsavailable after the call was accepted is . Thus, newcalls with service type 1 are blocked with probabilitywhen the system is in states where there are

channels available. As andare considered integer, then . That

is, the fractional parts of and are equal. Then, also newcalls with service type 2 are blocked with probabilitywhen the system is in states where there are channelsavailable.

V. ALGORITHM TO DETERMINE THE OPTIMUM NUMBERS OF

RESERVEDCHANNELS IN MFCR

System capacity is limited by QoS constrains, which in cir-cuit or virtual circuit switched communications are representedby maximum acceptable values of new call blocking and forcedtermination probabilities. In general, as it was explained, cellcapacity is the maximum offered traffic load for which all theblocking probabilities of the different call types do not exceedtheir maximum acceptable values [12]. The QoS promised tousers of the different service types are the new call blockingand forced termination probabilities at the nominal load (systemcapacity) with the system traffic engineered such that up to thenominal load, these probabilities are below the guaranteed levels[39]. We state that in the MFCR strategy, maximum system ca-pacity is achieved only when the blocking probabilities of thedifferent call types are simultaneously equal to their respectivemaximum acceptable values. Furthermore, these conditions areonly met when the optimal prioritization order and the rightnumber of reserved channels for each call type are used. Com-plex relationships exist between the different system variablesbecause of resource sharing. An alteration to any of them turnsinto system capacity variations. MFCR ensures that capacitymaximization is achieved since the numbers of reserved chan-nels can be finely adjusted by fractions of one resource unitrather than in full units of resources. In addition, since MFCRassumes that the prioritization level provided to a call type isdirectly proportional to the number of channels it has access to,traffic order is guaranteed [24]. Thus, an optimal system con-figuration can exist such that all the maximum acceptable QoSconstraints are simultaneously met.

To show that our proposed MFCR strategy achieves optimalor maximum system capacity as stated above, let us defineas the maximum aggregate offered traffic generated by all calltypes for which equals its maximum acceptable value (orQoS constraint) irrespective of the fact that othersmeet or not theirs. That is, the offered load for which equalsits maximum acceptable value is:

(14)


(Depending on the prioritization order selected, mayrefer to the new call blocking or the handoff failure probability.)(Note that here we are using the full notation to refer to ).Now, cell capacity, , is defined as the greatest total offeredload for which all the QoS constraints are still satisfied [12].That is, the cell capacity is the minimum of the aggregateoffered traffic loads generated by all call types for which

equals its QoS constraint:

(15)

with

(16)

Let us further assume that there is an optimal system con-figuration (where there are numbers ofreserved channels) for which all the blocking probabilities forthe different call types are equal to their respective maximumacceptable values at an offered traffic load . That is,

(17)

Now, for the sake of the explanation, let us also assume thatthe system is in such an optimal configuration where there are

channels that can only be accessed by all calls other thanthe ones with the lowest priority, channels that cannot beused by the calls with second lowest priority,, andchannels that cannot be used by the calls with the second highestpriority. If the number of channels that cannot be used by thecall type is increased from to , then the blocking

probability of the call type will increase,

. This is due to the fact that the blocking probabilityof each call type is a monotonically increasing function of thenumber of channels that cannot be used by the call type. Thus,

(18)

and then ; and by(15), therefore,

That is, if the number of channels calls of typehave accessto is reduced, then this call type meets its maximum acceptableblocking probability with an aggregated offered traffic which issmaller than the optimal case. On the other hand, if the numberof channels calls of type have access to is increased, then theblocking probability of the call type will decrease. However,

the blocking probability of at least another call type, say, will increase because its number of reserved channels will

decrease. Therefore,

(19)

and then ; and by(15),

That is, the aggregate offered traffic for which the blockingprobability of other(s) call type(s) is equal to its maximum ac-ceptable value is less than the optimal case. Thus, if it exists,there is a unique maximum for the system capacity (rememberthat it depends on the QoS constraints and system character-istics); and because of the traffic order [24], there is a uniqueoptimum prioritization order.

In summary, the different real numbers of reserved chan-nels for which all the individual maximum acceptable QoSconstraints are simultaneously met maximize the systemcapacity. These real numbers of reserved channels are linkedto a particular prioritization order and are called the optimumnumbers of reserved channels.

A. Algorithm for Service Types for Arbitrary PrioritizationOrder

In this section, we describe an algorithm to determine themaximum cell capacity and the optimum numbers of reservedchannels in the MFCR strategy assuming that the QoS con-straints are (for ). This algorithm is validfor any arbitrary prioritization order (recall that the prioritiza-tion order determines the channel restrictions for the differentcall types and the equilibrium state equations of the system).The algorithm requires the use of several variables and aux-iliary variables. The input variables are: , , , , ,and . As defined in Section IV-A, represents themean new call arrival rate for service type(for ),

represents the mean handoff arrival rate for service type(for ), represents the mean unencumberedservice time for service type (for ), rep-resents the mean cell dwell time for service typeusers (for

), and represents the fraction of the total newcall arrival rate produced from calls requesting the service type(for ). is the maximum acceptable value ofthe call blocking probability of call type (for ).The superscripts represent the iteration numbers for each ofthe loops. , and are auxiliaryvariables used in the successive bisections procedures. Finally,

(for ) are auxiliary variables used inthe calculation of the optimum numbers of reserved channels.The outputs of the algorithm are the optimum numbers of re-served channels and the maximum systemcapacity . The algorithm is as follows:


Inputs : , ,, ,

, and .Outputs : , and .Step 0 : Make ,

,, ,

. Go to step 1.Step 1 : Make , ,

,

, and . Go to step 2.

