Virtual Partitioning Resource Allocation for Multiclass ... - IEEE Xplore

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 53, NO. 3, MAY 2004

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Virtual Partitioning Resource Allocation for Multiclass Traffic in Cellular Systems With QoS Constraints Jianxin Yao, Jon W. Mark, Life Fellow, IEEE, Tung Chong Wong, Senior Member, IEEE, Yong Huat Chew, Member, IEEE, Kin Mun Lye, Senior Member, IEEE, and Kee-Chaing Chua, Member, IEEE

Abstract—Resource allocation is a vital component of call-admission control that determines the amount of resource to assign to new and handoff connections for quality-of-service (QoS) satisfaction. In this paper, we present approximate analytical formulations of virtual partitioning resource-allocation schemes for handling multiclass services with guard channels in a cellular system. Resource-allocation models for best effort and guarantee access with preemption for best effort traffic and virtual partition with preemption for all classes are investigated. The analytical models, derived using a -dimensional Markov chain, are solved using preemption rules for these schemes. Call-level grade of service, such as new-call-blocking probability, handoff-call-blocking probability, and system utilization, and packet-level QoS, such as packet-loss probability, are used as performance metrics. The performances of fast and slow mobile users are evaluated analytically and by simulation. The analytical and simulation results show excellent agreement. A method to maximize system utilization through joint optimization of call-/packet-level parameters is proposed. Numerical results indicate that significant gain in system utilization is achieved. Index Terms—Approximate analysis, call-admission control, code-division multiple-access (CDMA) cellular system, grade of service, multiclass traffic, quality of service, resource allocation, virtual partition.

I. INTRODUCTION

T

HE growing demand for wireless access with grade-of-service (GoS) and quality-of-service (QoS) satisfaction necessitates the efficient use and reuse of the scarce radio resource. Schemes to achieve effective and efficient resource allocation are extremely important. Two commonly used GoS measures in resource allocation are new-call-blocking and handoff-call-

Manuscript received July 8, 2002; revised June 19, 2003, October 17, 2003, and December 25, 2003. This work has been supported by grants from A STAR, Singapore, and MEST, Toronto, ON, Canada, under the Singapore–Ontario Collaborative Research Programme. T. C. Wong, Y. H. Chew, and K. M. Lye are with the Institute for Infocomm Research, Singapore 119613, Singapore (e-mail: [email protected]; [email protected]; [email protected]). J. Yao is with the Institute for Infocomm Research, Singapore 119613, Singapore (e-mail: [email protected]) and with the Electrical and Computer Engineering Department, National University of Singapore, Singapore 119260, Singapore (e-mail: [email protected]). K.-C. Chua is with the Electrical and Computer Engineering Department, National University of Singapore, Singapore 119260, Singapore (e-mail: [email protected]). J. W. Mark is with the Centre for Wireless Communications, Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada (e-mail: [email protected]). Digital Object Identifier 10.1109/TVT.2004.825746

dropping probabilities. Based on the fact that maintaining an ongoing call is more important than admitting a new call, the admission of new and handoff calls has to be treated differently in resource allocation. Many resource-allocation schemes have been proposed to meet both GoS constraints and the need to maintain service continuity [1]–[4]. In [1] and [2], a complete sharing (CS) resource-allocation scheme in which many users share a common resource is proposed. Schemes that use guard channels to assign higher priority to handoff calls over new calls, including new-call bounding, cutoff priority, and newcall-thinning schemes, are investigated [2]. In [3] and [4], some dynamic resource-allocation schemes are proposed and investigated. The dynamic resource-allocation schemes change the admission rules according to the variation in the system parameter values. Thus, these schemes are more complex, but give better system performance by lowering the blocking and dropping probabilities. However, the resource-allocation schemes in these papers pertain to no more than two classes of traffics and the extension to multiclass using this technique is very difficult. In this paper, we investigate the virtual-partitioning (VP) scheme proposed in [1] with guard channels in a code-division multiple-access (CDMA) cellular system. The contribution here is that we consider resource-allocation schemes in a more classes. Moreover, the general way that admit extension to technique used in this paper can also be employed in other resource-allocation schemes. Among the objectives of the third-generation (3G) wireless systems are the provision of 1) audio, data, video, and, particularly, multimedia services and 2) the same QoS to mobile users as they would enjoy in their home environment. That is, we have a QoS problem with multiclass traffic in cellular systems. In general, applications and services can be divided into different classes, depending on how they are considered. In 3G, four traffic classes have been identified: conversational, streaming, interactive, and background classes. One distinguishing factor between these classes is how delay sensitive the traffic is [5]. The conversational and streaming classes can be grossly classified as real-time (RT) connections, while the interactive and background classes are nonreal-time (NRT) packet data. In this paper, we divide the multiclass traffic into two groups that represent RT and NRT connections. There are two proposed VP schemes: VP with preemption for group 2, which gives a higher priority to group 1 over group 2, and VP with preemption for groups 1 and 2, which treats these two groups with equal priority. VP with preemption for groups 1 and 2 is a more general scheme, which is the basis of VP with preemption for group 2.

