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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 4, NO. 1, JANUARY 2005

Multiservice Allocation for Multiaccess Wireless Systems Anders Furuskär and Jens Zander, Member, IEEE

Abstract—This paper discusses principles for allocating multiple bearer services onto different subsystems in multiaccess wireless systems. Based on the included subsystem’s multiservice capacities, under certain constraints near-optimum subsystem service allocations that maximize combined multiservice capacity are derived through simple optimization procedures. These favorable service allocations are either extreme points where services, as far as possible, are allocated to the subsystems best at supporting them, or they are characterized by the relative efficiency of supporting services being equal in all subsystems. The consequences of this include that services should typically be mixed in subsystems with convex capacity regions and isolated in subsystems with concave capacity regions. Simple user assignment algorithms based on this are also discussed. Additionally, illustrating the main findings of the analysis, some system examples are given, including a case study with combined global system for mobile communications (GSM) and wideband code-division multiple-access (WCDMA) systems. The gain of using the proposed service allocation principles compared to a reference case of maintaining equal service mixes in all subsystems depends on the shape of the subsystem capacity regions; the more different the capacity regions, the larger the gain. In the GSM and WCDMA case study, capacity gains of up to 100% in terms of supported data users for a fixed voice traffic load are achieved. Index Terms—Global system for mobile communications (GSM)/EDGE, load sharing, multiaccess, multiservice, wideband code-division multiple access (WCDMA).

I. INTRODUCTION

T

WO EXPECTED characteristics of future wireless networks are support for multiple bearer services and the use of multiple radio access technologies. This raises the question of how to best allocate the different bearer services (henceforth simply denoted services) to the different radio access technologies (henceforth denoted subsystems). In this paper, principles for how this service allocation should be done to maximize the resulting combined capacity are discussed. Several interesting multiaccess concepts may be found in the literature. Based on strengths and weaknesses of homogeneous single-access networks, an overlaid architecture of different subsystems is proposed in [1]. In [2], a so-called always-best-connected concept comprising global system for mobile communications (GSM)/enhanced data rates for GSM Manuscript received November 24, 2002; revised October 27, 2003 and November 18, 2003; accepted November 19, 2003. The editor coordinating the review of this paper and approving it for publication is L. Hanzo. A. Furuskär is with Ericsson Research, SE-164 80 Stockholm, Sweden (e-mail: [email protected]). J. Zander is with the Wireless@KTH, the Center for Wireless Systems, Royal Institute of Technology, Electrum 418, 164 40 Stockholm, Sweden. Digital Object Identifier 10.1109/TWC.2004.840243

evolution (EDGE), wideband code-division multiple access (WCDMA), code-division multiple access 2000 (CDMA2000), and wireless local area networks (WLAN) access technologies is discussed as a candidate for a future generation wireless network. Convergence of the above cellular networks with broadcast networks such as digital audio broadcast (DAB) and digital video broadcast (DVB) is discussed in [3]. In terms of performance, analyses of the single-service trunking gain enabled by the larger resource pool when combining GSM/EDGE and WCDMA subsystems have been presented in [4]. One key problem among others in multiaccess systems, including, e.g., deployment of subsystems and architecture issues, is handover between subsystems and the basis it is performed on. An overview of issues related to handover in multiaccess systems is provided in [5]. A user-policy-based handover principle that allows users to connect to the subsystem that is preferred according to individual price and performance preferences is proposed in [6]. In standardization, the means for exchanging traffic load and quality information between GSM/EDGE and WCDMA-based systems to enable service and load-based handovers is being standardized by the Third Generation Partnership Project (3GPP) [7], [8]. In [9], Kalliokulju et al. discusses the problem of radio access selection for multistandard terminals. They compare capacity, coverage, and delay among different subsystems and discuss how these can be used for access selection. In the analysis of this paper, it is noted that the capability to handle services typically differs between subsystems in multiaccess networks. No previous studies have been found taking the relationship between the numbers of supportable users of different services in different subsystems into account when allocating users of different services to subsystems. It might be noted that this problem, however, has similarities with some problems studied outside the field of wireless networks. These include equilibrium analysis in economics, e.g., finding efficient allocations of goods between parties as described by Pindyck and Rubinfeld in [10], and the problem of scheduling or assigning jobs to machines studied within the field of operations research, see, e.g., Hillier and Lieberman [11]. This paper begins with a discussion of what differentiates user assignment in multiaccess systems from single-access systems in Section II. In Section III, definitions are given of the multiservice multiaccess system models and performance measures used. Derivations of capacity-wise favorable near-optimum subsystem service allocations are then provided in Section IV. Next, in Section V, some simple examples illustrating the derived principles and the achievable capacity are presented. A performance estimation for a combined GSM/EDGE and WCDMA system