Step 2 : Make , ,

. Go to step 3.

Step : Make , ,. Go to step .

Step : Make , ,. If , make

, otherwise ; if, make otherwise

; ; if ,

make , otherwise

. Go to step .

Step : If , make, otherwise ;

if , make ,otherwise ; ;

if , make

, otherwise

. Calculate thesteady state probabilities considering

, ,

and . The incoming handoff attemptrates per cell are calculatedby the iteration method describedin [34]. Then calculate the newcall blocking and forced terminationprobabilities for each service type. Goto step .Step : If ,then go to step . Otherwise, go tostep .Step : If , then in-crease the number of reserved channelsfor prioritization of call types 2, 3,

, and over call type 1. That is:, , increase

by 1 and go to step . Otherwise,decrease the number of reserved chan-nels for the call types 2, 3, , and

. That is: , ,increase by 1 and go to step .Step : If ,then go to step . Otherwise, go tostep .

Step : If , then in-crease the number of reserved channelsfor prioritization of call types 3, 4,

, and over call types 2 and 1. Thatis: , , increase

by 1 and go to step . Otherwise,decrease the number of reserved chan-nels for the call types 3, 4, , and

. That is: , ,increase by 1 and go to step .

Step : If, then go to step . Oth-

erwise, go to step .Step : If , thenincrease the number of reserved channelsfor prioritization of call type overcall types , and 1. That is:

, ,increase by 1 and go to step 2.Otherwise, decrease the number of re-served channels for the call type .That is: ,

, increase by 1 andgo to step 2.Step : The process ends if

. Otherwise, go tostep .Step : If , thenincrease offered traffic. That is:

, , increaseby 1 and go to step 1. Otherwise,

decrease the offered traffic. That is:, , increase

by 1 and go to step 1.

Basically, the algorithm consists of iterative loopsand essentially cutoff thresholds or channel restrictions forall call types are adjusted out until the experienced blockingrates achieve the maximum permissible values. The outermost loop determines the optimum cell capacity. The next

outer loops calculate the optimum numbers of reservedchannels . The second outer most loopdetermines the value of , the next loop determines thevalue of , and so on. These loops use the successivebisections method and they consider the fact that the blockingprobability (new call or handoff blocking) for a given calltype is a monotonically decreasing function of the number ofchannels that a call type has access to. Thus, if the blockingprobability for the call type , , is smaller (greater) thanits target value, then the number of channels that the calltype can use must be decreased (increased), as indicatedin step throughstep . The next inner loopcalculates the handoff arrival rate as described in [34] andthe innermost loop calculates the steady state probabilitiesusing the Gauss-Seidel method (both loops instep ). The


Fig. 4. Architecture of cells for MFCR for two service types and the prioritization orderN1�H1�N2�H2.

values of for which all the individual QoSconstraints simultaneously equal their respective maximumacceptable values (conditionsand and and

of step ,maximize the system capacity. If these conditions are not metafter a large number of iterations, another prioritization ordermust be investigated. Notice that when the optimum numbersof reserved channels are determined, the optimal prioritizationorder is also automatically determined.

B. Special Case for Two Service Types (For a ParticularPrioritization Order)

To illustrate how the algorithm can be simplified if the ob-jective is to offer the same blocking probability for new calls ofdifferent service types, an algorithm to determine the optimumnumbers of reserved channels for a system with two servicesand a particular optimal prioritization order is presented. Let usassume that the QoS constraints are

and that the order of increasingimportance is . Hence, for the prioriti-zation order assumed, it is necessary to reserve chan-nels to prioritize , , and over calls. From these

channels, channels are reserved to prioritizeand over and calls. And from these

channels, channels are reserved for exclusive use of

calls. Thus, . The cell architecturefor this prioritization order is shown in Fig. 4. Notice that bymaking , the equalityis achieved. Recall that the prioritization order determines thechannel restrictions to the different call types and the equilib-rium state equations of the system. The algorithm is as follows:

Inputs : , , , , , , ,, , , , , and

.Output : , , , and .Step 0 : Make ,

,, , , ,

. Go to step 1.Step 1 : Make , ,

, . Go to step 2.

Step 2 : Make , ,. Go to step 3.

Step 3: If , make

, otherwise

; if ,

make , otherwise

. Calculate the steadystate probabilities using (3)–(6)


Fig. 5. Flow chart of the algorithm to determine the optimum numbers of reserved channels in MFCR for two service types with the prioritization orderN1�

H1 � N2 � H2.

and considering , ,

, and . The incoming handoffattempt rates per cell arecalculated by the iteration method

described in [34]. Then calculate thenew call blocking and forced terminationprobabilities for each service using (7)and (9), respectively. Go to step 4.