0018-9545/04$20.00 © 2004 IEEE

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VP is a call-admission control (CAC) scheme that manages to combine the advantages of CS and complete partitioning (CP) and strikes a balance between unrestricted sharing in CS and unrestricted isolation in CP [6]. VP was originally proposed by Wu and Mark in [7]. The concept of VP is that each individual traffic class is allocated a nominal amount of resources with the provision that underutilized resources can be used by the excess traffic of an overloaded class, subject to preemption. The underutilized resources come from the traffic classes whose arrival rates are below thresholds that are set based on past statistics. In this situation, the nominal allocation for underloaded classes can be utilized by other traffic classes. However, VP performs preemption for the underloaded classes when their arrival rates revert to their thresholds. For traffic whose arrival rates are higher than the thresholds, if the overall traffic is light, the overloaded classes can use the nominal allocation of other traffic classes, just as in CS. If the overall traffic becomes heavy, the overloaded classes are preempted by other traffic classes and can only use the nominal allocation for themselves, just as in CP. VP behaves like unrestricted sharing when the overall traffic is light and like complete isolation when the overall traffic is heavy [9]. Thus, VP combines the best characteristics of CS and CP under different loadings. Research on VP has received much attention in recent years. In [8], Mitra and Ziedins applied VP in cellular system and considered only the single-class case. In [9], Borst and Mitra extend their work to two classes. In [10], Wong et al. consider CP and CS with guard channels for classes. The transmission bandwidth of each class can be an integer multiple of those for other classes. In [11] and [12], Wong et al. consider VP with preemption for groups 1 and 2 with guard channels for two classes. In this paper, we consider VP with preemption for group 2 (case 1) and VP with preemption for groups 1 and 2 (case 2) with guard channels for classes as the resource-allocation schemes in our analytical models. Resource allocation is basically a call-level problem, but satisfying GoS constraints at the call level alone may still sustain a larger load. When traffic flows are admitted into the network proper, QoS is measured in terms of packet-loss rate, packet delay, and packet-delay variation in the packet level. Scheduling and statistical multiplexing gains play a crucial role in determining the amount of traffic that can be admitted into the network proper while still satisfying the packet-level QoS. There could still be excessive allocation of resources between these two levels. We believe that making use of both the calland packet-level properties can enhance system utilization with QoS constraints in both levels. To our knowledge, Beshai et al. [13] are the first to suggest using the interaction between the call- and packet-level QoS in asynchronous transfer mode (ATM) networks to improve system performance. Cheung and Mark [14] proposed a resource-allocation strategy subject to joint packet/call-level QoS/GoS constraints in wireless networks. They found that there is a significant improvement in system utilization when the deployment of system resources is subject to simultaneous satisfaction of both packet- and call-level QoS/GoS constraints. The joint call/packet-level optimization method is also used in this paper. The system utilization is maximized subject to the GoS constraints such as new-call-blocking probability and handoff-call-dropping


probability at the call level, and the QoS constraint such as packet-loss probability at the packet level. The rest of the paper is organized as follows. Section II presents the system model for the ensuing analytical and simulation studies. The call- and packet-level parameters are listed in Section III. In Section IV, the analytical models for cases 1 and 2 are described and the equations for the call-blocking and -dropping probabilities, call-preemption probabilities, and packet-loss probabilities are derived. Section V presents numerical results to demonstrate system performance and Section VI concludes the paper. II. SYSTEM MODEL To simplify our analysis, the system capacity and transmission rate for each traffic class are normalized with respect to some basic units. Each such basic unit is referred to as one channel in the following discussion. With this normalization, the capacity and transmission rate required by each traffic class can be expressed in terms of an integer number of channels. We consider a typical generic radio cell with a physical capacity of channels per cell in a cellular arrangement. In this work, we assume that the traffic model of all classes are ON–OFF sources, with class traffic requiring channels to transmit during its ON state. Due to scheduling and statistical multiplexing gains, the cell site [base station (BS)] supports classes of traffics that is a decan be admitted into at most channels, where sign parameter to be chosen. is an important system-design may lead to a low packet-loss parameter. A small value of probability and a high call-blocking probability, while a large value of can give a low blocking probability, but may cause a high packet-loss probability. This is because the parameter will constrain the number of admitted calls and the physwill constrain the number of instantaneously ical capacity transmitted packets of admitted calls. In the scheme under consideration, blocked calls are lost to the system and the excess admitted call that cannot transmit packets during its ON state , there is no statistical suffers packet loss. In the case multiplexing gain. The generic cell is characterized by the following system parameters used throughout the paper: design parameter representing the upper bound for admitting calls (call-level capacity bound); total physical capacity in a cell; total number of traffic classes; instantaneous channel occupancy; instantaneous channel occupancy for a class call; number of basic channels (units) required by each class call; , , 2 nominal capacity for each group; group 1 includes the traffic classes from 1 to and group to , 2 includes the traffic classes from and . The dynamics of a radio cell are driven by new-call requests, call terminations, and handoffs induced by user mobility. Maintaining an ongoing call is more important than admitting a