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FURUSKÄR AND ZANDER: MULTISERVICE ALLOCATION FOR MULTIACCESS WIRELESS SYSTEMS

is also included in Section VI. Finally, in Section VII, some simple user assignment algorithms are presented that target the proposed near-optimum subsystem service allocations. Conclusions are drawn in Section VIII. A condensed version of this paper was presented earlier in [12]. II. MULTISERVICE ALLOCATION IN MULTIACCESS NETWORKS Within a single-access system, handover and cell selection procedures typically assign users to an access point or a set of access point with sufficiently good radio conditions. The more accurate the estimates of the radio conditions, the better the access point assignment. This principle may also be generalized for assigning users to access point in multiaccess systems. Some additional characteristics may need to be taken into account in the multiaccess case, however. These include the following. 1) The capability to handle various services may differ between the subsystems included in the multiaccess system. Therefore, the service types of the users need to be taken into account. 2) The amount and validity of information on individual users radio conditions that is available across subsystems may be less than that available internally within the subsystems. Based on the above characteristics, some interesting scenarios of intersubsystem information availability may be outlined. a) The subsystems have no information of the situation in other subsystems. Access attempts are accepted by the accessed subsystem if possible and otherwise redirected to another subsystem. b) The subsystems can exchange load information per service type. Access attempts may be directed based on service type. c) The same information is available across subsystems as within subsystems. Access attempts may now also be directed based on expected radio resource consumption. The focus of this paper is on scenario b). Scenario a) is seen as a reference case toward which the results are compared. A short discussion on principles to use in scenario c) and the expected performance is also included (Section VII). Apart from simplicity reasons, this scope is also motivated by the fact that current 3GPP standards include signaling means supporting it [7], [8]. Definition of system architectures and signaling principles for integration of further subsystems is an important multiaccess topic, but beyond the scope of this paper.

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share across subsystems is therefore willingly shared, and subsystems do not compete for users. A. Traffic Load and Service Mix denotes the number of service The random variable users offered to subsystem . may be measured over an arbitrary area covered by all subsystems. It is assumed that varies over time, and its expectation is used to measure the traffic load of service offered to subsystem . The expected total number of users in subsystem is (1) Turning to the multiaccess system as a whole, the expected total number of service users is (2) The expected total number of users of all services is further (3) A service mix is defined as a vector whose elements are the fractional contributions of each service to the expected total number of users. Thus, for subsystem the service mix is (4) Similarly, the total service mix is (5) The absolute service allocation of service is defined as the expected number of users of service in each subsystem, i.e., the ). Similarly, the relative service allocation vector ( of service is defined as the fraction of the expected number of users of service allocated to access technology (6) Not all combinations of subsystem service mixes and relative service allocations are feasible. For a total service mix , feasible service mixes and relative service allocations, i.e., those that result in a total service mix , fulfill the relationship

III. SYSTEM MODELS AND PERFORMANCE MEASURES Generally, a multiaccess system consisting of subsystems services is considered. The subsystems are assupporting sumed to have the same coverage area, and terminal capabilities and system architecture are assumed to be such that any terminal can connect to any subsystem. Beyond that, the access points of the subsystems may be arbitrarily located. It is further assumed that the subsystems are cooperated, e.g., by a single operator or a set of cooperating operators, with the aim to maximize the overall system performance. Information possible to

(7) where

.