TABLE IPOSSIBLEPRIORITIZATION ORDERS FOR ATWO SERVICESMOBILE CELLULAR SYSTEM (IN ORDER OFINCREASINGIMPORTANCE)

Step 4 : If go to step6. Otherwise, go to step 5.Step 5 : If , then increasethe number of reserved channels forservice 2 calls. That is: ,

, increase by 1and go to step 3. Otherwise, decreasethe number of reserved channels forthis service. That is: ,

, increase by 1 andgo to step 3.

Note: the conditionmust be met at all times if the assumedprioritization order is the optimalone (the one that achieves maximumcapacity).Step 6 : If , then go tostep 8. Otherwise, go to step 7.Step 7 : If , then increase thenumber of reserved channels for handoffcalls of service 2. That is, ,

, ,, and go to step 2. Other-

wise, decrease the number of channelsfor this call type. That is, ,

, ,, and go to step 2.

Step 8 : If andand and

, then increase the offeredtraffic. That is: ,

, , and go to step 9.Otherwise, decrease the offered traffic.That is: , ,

, and go to step 9.Step 9 : The process ends if

and andand

and . Oth-erwise, go to step 1.

This algorithm consists of five iterative loops instead of thesix iterative loops required by the algorithm for arbitrary pri-oritization order in the previous subsection and it is illustratedin the flow chart shown in Fig. 5. This is because the relation-ship between and is already known,

. The outer most loop determines the value ofoptimum cell capacity. The second outer most loop determinesthe value of and the next loop calculates . Theseloops use the successive bisections method and consider thefact that the blocking probability (new call or handoff blocking)for a given call type is a monotonically decreasing function ofthe number of channels that the call type has access to. Thus,if the blocking probability for the call type, , is smaller(greater) than its target value, then the number of channels thecall type has access to must be decreased (increased), as indi-cated insteps 5and7. The superscripts , , and representthe iteration numbers for the three outer most loops., ,


TABLE IISYSTEM CAPACITY FOR MFCR WITH THE OPTIMAL PRIORITIZATION ORDER ASFUNCTION OF THEMOBILITY PARAMETER 1=�

Fig. 6. Architecture of cells for MFCR for two service types and the prioritization orderN1�N2�H1�H2.

, , , and are auxiliary variables used in the succes-sive bisections procedures. The next inner loop calculates thehandoff arrival rate as described in [34] and the innermost loopcalculates the steady state probabilities using the Gauss-Seidelmethod (both loops instep 3). Note that by making

, the equality is achieved. This is

because the blocking condition for the new calls of the servicetypes 1 and 2 is the same. The values of , and

for which all the individual QoS constraints simultaneouslyequal their respective maximum acceptable values (conditions

andof step 6), maximize the system capacity. Recall that


if these conditions are not met after a large number of itera-tions, another prioritization order must be investigated. Noticethat when the optimum numbers of reserved channels are de-termined, the optimal prioritization order is also automaticallydetermined.

VI. GUIDE ON THE SELECTION OF THE OPTIMAL

PRIORITIZATION ORDER

An initial task in the determination of the optimum numbersof reserved channels is the selection of a prioritization order tobe tested. It can then be accepted as the optimal one or rejected.In this section, a guide on the selection of the optimal prioritiza-tion order is provided. It is explained by means of an example.

The first step toward the optimal selection involves identi-fying the types of service, followed by the determination of theirbandwidth requirements and QoS constraints. Then, call typesare classified based ona priori knowledge of the level of pro-tection required (i.e., handoff calls need to be more protectedthan new calls). If system characteristics were unknown, all pos-sible prioritization orders would have to be tested until the op-timal one were determined. However, this could be prohibitiveas there are different total possible prioritization orders.The specific optimal prioritization order depends on the QoSconstraints and the system characteristics (i.e., mobility, servicetime, bandwidth requirements, traffic proportions of the dif-ferent service types, etc.) Knowledge of a single QoS objectivemay ease the process, though. For instance, if one of the resourcemanagement objectives is to provide fair access among all ser-vice types, then calls with high bandwidth requirements must beconsidered the most delicate call types and must be assigned ahigher prioritization level than low bandwidth ones. This is be-cause in a complete resource sharing strategy, as shown in [40],they are blocked more often than low bandwidth calls regardlessof the arrival rates. In this way, as explained at the end of Sec-tion IV, the relationships among the prioritization levels of thedifferent types of new calls can be easily determined. Thus, it isprobable that the optimal prioritization order is among those or-ders that consider high bandwidth calls more delicate than lowbandwidth ones. If it is also necessary to provide additional pro-tection to handoff calls over new calls, to ensure acceptable QoSin terms of forced termination probability; then it is probablethat the optimal prioritization order is among the prioritizationorders that also consider that the handoff calls of a given servicetype are more delicate than the new ones of that same service.The prioritization relationships among the rest of the call typesare more difficult. Nevertheless the determination of the optimalprioritization order may be expedited if the initial prioritizationorders to be tested are chosen from those that consider that highbandwidth calls are more delicate than low bandwidth calls andthat handoff calls are more delicate than new calls. If the op-timal prioritization order is not within this group, then the nextprioritization orders to be tested can be chosen from those or-ders that consider that high bandwidth calls are more delicatethan low bandwidth calls. Finally, if the optimal prioritizationorder is not within the previous groups, then the next prioritiza-tion orders to be tested can be chosen from the rest of the prior-itization orders. Notice that the assumption that high bandwidth