YAO et al.: VIRTUAL PARTITIONING RESOURCE ALLOCATION FOR MULTICLASS TRAFFIC

new call. Hence, handoff calls should be given a higher access priority or a lower dropping probability than the probability of blocking new calls. One way to facilitate this is to reserve capacity for admitting handoff calls, which is not accessible by new requests. The reserved capacity is referred to as guard capacity. The number of channels available for admitting new and handoff calls is . Let denote the number of guard channels in a cell. We have the following admission rules: ; 1) Admit both new and handoff calls if 2) Reject new calls and admit only handoff calls if . As stated in the Introduction, call-level performance measures such as blocking and dropping probabilities are known as GoS. For convenience of representation, we will use QoS to represent call-level as well as packet-level performance measures in the remainder of this paper. III. PROBLEM STATEMENT user. Its QoS is specified by the Consider a class , handoff-call-dropping new-call-blocking probability , and system utilization at the call level probability and the packet-loss probability at the packet level. At the BS, the estimation of call-arrival rate can be done by using a jumping- or moving-window method. With a generally accepted approach, we assume that the arrivals of calls are Poisson distributed and that the call-holding times are exponentially distributed. Although these assumptions may not be true in practical mobile networks, they have been widely used [1], [2], [4], [15], [16] to provide approximate solutions for cellular systems. The call- and packet-level parameters used throughout the paper are listed below.

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call and packet levels. At the call level, the resource-allocation scheme determines the way that the users share a common resource. The traffic classes are divided into two groups. The resource-allocation schemes considered in this paper are VP with preemption of group 2 (case 1) and VP with preemption of groups 1 and 2 (case 2). More details on the resource-allocation schemes are described as follows. Case 1) Group 1 is offered guaranteed access while group 2 is offered best-effort service. With the nominal caand , the allocation is pacity partitioned into (guarantee access) and (best effort), where is the ratio of the number of class calls admitted into the cell without being preempted during the lifetimes to the number of admitted class calls. Group 1 is given hard capacity to guarantee access. This group is given higher QoS protection and can preempt group 2 calls. Unused capacity during any epoch is available to group 2. Within group 1, we have CS. Case 2) Total channels are to be shared by groups 1 and 2 , group using virtual partition. If , 1 is in the underload state; if group 2 is in the underload state; if , group 1 is in the overload state; and if , group 2 is in the overload state. The way to implement the VP with preemption for groups 1 and 2 is as follows. When group 1 (2) is in the underload state while group 2 (1) is in the overload state, group 1 (2) can preempt group 2 (1) users, up to the channel occupancy tending to the call-level capacity bound . IV. ANALYTICAL MODELS

Call-Level Parameters : new-callblocking probability for class ; : total new-call-blocking probability; : handoff-call-dropping probability for class ; : total handoff-call-dropping probability; : sum of new-call-blocking and handoffcall-dropping probabilities; : system utilization for class calls; : total system utilization (average ); channel occupation, arrival rate of new class calls; arrival rate of class handoff calls; : total arrival rate of class calls; mean class call-holding time (lifetime); mean class call dwell time (interhandoff time). Packet-Level Parameters packet-loss probability for class call. The main concern of this work is the maximization of system utilization subject to satisfaction of QoS constraints at both the

A. Formulation denote the probability that the next arrival is a new Let call from class (1)

Let denote the probability that the next arrival is a handoff call from class (2)

Let

denote the probability that the next arrival is from class

(3)

We assume that all cells are statistically identical. Thus, the rate of handoff departing from a cell equals the rate at which

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handoff calls entering the cell. From the complete partitioning handoff call-arrival rate to the policy, equating the class for a call and the product of the average handoff rate average number of class calls, we can get the class handoff call arrival rate as [10], [17]

(4a) Solving for

in (4a), we get

(4b)

where is the new class call-blocking probis the ability considering only class traffic, handoff class call-dropping probability considering only class traffic, , is the speed of the class mobile, and is the size of a square cell. Note that the new-call-blocking and handoff-call-dropping probabilities are functions of the new- and handoff-call-arrival rates, respectively. The handoff-call-dropping probability can only be calculated after the handoff rate has been determined. On the other hand, the handoff-call-arrival rate can only be caland are known. To resolve culated using (4b) when this paradox, (4b) can be written as a set of recurrence equa, the handoff rate tions. At the initial time instant is set equal to on the assumption that and are negligibly small. Then, is used to compute and using the analytical results presented in Sections IV-B and IV-C. For example, in case 1, (8) is used to . solve for the equilibrium system-state probability is then used in (12)–(15) to evaluate the new-call-blocking and handoff-call-dropping probabilities, which in turn are substituted into (4b). Iterating in this manner, the recurrence equations can be written as (5a) (5b) (5c) and are notations used to denote the analytical where procedure as described above. B. Case 1—VP With Preemption for Group 2 1) Call Level: Assuming Poisson-distributed arrivals for new and handoff calls and exponentially distributed call-holding time, we can model the channel occupancy as a -dimensional Markov chain and solve it using the techniques in [18]–[20]. The key of the techniques is to formulate the global-balance -dimensional Markov chain. The equations based on a global-balance equations for CS have been presented in [10]. The difference between CS and VP lies on the preemptions in VP. denote the state of the system Let in the th class and with the number of class users