B. User and System Quality The quality experienced by a user of service in subsystem is measured by the real-valued scalar random variable . The distribution function depends on a complex variety of parameters, including, e.g., traffic, mobility, and system characteristics. Typically, however,

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(a) Fig. 1.

(b)

Example of quality versus aggregate load behavior for (a) a fixed service mix and (b) capacity region.

for a fixed set of other parameters, such as traffic and mobility increases with the expected number of models, of each service in subsystem . A system level users quality of service in subsystem may be defined as a function of the distribution of individual user quality, i.e., . For example, assuming that users of service are satisfied if they experience a quality exceeding , then is the probais satisfied, i.e., bility that a user of service in subsystem roughly measuring the fraction of satisfied users.

D. Multiaccess Combined Capacity Regions

C. Multiservice Quality, Capacity, and Capacity Regions

where the expected quality

The above performance measure may also be applied to multiaccess multiservice systems. Noticeably, apart from the abovementioned set of traffic, mobility, and system assumptions, etc., the combined capacity is also affected by how services are allocated onto the subsystems. Two alternative combined capacity definitions exist. In the first case, for a given total service mix , the combined capacity is defined as

(10)

To measure capacity in multiservice systems, a set of minfor each service are seimum system-level qualities lected. Then, for a certain set of traffic, mobility, and system assumptions, etc., the subsystem capacity is measured as the for which the systemmaximum expected number of users of all services exceeds . level quality The maximum expected number of users typically depends on the subsystem the service mix. Thus, for a given service mix capacity is defined as follows:1 (8) For a two-service case this is depicted in the left part of Fig. 1. By repeating this analysis for the range of all possible service , a capacity region may be constructed. The capacity mixes region is defined as (9) The capacity region, hence, is the set of expected number of user combinations for which acceptable system-level quality is sustained for all service types. An example of a capacity region for two services is depicted in the right part of Fig. 1. The func. This cation delimiting the capacity region is thus pacity region limit may also be expressed as a nonparameterized function , i.e., the maximum expected number of service- users as a function of . Which representathe capacities of the services tion is used depends on which best fits the analysis in question. 1Note that capacity as defined here depends on the same set of parameters as the quality, including, e.g., radio resource management solutions.

of service

is given by (11)

is defined as in the single-access case, but may differ somewhat due to trunking or diversity effects. The second condition in (10) is identical to (7), i.e., simply the requirement that the subsystem user allocations and service mixes results in the desired total service mix. The combined capacity region is in this case, consequently, the set of expected number of users combinations that can be accommodated by all subsystems while maintaining acceptable quality for all service types averaged over all subsystems (12) The combined capacity definition in (10) allows system-level below the minimum requirement as long qualities exceeds . This the expectation over all subsystems poses a problem for users with terminals that are not capable of communicating in all subsystems. Such users may then experiand, hence, are less ence a system level quality less than likely be satisfied. To ensure that this does not happen, acceptable system-level quality must be required in all subsystems. In this case, the combined capacity is defined as

(13) The corresponding combined capacity region is, in this case, the set of expected-number-of-users vectors that can be accommo-

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dated by all subsystems while maintaining acceptable quality for all service types in all subsystems

(14) In this paper, the latter capacity and capacity region definitions (13) and (14) are used. Appendix A2 discusses the applicability and implications on capacity of the different definitions. For large numbers of users, the capacity difference is limited. Under certain assumptions the capacities will be equal as the expected relative resource consumption per user approaches zero. The combined capacity may be expressed as the sum of the subsystem multiaccess capacities

(15) The subsystem multiaccess capacity definition is similar to the single-access case in (8)