Fig. 7. System capacity in Erlangs/cell for the different CR strategies in thescenario with1=� = 900 s.


calls are more delicate than low bandwidth calls (and thereforegreater priority should be assigned to them) is only a mere as-sumption to illustrate how thea priori knowledge of the qualityof service requirements can be used to determine the prioriti-zation order. The fact that we have selected that particular pri-oritization order does not necessarily mean that another ordercannot be used. There is no impediment for the network oper-ator/system administrator to select another prioritization ordersbased on different quality of service requirements and/or rev-enue restrictions.

As an example, consider a system with two services. Let usassume that the QoS constraints are , ,and , for and 2, and suppose that .For the considered two services system, all the pos-sible prioritization orders are shown in the left column of Table I.



There are 12 prioritization orders that consider that high band-width calls are more delicate than low bandwidth ones, these areshown in the central column of Table I. And there are three pri-oritization orders that also consider that handoff calls are moredelicate than new ones. These are shown in the right columnof Table I. In our example, the initial prioritization orders tobe tested can be chosen from the three shown in the rightmostcolumn of Table I. Thus, the number of possible prioritizationorders, among which the optimal one exists, is drastically re-duced from 24 to only three. If the optimal prioritization orderis not within this group, then the next prioritization orders to betested can be chosen from those 12 shown in the central columnof Table I. Thus, the number of possible prioritization orders,among which the optimal one can exist, is reduced from 24 to12. Finally, if the optimal prioritization order is not within theprevious groups, then the next prioritization orders to be testedcan be chosen from the rest of the prioritization orders shownin the left column of Table I. It is important to highlight that theprioritization order depends on the bandwidth requirements andthe QoS constraints of the different service types, the servicetimes, the cell dwell times, and on the traffic proportions gen-erated by each service time. Hence, could be a combination ofthe different parameters that might produce an optimal prioriti-zation order that has H1/N1 after H2/N2.

VII. N UMERICAL EVALUATIONS

A cellular system with two services is considered as a numer-ical example to illustrate the performance analysis techniquespresented here and the performance of four strategies is evalu-ated: the No Priority Scheme (NPS), the CR, the FCR and theMFCR. The CR (FCR) scheme is used to prioritize new andhandoff calls with service 2 [referred to as CR-2 (FCR-2)] andto prioritize handoff calls of both services [referred to as CR-H(FCR-H)]. The values of the different parameters involved inthe numerical evaluations are , , ,

, , ,

TABLE IIICELL CAPACITY FOR THE DIFFERENTSCHEMES IN THESCENARIO WITH

1=� = 900 s

, , and . To determine thecell capacity, the QoS constraints to be met are ,

, , and .It is important to mention that the MFCR strategy was tested

in a set of different mobility conditions (including different op-timal prioritization orders). However, for the sake of space, re-sults are provided for three scenarios only. Each scenario ischaracterized by different values of the mean cell dwell timefor users with service type 1 . To show the influence ofsystem characteristics on the determination of optimal priori-tization order, Table II shows maximum system capacity forMFCR as function of the mean dwell time for service type 1users . Only the optimal prioritization order is shownalong with the optimum number of reserved channels for eachoptimum order. Table II shows that for values of the mean dwelltime greater than or equal to 200 s and smaller than or equal to500 s, the optimal prioritization order is(see Fig. 6). When the mean dwell time is higher than or equalto 600 s, the optimal prioritization order is(the cell architecture for this prioritization order is shown inFig. 4). Finally, when the mean dwell time is smaller than orequal to 100 s, the optimal prioritization order is

. Table II also shows that as the mean cell dwell time ofusers with service type 1, , decreases the system capacitydecreases. This is because when decreases, the speed ofusers with service type 1 increases creating, therefore, morehandoff calls. This requires, in turn, the reservation of morechannels to prioritize calls with service type 1, decreasing, con-sequently, system capacity.

Figs. 7–9 show the offered traffic for FCR-H (FCR-2) versusthe number of reserved channels to prioritize handoff calls[calls (new and handoff) with service 2] for which all the QoSconstraints are satisfied. Note that because the FCR-H andFCR-2 schemes reserve a real number of channels, the curvesrepresenting their performance are continuous. CR-2 and CR-Hare particular cases of FCR-2 and FCR-H, respectively. Hence,their performance can be derived from those representingFCR-H and FCR-2, if only integer values are considered for thenumber of reserved channels. As it can be observed from Fig. 7(8) {9}, the maximum offered load that the CR-H strategycan carry to meet the QoS constraints mentioned above is25.6501 (25.499 52) {25.133 28} Erlangs. This happens whenthe number of reserved channels is equal to 1 (2) {2}. For other


TABLE IVCELL CAPACITY FOR THE DIFFERENTSCHEMES IN THESCENARIO WITH

1=� = 300 s

cases, the QoS constraints are either not met or the maximumoffered load supported is lower. On the other hand, FCR-Hstrategy can cope with 26.2556 (26.091 12) {25.242 48}Erlangs when the number of reserved channels is 1.26 (1.35){2.1}. Fig. 7 (8) {9} also shows that the maximum offered loadthat the CR-2 strategy can carry to meet the QoS constraintsmentioned above is 25.3847 (24.665 16) {22.855 44} Erlangs.This happens when the number of reserved channels is equalto 1 (0) {0}. On the other hand, FCR-2 strategy can cope with25.968 24 (24.790 92) {22.855 44} Erlangs when the numberof reserved channels is 1.36 (0.2) {0}.