denote the vector of basic channels, where is the number of basic channels required for each class call. denote the arrival rate and the departure rate in Let the system. Thus, the state space of the system, denoted by , is . Group 1 ( , ) contains classes given by from 1 to with the nominal capacity of ; group 2 ( , ) to with the nominal capacity of contains classes from . Focusing on the characteristic of case 1, we define five preemption rules, which will describe all characteristics of preemptions that are possible in case 1. They will be used as the criteria to determine whether or not the preemption can happen in a particular state of the system. Preemption rules for case 1: 1) Preemption could happen only under the condition that , i.e., group 2 users occupying capacity nominally allocated to group 1. call arrives 2) Preemption happens when new class under the conditions that or { and }. Note that no matter which type of preemption happens, new calls can only be admitted into the system when the guard channels are not occupied. call ar3) Preemption happens when handoff class rives under the condition that . over group 4) When there is preemption for class 2 (class adds one user and one/some user(s) is/are deleted from group 2), the number of terminated users from each class within group 2 must be calculated individually. Here, we simplify the problem to assume that the termination happens to only one class, e.g., class . So, the number of class users terminated from the , where is system will be less than or equal to the ceiling function that gives the smallest integer larger than or equal to . 5) If preemption happens over class , it means that class is the most overload class in group 2 and the class will be determined by the criterion . Another criterion is to preempt the lowest priority class in that group; this is a subject for future investigation. In this paper, we use the most overload criterion. The admission policy for CS is defined here. When the system is in state and a class call (new or handoff) arrives, an admission policy determines whether or not the call is admitted into the system. We specify the admission policy for both by mapping new and handoff calls, excluding the guard channels, and for only handoff calls within the guard channels, where the union of and gives the system-state space and and each takes on the value 0 or 1 if a class call is rejected or admitted, respectively, when the system state is . They are defined by condition 1 otherwise

(6)


where condition 1 refers to: for ; or for ,

,

blocking probability for a new class all classes, is given by

. condition 2 otherwise

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call, considering

(7)

, where condition 2 refers to: for ; or for , . Due to the fact that the only difference between CS and VP is the preemption in VP, when we formulate the global-balance equations for VP, the global-balance equations for CS will be formulated first and each state will then be filtered by the five preemption rules. If preemption happens in that state, the corresponding state transitions will be added to complete the globaldenote the equilibrium probability balance equations. Let that the system is in state . The global-balance equations for the Markov process under the preemption rules and the admission policy for case 1 are given by

(8)

(12)

where is a -dimensional vector of all zeros except for one in the th place, i.e., means to admit a class call and means to terminate a class call, who is preempted by another call or just completes its communication

, where for all satisfying is the preemption probability for class call when a new class call arrives, which is defined in (16). is the floor function that gives the largest integer less than or equal to . new Similarly, the blocking probability for a class call, considering all classes, is given by

if if

(9) (10)

and

is defined as by rule 2 by rule 3.

(11)

Without the terms, (8) is equivalent to the global-balance equations for CS. Equation (8) can be solved using lower triangular/upper triangular (LU) decomposition together with the condition that the sum of all the state probabilities is 1 to . LU decomposition is a common numerical techobtain nique to solve linear algebraic equations [21]. A new class call is blocked from entering the system (and is assumed lost) if, upon arrival, it finds that it cannot be accommodated because the number of available channels (excluding the guard channels) is less than . Therefore, the

(13)

for all satisfying . A class handoff call is blocked from entering the system (and is assumed lost) if, upon arrival, it finds that it

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cannot be accommodated because the number of available channels (including the guard channels) is less than . Therefore, handoff call, conthe blocking probability for a class sidering all classes, is given by

The preemption probability for a class handoff call arrives, is given by class

call, when a

(17) (14)

for all satisfying . Similarly, the blocking probability for a class call, considering all classes, is given by

for all satisfying rules 3 and 5. The utilization for class is given by

handoff

(18) The total utilization is thus (19)

(15)

2) Packet Level: At the packet level, we mainly consider statistical multiplexing. Assuming exponentially distributed ON/OFF sources for each call, the fraction of time a class call spends in the ON state is given by (20)

. for all , satisfying The preemption probability for a class new call arrives, is given by class

call, when a

denote the number of in-progress calls. The probaLet bility that in-progress calls are in the ON state given that there calls in progress is given by are (21)

(16)

for all

satisfying rules 2 and 5.