(16) Noticeably, however, the subsystem capacity may differ between the multiaccess and single-access cases, hence . This, in turn, depends on the fact that due to trunking or diversity gains in the multiaccess case, there exist user assignments so that . As a result of this, . In blocking limited systems, it is well known that larger resource pools yield reduced blocking and, hence, higher capacity per resource. Similar effects appear in interference limited systems, where a diversity gain is achieved from the reduced the risk of outage in all subsystems as compared to in one single subsystem. These effects may be dramatic for a small expected number of users but become less significant for large expected number of users. In this paper, . the latter case is assumed and that Consequently, the combined capacity region is approximated by the sum of the subsystem single-access capacities

(17) The accuracy of this approximation depends on the difference and . In Appendix A1, it is shown between that under certain assumptions the approximation error asymptotically approaches zero as the relative resource consumption per user approaches zero. Fig. 2 depicts a simple example of an approximated combined capacity with two subsystems supporting voice and data services. One may note that the combined capacity depends on the subsystem service allocation. Other subsystem service allocations than those depicted in Fig. 2 are possible for the same total service mix and would have resulted in different combined capacities. This fact is utilized in the next section when maximizing the combined capacity.

Fig. 2. Multiaccess combined capacity is approximated with the sum of the subsystem capacities. Note that other subsystem service allocations than those depicted are possible for the same total service mix and would result in different combined capacities.

IV. SERVICE ALLOCATION STRATEGIES As discussed above, the combined capacity depends on how services are allocated onto the subsystems. In this section, subsystem service allocations that maximize the combined capacity are derived. First, a general solution to the problem with arbitrary number of services and subsystems is outlined. The general solution is somewhat abstract and may be hard to interpret. Therefore, a detailed solution for the simpler case of two subsystems and two services is also given. Since the objective function is an approximation of , the resulting service allocations are approximations of the true optimum solution. Motivated by the relatively small expected approximation error, discussed in Appendix A1, they may, however, be considered near optimum and also referred to either as such or simply as favorable. A. General Solution In the general case, finding the near-optimum subsystem service allocations may be done as follows. Problem: Given the subsystem capacities , , for a total service mix , what relative service allo, and , maximize the cations ? combined capacity Solution: It is somewhat tedious to analytically directly maxwith regard to . To simplify the analysis, the imize subsystem capacities are first expressed on the form . Then, the combined capacity of services , i.e., , is held constant, and the ser(note that at the capacity limit vice allocations ) that maximize the combined service- -capacity are derived. Having done this optimization, corresponding values of the total service mix and the subsystem service allocations may be calculated. By repeating the procedure for the , a full range of combined capacities for services mapping between total service mixes and near-optimum relative subsystem service allocations is thus obtained. The approximate combined service- -capacity is given by

(18) For fixed combined capacities , the capacities of the th subsystem for these services are implicitly given by the

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capacities of subsystems becomes Utilizing this

:

.

Problem: Given the voice-data capacities of two subsystems, and , for a total voice load , what subsystem and fulfilling service allocations maximize the sustainable data load ? Solution: For a fixed voice load , is given by

(22) To maximize , its derivative with respect to

may be taken

(19) To maximize taken

, the partial derivatives with respect to

are (23) The zeros are thus found at that

and

such

(24)

for

(20)

At local extreme points, all the partial derivatives are zero. Local near optimums are thus found at subsystem service allocations such that the partial derivatives with respect to service in all subsystems equal the corresponding partial derivatives in subsystem . Further, since this holds for all

Whether these correspond to local maximum or minimum values of depend on whether the second derivative of is smaller than or greater than zero (25) If no zeros of the first derivative are found, maximum values of are found at the extreme values of If

(21) Thus, near-optimum service allocations are characterized by that the partial derivatives with respect to all services are equal in all subsystems. Whether these points correspond to depend local maximums, minimums, or saddle points of on the characteristics of the second-degree partial derivatives ; see e.g., [14]. Further, boundary points must also be searched and compared to the inner local maximums before a global maximum can be established. Having determined the near-optimum subsystem service alloand the resulting and , a pair of total service cations mix and near-optimum relative subsystem service allocations . By repeating the may easily be calculated by , procedure for the range of capacities for service a full mapping between total service mixes and near-optimum subsystem service allocations is obtained. B. Two Subsystems and Two Services In this most simple case, finding the near-optimum service allocations may be done as described below. In the below analysis a simplified terminology is used to ease tractability and under; ; ; ; ; standing: .