To compare MFCR against the other strategies in the sce-nario with , Fig. 7 plots cell capacity obtainedwith the MFCR strategy for two different cases. The first oneshows cell capacity plotted versus whenand . The second case plots it versus when

and . The different numbers of re-served channels (determined using the algorithm in Section V)were chosen deliberately to show the optimum capacity point.Notice that for both cases, the conditionsmust be satisfied. As it can be observed from the figure, themaximum offered load that the MFCR strategy can carry tomeet the QoS constraints mentioned above is 27.6904 Erlangs.This happens when , , and

. Table III shows the maximum cell capacity achievedwith the particular QoS constraints specified above for the dif-ferent schemes. As it is observed, the MFCR strategy achieves12.31% capacity gain relative to the NPS and more than 5.46%relative to the prioritization schemes CR-2, CR-H, FCR-2, andFCR-H in the scenario with .

On the other hand, to compare MFCR against the other strate-gies in the scenario with , Fig. 8 plots cell ca-pacity obtained with the MFCR strategy for two different cases.The first one shows cell capacity plotted versuswhen

and . The second case plots it versuswhen and . The different num-bers of reserved channels were chosen deliberately to show theoptimum capacity point. As it can be observed from the figure,the maximum offered load that the MFCR strategy can carry tomeet the QoS constraints mentioned above is 27.2872 Erlangs.This happens when , , and

. Table IV shows the maximum cell capacity achievedwith the particular QoS constraints specified above for the dif-

TABLE VCELL CAPACITY FOR THE DIFFERENTSCHEMES IN THESCENARIO WITH

1=� = 100 s

ferent schemes. As it is observed, the MFCR strategy achieves10.63% capacity gain relative to the NPS and more than 4.58%relative to the prioritization schemes CR-2, CR-H, FCR-2, andFCR-H in the scenario with .

In a similar way, to compare MFCR against the other strate-gies in the scenario with , Fig. 9 plots cell ca-pacity obtained with the MFCR strategy for two different cases.The first one shows cell capacity plotted versuswhen

and . The second case plots it versuswhen and . The different num-bers of reserved channels were chosen deliberately to show theoptimum capacity point. As it can be observed from the figure,the maximum offered load that the MFCR strategy can carryto meet the QoS constraints mentioned above is 25.953 96 Er-langs. This happens when , , and

. Table V shows the maximum cell capacityachieved with the particular QoS constraints specified abovefor the different schemes. As it is observed, the MFCR strategyachieves 13.56% capacity gain relative to the NPS and morethan 2.82% relative to the prioritization schemes CR-2, CR-H,FCR-2, and FCR-H in the scenario with .

As for the MFCR strategy, it was found that (see Table II),with the specified QoS constraints and assumed parame-ters values, the algorithm presented in Section V convergeswhen the prioritization order is

when. If such order

is used, the MFCR strategy achieves the maximum capacity.Notice that as the mean cell dwell time for service type 1users is reduced, the handoff calls of service type 1users become more delicate. Then the optimal prioritizationorder is such that H1 appears neat the end or at the end ofthe list. Plotting the MFCR performance requires, in thiscase, a four-dimensional plot as it has three control parameters( , , for the prioritizationorder ; , ,

for the prioritization order ;and , , for the priori-tization order ). However, if we makeone variable a function of the others, a 3-D plot can be used.Three cases are considered as shown in Figs. 10–12. Fig. 10shows the system capacity versus and for the scenariowith assuming that . Observe that


there is a unique maximum atand . Fig. 11 shows the system

capacity versus and for the scenario withassuming that . This figure shows that there isa unique maximum in this plotat and . Finally, Fig. 12 showsthe system capacity versus and for the scenario with

assuming that . This figure showsthat there is a unique maximumin this plot at and .

VIII. C ONCLUSION

With the aim of maximizing system capacity in multiser-vice mobile cellular networks for given requirements on newcall blocking and forced termination probabilities for the dif-ferent service types, a call admission strategy was proposed.The strategy is called MFCR and reserves, on average, severalreal numbers of channels to provide a certain protection level toeach of the diverse call types. Capacity increase is obtained withMFCR via service differentiation. We noticed that the processof selecting the optimal prioritization order is complicated, as itdepends on QoS constraints and system characteristics. In addi-tion, it is affected by resource sharing. By considering all pos-sible prioritization orders, an order can be found that yields thehighest capacity. However, for multiservice mobile systems, thiscould be prohibitive because of the huge number of possible pri-oritization orders. A guide on the selection of the optimal prior-itization order was given.