Because the design parameter must not be less than the physical capacity , when the total number of channels from calls in the ON state exceeds the physical capacity, they will suffer packet losses. Assuming a priority structure with class 1 having the highest priority and no packet buffer, the equivalent class packet-loss probability is given by [10] (22) and (23), . shown at the bottom of the next page, and The total packet-loss probability is given by (24)


C. Case 2—VP With Preemption for Groups 1 and 2

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under the preemption rules and the admission policy for case 2 are given by

1) Call Level: In mathematical terms, the admission policy for case 2 is defined as

(25)

otherwise

and

(26)

otherwise.

(27)

Preemption in case 2 is governed by the following rules. 1) Preemption could happen only under the condition that or , i.e., group 2 users occupying capacity nominally allocated to group 1; group 1 users occupying capacity nominally allocated to group 2. 2) Preemption happens when a new class call arrives under or { the conditions that and }. 3) Preemption happens when a handoff class call arrives under the condition that . 4) If preemption happens over class , it means that this class is the most overload class in its own group and will be determined by the criteria for and for . Let denote the equilibrium probability that the system is in state . The global-balance equations for the Markov process

A new class call is blocked from entering the system (and is assumed lost) if, upon arrival, it finds that it cannot be accommodated because the number of available channels (excluding the guard channels) is less than . Therefore, the blocking probability for a new class call, considering all classes, is given by

(28) in the other group for all satisfying , where is the preemption probability for the class call when a new class call arrives, as defined in (30).

if if (22) where

(23)

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Fig. 1. New-call-blocking probabilities for classes 1 and 2.

Fig. 2. New-call-blocking probabilities for classes 3 and 4.

A class handoff call is blocked from entering the system (and is assumed lost) if, upon arrival, it finds that it cannot

be accommodated because the number of available channels (including the guard channels) is less than . Therefore, the


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Fig. 3. Handoff-call-dropping probabilities for classes 1 and 2.

blocking probability for a class classes, is given by

handoff call, considering all

The preemption probability for a class handoff call arrives is given by

call when a class

(31) (29)

for all , satisfying , where is the preemption probability for a class call when a handoff class call arrives, as defined in (31). The preemption probability for a class call, when a class new call arrives, is given by

(30)

for all

satisfying rules 2 and 4.

for all satisfying rules 3 and 4. The utilization for class is given by (18) and the total utilization is given by (19). 2) Packet Level: The analytical formulation of the packet-loss probability for case 2 is the same as that for case 1. D. Joint Call- and Packet-Levels QoS Optimization The formulations of all QoS metrics, such as new-callblocking probability, handoff-call-dropping probability and system utilization at the call level, and packet-loss probability at the packet level, have been defined. Maximizing system utilization can translate to more revenue for the network providers, who in turn can lower the charges for the mobile users. Therefore, the goal of joint call- and packet-levels optimization is to maximize system utilization subject to the QoS constraints in both levels, which can be achieved by choosing the optimal parameter . We test every values of as system that parameter in a range of values and find the optimum

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Fig. 4. Handoff-call-dropping probabilities for classes 3 and 4.

Fig. 5. System utilization for fast mobiles.

gives the maximum system utilization and satisfies the QoS constraints at the same time. The optimization problem is then presented as (32)

subject to


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Fig. 6. System utilization for slow mobiles.

Fig. 7. System utilization with and without joint call/packet-level QoS optimization for fast mobiles.

Numerical results for maximum system utilization are obtained in Section V by iteratively increasing the call-level capacity bound until the target constraints are met.

V. NUMERICAL RESULTS Numerical results have been obtained by means of numerical analysis and simulation. The widely used Manhattan model

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Fig. 8. System utilization with and without joint call/packet-level QoS optimization for slow mobiles.

is employed in the simulation [22]–[24]. The block length is 200 m with 100 BSs placed at every street corner. The simulation is based on an “event-oriented” approach: a sequence of events corresponding to the actions that modify the state of the system is processed. The events include a new call arrival, a handoff call arrival, a call departure, and a new system-utilization updating. The resource-allocation schemes are negotiated in each BS when a new or handoff call arrives. The assumptions of Poisson-distributed arrivals for new calls and exponentially distributed call-holding time are used. The handoff call arrival rate is not determined by (4b) or (5), but is based on the mobility of the calls. Performance statistics are obtained from the middle cell in the system. By collecting the number of arriving calls, new blocked calls, and handoff blocked calls and the system utilization per time unit, we can compute the blocking probability and system utilization as described in Section III. Furthermore, when a new call is generated, it can move in any one of the four directions: north, south, east, or west. The movement of the mobiles is restricted along the streets and the birth positions of the new calls are randomly selected. Handoff occurs only when the residual call-holding time is longer than the time duration that a mobile will travel in a cell. Therefore, the residual dwell time is determined by the birth position of the new calls, the moving directions, and the speed of the mobiles. In the simulation, the mobiles travel in one of the directions at a constant speed. Thus, excluding the cases for the dwell times in the birth cell and the ending cell of a call, the dwell times of a call in the cells between the birth and ending cells are fixed constant times. That is, these dwell times are equal to the block length