If (26) To find global maximums of , all local maximums must be compared including the extreme values of . From this global favorable solution , the full favorable near-optimum service , , and allocation is given by . The relative service allocations are given by , etc. Further, to find favorable service allocations for the whole range of service mixes the above procedure must be repeated . From these, the for all total voice loads desired mapping between total service mix and favorable relative subsystem service allocation , , , may be calculated easily. and Some interesting characteristics of the above solution may be observed. First, inner favorable sharing points are characterized by that the capacity region slopes are equal, i.e., the cost in data users per voice user is equal in both subsystems. This is intuitively pleasing, since if this was not the case, a better solution could be found by moving data users from the more expensive subsystem to the other.

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It is further seen that a maximum in between the endpoints is only found if the sum of the second derivatives is less than zero. Intuitively, this means that services should be mixed within the subsystems if a point with equal capacity region slopes can be found and either both subsystem capacity regions are convex , i.e., is ac(which is the case if tually concave) or one of them is more convex than the other is concave. If this is not the case, the most efficient service allocation is found at the extreme points, i.e., by separating voice and data users as far as possible. This further means that one of the subsystems will serve only voice or only data users. This is also is the case when the capacity regions are linear; i.e., constant. Then, the following rules apply. 1) If 2) If

: maximize : minimize

(or equally (or equally

) )

The intuitive meaning of these rules gets somewhat blurred by the fact that the derivatives are negative. However, the first rule decreases slower with than may be interpreted as if does with , should be increased at the expense of . It may be noted that the above results are similar to results achieved within the field of equilibrium analysis in economics. For instance, a so-called efficient allocation of goods between trading parties is characterized by the parties’ so-called marginal substitution rates being equal [10]. This roughly corresponds to the result of (24).

Fig. 3. Combined capacity region and favorable service allocations for a case with linear subsystem capacity regions. Significant gain over equal-service-mix-allocation is achieved.

V. SOME SIMPLE ILLUSTRATIVE EXAMPLES This section presents some fabricated, but illustrative, examples of combined capacity regions achievable through employing the service allocation rules of Section IV. Figs. 3–6 show examples of capacity regions, both per subsystem and combined. The favorable service allocations used to construct the combined capacity region are also depicted. Starting from a point on the combined capacity region limit, vectors corresponding to the service allocations in the subsystems can be followed toward the origin. Fig. 3 depicts a case with linear capacity regions in both subalways systems. Since in this example holds, favorable service allocations are found, for any service mix, by allocating as many voice users as possible to subsystem 2 and as many data users as possible to subsystem 1. Intuitively, this is correct since subsystem 2 is relatively better at handling voice users than subsystem 1 and vice-versa for data users. The performance of a scheme that allocates services to achieve equal service mixes in both subsystems is also depicted. Noticeably, this scheme results in a concave combined capacity region (see Appendix A3). Further, the gain over such a scheme is determined by the difference in the slope of the capacity regions. Thus, the more different the subsystem capacity regions, the larger the gain. As seen in Fig. 3, with linear capacity regions, the allocation principles become simple: service should as far as possible be allocated to the subsystem relatively best at supporting them. As a result, services are mixed in only one of the subsystems; whereas, the other only serves one type of users. With

Fig. 4. Services should be mixed within subsystems with convex capacity regions.