The numbers of reserved channels are determined by theconnection-level QoS requirements, and could be made static(predetermined) or dynamic (adaptively changed). The com-putational complexity of the MFCR should be addressed if itis used as an adaptive algorithm for call admission controland operates in highly time variant offered traffic systems.This is because to determine the optimal numbers of reservedchannels, it is necessary to solve multidimensional birth anddeaths equations. An alternative is to use look up tables to de-termine system configuration depending on the current systemcharacteristics. Such tables can be built at the design stage.Once the optimum prioritization order has been determinedand if the traffic conditions show no dramatic changes, thenthe prioritization order will most likely not change or if it does,it will change moderately. This means that only during theinitial phase of the implementation of MFCR an exhaustivesearch of the optimum prioritization order is necessary but,once the system is in operation, the search for it can easily berestricted to a very small set of prioritization orders. Also, theproposed MFCR could be used to maximize system capacityin a scenario with time varying traffic conditions as in [46]. In[46] the system projects the future network state based on thecurrent network state and, upon detecting or anticipating sig-nificant changes in the traffic intensity, recommends an optimalchannel allocation. Then, the resulting plan is implementedin the network until the next run. Once the optimum priorityorder is determined, MFCR implementation is very simple asit only requires the generation of random numbers with uni-form distribution between zero and one and their comparisonwith certain thresholds (i.e., the number of available resources)

Fig. 10. System capacity versus R2 and R3 for the scenario with1=h1 =

900 s and assumingR = R + 1.

Fig. 11. System capacity versusR andR for the scenario with1=� =


Fig. 12. System capacity versusR andR for the scenario with1=� =


known locally in each cell. Although fixed cell capacity anduniform spatial traffic distribution was assumed for the sake


of clarity, the proposed concepts can also be applied to themore general problem of system capacity optimization in dy-namic channel allocation schemes and/or in nonuniform spatialtraffic. The MFCR strategy proposed here can also be com-bined with other resource management schemes (i.e., queuingand/or pre-emptive schemes, etc.) and used in multimobilityenvironments (static, pedestrian, vehicular, etc.). The use ofthe MFCR strategy in adaptive multimedia service environ-ments can also be investigated. All these issues along withothers considerations (such as the dropping of queued callsattempting handoff due to unavailability of channels duringthe handoff area dwell time, the case when the new channelholding time and the handoff call channel holding time havedifferent distributions or different average values [41]–[43],and the multiple handoffs problem [44], [45]) are subjects offurther research.

ACKNOWLEDGMENT

The authors would like to thank to the anonymous reviewersfor their valuable comments and suggestions, which enhancedthe quality of the paper.

REFERENCES

[1] W. Huang and V. K. Bhargava, “Performance evaluation of a DS/CDMAcellular system with voice and data traffic,” inProc. IEEE PIMRC,Taiwan, Taipei, ROC, Oct. 1996, pp. 588–592.

[2] B. Epstein and M. Schwartz, “Reservation strategies for multi-mediatraffic in a wireless environment,” inProc. IEEE VTC, Chicago, IL, July1995, pp. 165–169.

[3] R. S. Lunayach, S. S.S. Subba Rao, and S. C. Gupta, “Analysis of amobile radio communication system with two types of customers andpriority,” IEEE Trans. Commun., vol. 30, pp. 2470–2475, Nov. 1982.

[4] E. Posner and R. Guerin, “Traffic policies in cellular radio that minimizeblocking of handoff calls,” inProc. ITC, Kyoto, Japan, Sept. 1985, pp.294–298.

[5] D. Hong and S. S. Rappaport, “Traffic model and performance analysisfor cellular mobile radio telephone systems with prioritized and non-prioritized handoff procedures,”IEEE Trans. Veh. Technol., vol. 35, pp.77–92, Aug. 1986.

[6] R. Guérin, “Queueing blocking system with two arrival streams andguard channels,”IEEE Trans. Commun., vol. 36, pp. 153–163, Feb.1988.

[7] C. H. Yoon and K. Un, “Performance of personal portable radio tele-phone systems with and without guard channels,”IEEE J. Select. AreasCommun., vol. 11, pp. 911–917, Feb. 1993.

[8] Q.-A. Zeng, K. Mukumoto, and A. Fukuda, “Performance analysisof mobile cellular radio systems with two-level priority reservationhandoff procedure,”IEICE Trans. Commun., vol. E80-B, pp. 598–607,Apr. 1997.

[9] R. Ramjee, R. Nagarajan, and D. Towsley, “On optimal call admissioncontrol in cellular networks,” inProc. IEEE Infocom, San Francisco,CA, Mar. 1996, pp. 43–50.

[10] C. J. Ho and C. T. Lea, “Improving call admission policies in wire-less networks,”ACM/Baltzer J. Wireless Networks, vol. 5, pp. 257–265,1999.

[11] F. A. Cruz-Pérez, D. Lara-Rodríguez, and M. Lara, “Fractional channelreservation in mobile communication systems,”IEE Elect. Lett., vol. 35,pp. 2000–2002, Nov. 1999.