divided by the speed of the mobile. The frequency of handoffs is determined by the speed of the mobiles. The performances of fast and slow mobile users, representing users in vehicles and pedestrian users, respectively, are compared. Each simulation result is generated up to 100 million simulation minutes. A warm-up period of 10 million simulation minutes has also been used to minimize the effects of initial . simulation transients. We consider four traffic classes The parameters used in the numerical examples are as fol, , , , , , lows: , , , , , , , , and for slow mobiles; for fast mobiles; cell , , , and . size A. Performance of Fast and Slow Mobiles for Case 1 1) Call-Level Blocking Probability and System Utilizations for Case 1: The call-level analytical and simulation results of new-call-blocking and handoff-call-dropping probabilities for classes 1 and 2, and 3 and 4 with fast and slow mobiles are shown in Figs. 1, 2, 3, and 4, respectively. The analytical results are close to the simulation results. Although this is expected because our simulations are using the same model and assumptions, it does verify the reasonableness of our formulation and showed that two iterations of (5) are sufficient to obtain quite accurate results. The effect of iterations is shown in Fig. 1.


Fig. 9.

Fig. 10.

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New-call-blocking probabilities for classes 1 and 2.

New-call-blocking probabilities for classes 3 and 4.

Note that because the fast mobiles case causes more handoffs, the handoff-call-dropping probabilities are larger than those for the slow mobiles case (shown in Figs. 3 and 4). On the other hand, the total new-call-arrival rate determines the total number of users in the whole system, so the system load for the fast mobiles case is the same as that for slow mobiles case. While,

for the fast mobiles case, the larger handoff-call-dropping probabilities means that more calls are rejected due to their mobility. As a result, the fast mobiles case will have lower number of total users in the whole system, which converts to a lower new-call-blocking probabilities (shown in Figs. 1 and 2). The numerical results have been obtained only using two iterations

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Fig. 11.

Handoff-call-dropping probabilities for classes 1 and 2.

Fig. 12.

Handoff-call-dropping probabilities for classes 3 and 4.

in the calculation of the handoff-arrival rate. The analytical and simulation results agree better for the slow mobile case than those for the fast mobile case. Figs. 5 and 6 show the analytical and simulation call-level results of system utilization for fast and slow mobiles, respectively.

2) Joint Call- and Packet-Level QoS Optimization for Case 1: Figs. 7 and 8 show the effect of the gain in system utilization through joint call- and packet-level QoS optimization for fast mobiles and slow mobiles, respectively. Without joint call/packet-level optimization, we set equal to the physical capacity. Thus, the packet-loss probability


Fig. 13.

System utilization for fast mobiles.

Fig. 14.

System utilization for slow mobiles.

will be zero for the case without optimization. With joint is maximized. call/packet-level optimization, the parameter The system can admit more new and handoff calls when the load is increased, although the packet-loss probabilities are also increased but still are subject to the QoS constraint. From the figures, we can see that the larger the load (total mean new-call arrival rate), the larger the gain in system utilization, i.e., the difference between the curves with and without optimization.

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Slow mobiles have better gain in system utilization than do fast mobiles in these numerical examples. B. Performance of Fast and Slow Mobiles for Case 2 1) Call-Level-Blocking Probability and System Utilizations for Case 2: The call-level analytical and simulation results of new-call-blocking and handoff-call-dropping probabilities for classes 1 and 2, and 3 and 4 for fast and slow mobiles are shown

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Fig. 15.

System utilization with and without joint call/packet-level QoS optimization for fast mobiles.

Fig. 16.

System utilization with and without joint call/packet-level QoS optimization for slow mobiles.

in Figs. 9, 10, 11, and 12, respectively. The analytical results are close to the simulation results. Figs. 13 and 14 show the call-level analytical and simulation results of system utilization for fast and slow mobiles, respectively. Similarly, the analytical and simulation results agree better for the slow mobiles case than those for the fast mobiles case.

2) Joint Call- and Packet-Level QoS Optimization for Case 2: Figs. 15 and 16 show the effect of the gain in system utilization through joint call- and packet-level QoS optimization for fast mobiles and slow mobiles, respectively. Similar to case 1, the larger the load (total mean new-call arrival rate), the larger will be the gain in system utilization. Slow mobiles have better gain in system utilization than do fast


mobiles in these numerical examples. For group 1 (classes 1 and 2), case 1 has better gain in system utilization than case 2. For group 2 (classes 3 and 4), case 2 has better gain in system utilization than case 1. These are expected, because case 1 gives group 1 a higher priority than group 2 and groups 1 and 2 have the same priority in case 2. So, based on the same system parameters, performance of group 1 in case 1 will exceed that in case 2 and performance of group 2 in case 2 will exceed that in case 1. VI. CONCLUSION We have presented an approximate analytical formulation of virtual partitioning resource-allocation schemes for handling multiclass traffic with guard channels in a cellular system. The analytical models are based on a -dimensional Markov chain and are solved using the preemption rules for the schemes. The results show the reasonableness of our analysis. The QoS performance metrics are call-blocking probability, system utilization, and packet-loss probability. Joint optimization through call- and packet-level QoS is investigated. Numerical results illustrate that higher gain in system utilization is achieved through the joint optimization. This translates to more revenue for network providers who can, in turn, lower the charges for mobile users. In a CDMA system, the system capacity is also constrained by signal-to-interference ratio (SIR). Research on the determination of system capacity for SIR requirements has been proposed in [25] and [26]. Based on the system capacity bound, we can use the technique in this paper to solve the resource-allocation problem for multiclass traffic. This approach has been defined as the interference-based resource allocation.