at least one convex capacity region, the situation becomes different, as depicted in Fig. 4. Here, an inner near-optimum may be found for some values of . with To reach this favorable solution, for those values of services should be mixed in the subsystem with a convex capacity re. A consequence of mixing gion to obtain services in the subsystem with a convex capacity region is that services are mixed also in the subsystem with a linear capacity region. Hence, services are mixed here in both subsystems. Fig. 5 depicts a situation with one linear and one concave capacity region. Noticeably, here service mixes fulfilling may also be found. These, however, correspond to local minimums. The favorable service mixes are found instead at the endpoints of the concave capacity regions. Consequently, services are isolated in the subsystem with the concave capacity region. Noticeably, it is still possible to achieve a linear combined capacity limit. Fig. 6 depicts an example similar to the above, but with three subsystems. The conclusions regarding service allocations are the same as in the cases with two subsystems.

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Fig. 5. Services should be isolated in subsystems with concave capacity regions.

Fig. 6. Example with three subsystems. Service should still be mixed in the subsystem with convex capacity region and isolated in the subsystem with concave capacity region.

VI. GSM/WCDMA WITH MIXED VOICE AND WWW Mixed voice and WWW capacity regions for both GSM/EDGE and WCDMA exist and are presented in, e.g., [13]. In both cases, rather linear regions are often achieved, which is what can be expected under interference limited conditions with interference averaging. Although typical, this will not, however, always be the case. In systems with some form of blocking or queuing, as well as in cases where the maximum tolerable interference depends on the service mix, nonlinear capacity regions appear. Examples of such scenarios include sparse reuse GSM/EDGE-based systems for which voice bearers become blocking limited, and WCDMA with a mix of regular and so-called high-speed downlink packet access-based bearers. A more detailed analysis of what factors determine the capacity region shape is outside the scope of this paper but may be found in [13]. Unfortunately, the above capacity regions are derived under different systems, radio and traffic assumptions, and thus cannot be directly used for multiaccess capacity evaluations. However, assuming that the shapes of the capacity regions do not change dramatically with the above assumption differences, they may simply be rescaled to fit the single-service endpoints under equal

Fig. 7. Combined capacity region and favorable service allocations for a GSM/EDGE and WCDMA. Gain of up to 50% in terms of supported WWW users for a fixed voice load is achieved over equal-service-mix allocation.

assumptions. This should be a fair approximation as long as the systems stay interference limited. The necessary single-service voice and WWW capacity comparisons, based on equal assumptions, indeed exist and are used in the following analysis.2 Assuming a spectrum allocation of 10 MHz, for a certain voice service and certain systems, radio and traffic assumptions, the WCDMA voice capacity is about 150 Erlang per sector. The corresponding figure for GSM/EDGE is 125 Erlang per sector. For a perceived user throughput of 150 kb/s, the WWW capacity is about 80 users sector for WCDMA and about 30 users for GSM/EDGE. In addition to this, the capacity regions are approximated to be linear. Fig. 7 shows the resulting combined capacity region and favorable subsystem service allocations. As far as possible, voice users are allocated to GSM/EDGE, and WWW users are allocated to WCDMA. A gain of up to 50% in terms of supported WWW users for a fixed voice load is achieved over equal-service-mix-allocation. For a fixed number of WWW users, a gain of up to 100% is achievable. It should be noted that the difference in slope of the capacity regions depends on the quality requirements of the services, especially for WWW. With other requirements other results are achieved. Also, with other system capabilities the results become different. For example, for a combined WCDMA and GSM/GPRS system, the capacity gain over the equal service mix allocation is larger, since the capacity region slopes differ more in this case. VII. SIMPLE USER ASSIGNMENT ALGORITHMS The principles of Section IV yield subsystem service allocations that maximize combined capacity. A simple user assignment algorithm making use of these results may be realized by measuring the total service mix and allocating users of seraccording to the associated favorable vice to subsystem . It should be noted that this relative service allocations procedure may be regarded as near-optimum only in an average 2The quoted figures are valid only for the set of assumptions made. Different assumptions may yield different results.