[12] J. G. Markoulidakis, J. E. Dermitzakis, G. L. Lyberopoulos, and M. E.Theologou, “Optimal system capacity in handover prioritised schemesin cellular mobile telecommunication systems,”Comput. Commun. J.,vol. 23, pp. 462–475, Mar. 2000.

[13] W. Huang and V. K. Bhargava, “Channel reservation for high rate ser-vice in cellular networks,” inProc. IEEE Pacific Rim Conf. Commun.,Comput. Signal Processing, Victoria, Canada, Aug. 1997, pp. 350–353.

[14] D. K. Kim and D. K. Sung, “Handoff management in cdma systems witha mixture of low rate and high rate traffics,” inProc. IEEE VTC, Ottawa,ON, Canada, May 1998, pp. 1346–1350.

[15] C.-W. Lam and T.-M. Ko, “Dynamic channel assignment for multi-ratecellular networks,” inProc. IEEE VTC, Ottawa, ON, Canada, May 1998,pp. 1538–1542.

[16] Y. Fang and Y. Zhang, “Call admission control schemes and performanceanalysis in wireless mobile networks,”IEEE Trans. Veh. Technol., vol.51, pp. 371–382, Mar. 2002.

[17] Y. Zhang and D. Liu, “An adaptive algorithm for call admission controlin wireless networks,” inProc. IEEE Globecom, San Antonio, TX, Nov.2001, pp. 3628–3632.

[18] E.-S. El-Alfy, Y.-D. Yao, and H. Heffes, “Adaptive resource allocationwith prioritized handoff in cellular mobile networks under qos provi-sioning,” in Proc. IEEE VTC-Fall, Atlantic City, NJ, Sept. 2001, pp.2113–2117.

[19] Q.-A. Zeng and D. P. Agrawal, “Performance analysis of a handoffscheme in integrated voice/data wireless networks,” inProc. IEEEVTC-Fall, Boston, MA, Sept. 2000, pp. 1986–1992.

[20] F.-N. Pavlidou, “Two-dimensional traffic models for cellular mobile sys-tems,” IEEE Trans. Commun., vol. 45, pp. 1505–1511, Feb./Mar./Apr.1994.

[21] D. Hong and S. S. Rappaport, “Priority oriented channel access forcellular systems serving vehicular and portable radio telephones,”IEEProc., pt. I, vol. 136, pp. 339–346, Oct. 1989.

[22] Y. Jiang and V. K. Bhargava, “Mobility-oriented guard channel assign-ment for personal communication systems,” inProc. IEEE Int. Conf.Personal Wireless Commun. (ICPWC), Mumbai (Bombay), India, Dec.1997, pp. 15–18.

[23] D. C. Lee, S. J. Park, and J. S. Song, “Performance analysis of queueingstrategies for multiple priority calls in multiservice personal communi-cations services,”Comput. Commun. J., vol. 23, pp. 1069–1083, June2000.

[24] H. Kröner, “Comparative performance study of space priority mecha-nisms for ATM networks,” inProc. IEEE Infocom, San Francisco, CA,June 1990, pp. 1136–1143.

[25] L. Yin, B. Li, Z. Zhang, and Y.-B. Lin, “Performance analysis of a dual-threshold reservation (DTR) scheme for voice/data integrated mobilewireless networks,” inProc. IEEE WCNC, Chicago, IL, Sept. 2000, pp.258–262.

[26] Q. An Zeng and D. P. Agrawal, “Modeling and analysis of preemptivepriority based handoffs in integrated wireless networks,” inProc. IEEEVTC-Fall, Atlantic City, NJ, Sept. 2001, pp. 281–285.

[27] S. Tekinay, B. Jabbari, and A. Kakaes, “Modeling of cellular commu-nication networks with heterogeneous traffic sources,” inProc. IEEEICUPC, Ottawa, ON, Canada, Oct. 1993, pp. 249–253.

[28] S. S. Rappaport and C. Purzynski, “Prioritized resource assignment formobile cellular communication systems with mixed services and plat-form types,” IEEE Trans. Veh. Technol., vol. 45, pp. 443–458, Aug.1996.

[29] G. I. Chae, B. D. Choi, and J. Chung, “Performance analysis for cel-lular mobile network with mixed services and platform types,”IEE Proc.Commun., vol. 146, pp. 246–250, Aug. 1999.

[30] J. Chi-Chao and W. Chen, “Connection admission control for mobilemultiple-class personal communications networks,”IEEE J. Select.Areas Commun., vol. 15, pp. 1618–1626, Oct. 1997.

[31] B. Li, C. Lin, and S. Chanson, “Analysis of a hybrid cutoff priorityscheme for multiple classes of traffic in multimedia wireless networks,”ACM/Baltzer J. Wireless Networks, vol. 4, pp. 279–290, Aug. 1998.

[32] T. Kwon, S. Kim, Y. Choi, and M. Naghshineh, “Threshold-type calladmission control in wireless/mobile multimedia networks using priori-tised adaptive framework,”IEE Elect. Lett., vol. 36, pp. 852–854, Apr.2000.