[11]

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, “Resource Allocation in Mobile Multimedia Networks With User Mobility—Case 4: Virtual Partitioning With Preemption for Groups 1 and 2,” Centre for Wireless Communications, Nat. Univ. Singapore, Singapore, Tech. Rep.RA-002-10-2001, Oct. 2001. T. C. Wong, J. W. Mark, M. Jin, B. Bensaou, and K. C. Chua, “Resource Allocation in Mobile Multimedia Networks—Analytical and Simulation Results for Case 1 to 4 With Fixed Guard Channels,” Centre for Wireless Communications, Nat. Univ. Singapore, Singapore, Tech. Rep. RA-001-07-2000, July 2000. M. Beshai, R. Kositpaiboon, and J. Yan, “Interaction of call blocking and cell loss in an ATM network,” IEEE J. Select. Areas Commun., vol. 12, pp. 1051–1058, Aug. 1994. M. Cheung and J. W. Mark, “Resource allocation in wireless networks based on joint packet/call levels QoS constraints,” in Proc. IEEE GLOBECOM ’00, vol. 1, Nov. 2000, pp. 271–275. P. Lin and Y. Lin, “Channel allocation for GPRS,” IEEE Trans. Veh. Technol., vol. 50, pp. 375–387, Mar. 2001. W. Shan, P. Fan, and Y. Pan, “Performance evaluation of a hierarchical cellular system with mobile velocity-based bi-directional call-overflow scheme,” IEEE Trans. Parallel Distrib. Syst., vol. 14, pp. 72–83, Jan. 2003. G. Haring, R. Marie, R. Puigjaner, and K. Trivedi, “Loss formulas and their application to optimization for cellular networks,” IEEE Trans. Veh. Technol., vol. 50, pp. 664–673, May 2001. K. W. Ross, Multiservice Loss Models for Broadband Telecommunication Networks: Springer-Verlag, 1995. C. N. Wu, Y. R. Tsai, and J. F. Chang, “A quality-based birth-and-death queueing model for evaluating the performance of an integrated voice/data CDMA cellular system,” IEEE Trans. Veh. Technol., vol. 48, Jan. 1999. R. P. Narrainen and F. Takawira, “A traffic model for CDMA cellular systems with soft capacity taken into account,” in Proc. IEEE 6th Int. Symp. Spread Spectrum Techniques and Applications, vol. 1, 2000, pp. 325–329. W. H. Press, S. A. Teukolsky, W. T. Vettering, and B. P. Flannery, Numerical Recipes in C—The Art of Scientific Computing, 2nd ed. Cambridge, U.K.: Cambridge Univ. Press, 2002. M. D. Kulavaratharasah and A. H. Aghvami, “Teletraffic performance evaluation of microcellular personal communication networks (PCN’s) with prioritized handoff procedures,” IEEE Trans. Veh. Technol., vol. 48, pp. 137–152, Jan. 1999. M. Bozinovski, P. Popovski, and L. Gavrilovska, “QoS-based policy for call admission control in mobile cellular network,” in Proc. Wireless Communications and Networking Conf., vol. 2, 2000, pp. 502–506. D. Calin and M. Areny, “Impact of radio resource allocation policies on the TD-CDMA system performance: Evaluation of major critical parameters,” IEEE J. Select. Areas Commun., vol. 19, pp. 1847–1859, Oct. 2001. M. Do, Y. Park, and J. Lee, “Channel assignment with QoS guarantees for a multiclass multicode CDMA system,” IEEE Trans. Veh. Technol., vol. 51, pp. 935–948, Sept. 2002. T. C. Wong, J. W. Mark, K. C. Chua, J. Yao, and Y. H. Chew, “Performance analysis of multiclass services in the uplink of wideband CDMA,” in Proc. IEEE Int. Conf. Communication Systems, Nov. 2002, pp. 694–698.

Jianxin Yao received the B.S. and M.S. degrees in electrical engineering from Huazhong University of Science and Technology, Wuhan, China, in 1999 and 2001, respectively. He is working toward the Ph.D. degree at National University of Singapore, where he is with the Institute for Infocomm Research. His research interests include wireless communications, communication networks, and resource allocation.

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Jon W. Mark (M’62–SM’80–F’88–LF’03) received the B.A.Sc. degree from the University of Toronto, Toronto, ON, Canada, in 1962 and the M.Eng. and Ph.D. degrees from McMaster University, Hamilton, ON, Canada, in 1968 and 1970, respectively, all in electrical engineering. From 1962 to 1970, he was an Engineer and then Senior Engineer with Canadian Westinghouse Co. Ltd., Hamilton. From October 1968 to August 1970, he was on a leave of absence from Canadian Westinghouse to work toward the Ph.D. degree at McMaster University under the auspices of an NRC PIER Fellowship. In September 1970, he joined the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada, where he is currently a Distinguished Professor Emeritus. He served as Department Chairman from July 1984 to June 1990. In 1996, he established the Centre for Wireless Communications (CWC) at the University of Waterloo and is currently serving as its Founding Director. He was on sabbatical leaves at the IBM Thomas J. Watson Research Center, Yorktown Heights, NY, as a Visiting Research Scientist from 1976 to 1977; at AT&T Bell Laboratories, Murray Hill, NJ, as a Resident Consultant from 1982 to 1983; at the Laboratoire MASI, Universite Pierre et Marie Curie, Paris, France, as an Invited Professor from 1990 to 1991; and at the Department of Electrical Engineering, National University of Singapore, as a Visiting Professor from 1994 to 1995. He has worked in the areas of adaptive equalization, spread spectrum communications, and antijamming secure communication over satellites. His current research interests are in broad-band and wireless communication networks, including network architecture, routing and control, and resource and mobility management in wireless and hybrid wireless/wireline communication networks. He is currently an Editor of the ACM/Baltzer Wireless Networks journal and an Associate Editor of Telecommunication Systems. Dr. Mark was an Editor of the IEEE TRANSACTIONS ON COMMUNICATIONS from 1983 to 1989. He served as the Technical Program Chairman of INFOCOM ’89 and was a Member of the Inter-Society Steering Committee of the IEEE/ACM TRANSACTIONS ON NETWORKING from 1992 to 2003.

Tung Chong Wong (S’90–M’95–SM’03) received the B.Eng. and M.Eng. degrees from the National University of Singapore (NUS), Singapore, in 1992 and 1994, respectively, and the Ph.D. degree from the University of Waterloo, Waterloo, ON, Canada, in 1999, all in electrical engineering. He has been with the Institute for Infocomm Research, Singapore, (formerly the Centre for Wireless Communications, NUS, and Institute for Communications Research) since 1994, first as a Research Engineer and currently as a Scientist. His research interests include communications networks and 3G/4G wireless mobile multimedia networks. His areas of research include medium access control, resource allocation with quality of service constraints, and traffic policing with heterogeneous traffic. Dr. Wong was on the Technical Program Committee of the IEEE Wireless Communications and Networking Conference, 2003.


Yong Huat Chew (S’85–M’97) received the B.Eng., M.Eng., and Ph.D. degrees in electrical engineering from the National University of Singapore (NUS), Singapore. He has been with the Institute for Infocomm Research (formerly the Center for Wireless Communications, NUS, and Institute for Communications Research), an institute under Agency for Science, Technology and Research, since 1996, where he is presently a Lead Scientist. His research interests include high spectrally efficient wireless communication systems and transmission over HFC and DSL.

Kin Mun Lye (S’80–M’83–SM’91) received the B.Sc., M.Eng., and Ph.D. degrees from the University of Alberta, Edmonton, AB, Canada, the University of Singapore, and the University of Hawaii, Honolulu, respectively. He was with the University of Singapore in 1979 and became Professor in 1999. He is currently Deputy Executive Director (Industry) at the Institute for Infocomm Research, A STAR, Singapore. He is a Director of Powermatic Data Systems, Ltd., and Cellonics, Inc., a startup company he cofounded. He has authored 80 technical publications and holds two patents with another ten filed. Dr. Lye received Singapore’s National Technology Award in 2001. He has served on the Boards of Singapore and Ngee Ann Polytechnic. He is a Member of the Asia-Pacific Cadence Advisory Board and the Advisory Committee for Next Generation Mobile Networks Project, Communications Research Laboratory,Yokosuka, Japan. He also served as Chairman of the Strategic Programmes Review Panel of the Science and Engineering Research Council, A STAR, Singapore, and as an Expert Assessor for the Australian Research Council’s Discovery Projects.

Kee-Chaing (K-C) Chua (M’87) received the Ph.D. degree in electrical engineering from the University of Auckland, Auckland, New Zealand, in 1990. He joined the Department of Electrical Engineering, National University of Singapore (NUS), Singapore, as a Lecturer and became a Senior Lecturer in 1995 and an Associate Professor in 1999. From 1995 to 2000, he was seconded to be the Deputy Director of the Center for Wireless Communications (now the Institute for Infocomm Research), a national telecommunication research and development institute funded by the Singapore Agency for Science, Technology and Research. From 2001 to 2003, he was on a leave of absence from NUS to work with Siemens Singapore, where he was the Founding Head of the ICM Mobile Core research and development department. He has carried out research in various areas of communication networks and his current interests are in ensuring end-to-end quality of service in both wired and wireless IP-based networks. Dr. Chua is a Recipient of an IEEE 3rd Millennium medal.