[33] F. Santucci, W. Huang, P. Tranquilli, and V. K. Bhargava, “Admissioncontrol in wireless systems with heterogeneous traffic and overlaidcell structure,” inProc. IEEE VTC-Fall, Boston, MA, Sept. 2000, pp.1106–1113.

[34] Y. B. Lin and A. Noerpel, “The sub-rating channel assignment strategyfor pcs hand-offs,”IEEE Trans. Veh. Technol., vol. 45, pp. 122–130, Feb.1996.

[35] Y. B. Lin and I. Chlamtac, “Large effective call holding times for a pcsnetwork,” inProc. IEEE PIMRC, Taipei, Taiwan, ROC, Oct. 1996, pp.143–147.

[36] F. Khan and D. Zeghlache, “Effect of cell residence time distributionon the performance of cellular mobile networks,” inProc. IEEE VTC,Phoenix, AZ, May 1997, pp. 949–953.

[37] R. B.Robert B. Cooper, Introduction to QueueingTheory. Washington, D.C.: CEE, 1990.

[38] M. Casoni and M. L. Merani, “Erlang capacity of a TDD-TD/CDMAarchitecture supporting heterogeneous traffic,” inProc. IEEE Globecom,San Antonio, TX, Nov. 2001, pp. 637–641.

[39] M. Naghshineh and M. Schwartz, “Distributed call admission control inmobile/wireless networks,”IEEE J. Select. Areas Commun., vol. 14, pp.711–717, May 1996.

[40] J. M. Aein, “A multi-user-class, blocked-calls-cleared, demand accessmodel,” IEEE Trans. Commun., vol. 26, pp. 378–385, Mar. 1978.


[41] P. V. Orlik and S. S. Rappaport, “Traffic performance and mobility mod-eling of cellular communications with mixed platforms and highly vari-able mobilities,”Proc. IEEE, vol. 86, pp. 1464–1479, July 1998.

[42] Y. Fang and I. Chlamtac, “Teletraffic analysis and mobility modelingfor pcs networks,”IEEE Trans. Commun., vol. 47, pp. 1062–1072, July1999.

[43] W. Li and A. S.A. Sule Alfa, “Channel reservation for handoff calls inpcs a network,”IEEE Trans. Veh. Technol., vol. 49, pp. 95–104, Jan.2000.

[44] S. S. Rappaport, “The multiple-call handoff problem in high-capacitycellular communications systems,”IEEE Trans. Veh. Technol., vol. 40,pp. 546–557, Aug. 1991.

[45] Y.-K. Suh, S.-H. Wie, H.-H. Choi, and D.-H. Cho, “Performance anal-ysis of bulk handoff in integrated voice/data wireless networks,”IEICETrans. Commun., vol. E85-B, pp. 1396–1401, July 2002.

[46] T. S. Randhawa, S. Hawthorne, K. Moir, and R. H. S. Hardy, “An inte-grated capacity manager for multimedia cellular network,” inIEEE/IFIPInt. Symp. Integrated Network Management, Seattle, WA, May 2001, pp.257–270.

Heraclio Heredia-Ureta (S’03) was born inCuliacán, Sinaloa, México, in 1977. He receivedthe B.Sc. degree in electronics and communicationsengineering from the Instituto Tecnológico deCuliacán in 2000, and the M.Sc. degree in electricalengineering from the Center for Research andAdvanced Studies from the Instituto PolitécnicoNacional (CINVESTAV-IPN) Mexico City, Mexico,in 2003.

Currently, he is with the Universidad de Occidente,Campus Culiacán. His research interest is in resource

management, teletraffic analysis, and prioritized resource allocation in mobilewireless communication systems.

Felipe A. Cruz-Pérez (S’98–M’02) was bornin Mixquiahuala, Hidalgo, México, in 1972. Hereceived the B.Sc. degree from the Technolog-ical Institute and Superior Studies of Monterrey(ITESM), Mexico, in 1994 and the M.Sc. and Ph.D.degrees from CINVESTAV-IPN in 1997 and 2001,respectively, all in electrical engineering.

Currently, he is with the CINVESTAV-IPN andhis research interest is in resource management,teletraffic analysis, quality of service provisioning,call admission control, and prioritized resource

allocation in mobile wireless communication systems, microcellular systems,CDMA cellular systems, and wireless communication systems with linkadaptation.

Lauro Ortigoza-Guerrero received the B.Sc. degreein electronics and communications engineering fromESIME-UPC in 1993 and the M.Sc. degree in elec-trical engineering from CINVESTAV in 1996, bothfrom the Instituto Politécnico Nacional, Mexico City,Mexico. He received the Ph.D. degree in electric en-gineering from King’s College London, University ofLondon, London, England, in 1999.

In 1998, he joined King’s College London as aResearch Assistant. Since 2000, he has been withWireless Facilities, Inc., San Diego, CA, where he

has been a technical consultant to multiple companies. He has coauthored threebooks on mobile radio communications. His area of interest consists of, but isnot limited to, mobile cellular communication networks with emphasis in radioresource management, teletraffic analysis, and system performance evaluation.

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