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sense, provided that the only basis for the allocation is the service type. Hence, in each single realization better allocations may well exist. As discussed in Section II, in addition to the service type, which may be considered to reflect the expected resource consumption of a user, the actual resource consumption of each user in each subsystem may also be used as a basis for user assignment. If available, such information may be used to assign users where they consume the least radio resources, thereby increasing capacity. An assignment rule combining both service type and resource consumption-based allocation may be realized, e.g., by multiplying favorable relative service allocations with inverse functions of the expected resource consumption in the different subsystems. The relative assignment rate is thus increased in subsystems where the resource consumption is smaller. A set of combined service and resource consumption-based user assignment algorithms is proposed and evaluated in [13]. With individual resource consumption data available, the user assignment problem may further be modeled similarly to that of scheduling or assigning jobs to machines studied within operations research [11] and results from this field used. Note, however, that although taking individual resource consumption into account has a large capacity potential, these may vary rapidly; consequently, the user assignment needs to be frequently updated. Simple analyses in [13] indicate that the capacity gain falls quickly with the inaccuracy of the resource consumption estimates.

VIII. CONCLUSION Using a straightforward maximization procedure, favorable near-optimum assumed constraints on input variables subsystem service allocations in multiaccess systems may be found. A necessary input is the capacity regions of the included subsystems. These favorable service allocations are either extremes where services are isolated in different subsystems, or they are characterized by the fact that the relative efficiency of supporting services is equal in all subsystems. The former solution typically appears with linear or convex subsystem capacity regions. In this case, services should be allocated as far as possible to the subsystem relatively best at supporting them. The latter solution typically requires at least one convex subsystem capacity region. In this case, services should be mixed in the subsystems so that the relative efficiency of supporting services is kept equal. The capacity gain achievable by employing the above service allocation strategy depends on the characteristics of the individual subsystem capacity regions. Roughly, the more different capacity regions, the higher the possible gains. In a case study with combined GSM and WCDMA systems, capacity gains of up to 100% in terms of supported data users for a fixed voice traffic load, or up to 50% in terms of supported voice users for a fixed data traffic load, are achieved. It is further possible to combine the near-optimum-service-mix allocation principles with assigning individual users in the subsystem where their resource cost is minimized. This is expected to yield increased capacity.

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The principles proposed in this paper were derived largely neglecting time dynamics in radio and traffic conditions. Utilizing such dynamics is expected to enable further capacity gains. Many additional access selection parameters, such as resource availability, price, and mobility pattern, may also be considered for further studies, as well as scenarios with multiple operators. APPENDIX A ASYMPTOTIC BEHAVIOR OF COMBINING GAIN The approximation of the combined capacity in (17) disregards potential effects of trunking or diversity from combining several resource pools. Neglecting such combining gains may yield an underestimated combined capacity and, further, an error in the derived service allocations. Taking the combining gain into account, the combined capacity may be expressed as

(27) The

combining

gain

is defined as the factor and thus represents the gain resource pools of sizes in capacity from combining . This is also the approximation error made when linearly summing the single-access subsystems capacities. In this appendix, it is shown that under certain assumptions, the combining gain approaches zero as the relative resource consumption per user approaches zero. Consider a subsystem where the total amount of available resources in an access point (covering, e.g., a cell or a sector) . Examples of are a is given by the real-valued scalar number of available channels (timeslots, frequencies, spreading codes, etc.), an available downlink power budget, or an available uplink interference budget. The resource consumption for each user connected to the access point is given by the real-valued scalar random variable , with . The randomness of includes effects of, e.g., service type, radio environment, and the applied radio resource management solutions. The relative resource consumption is similarly given by the random variable , with . The number of users connected to the access point is given by the random variable . To estimate the system-level quality, first assume: 1) that the total resource consumption in the access point for a given is given by the random expected number of users variable (28) Similarly, the total relative resource consumption is given by

(29)

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Two cases of combined capacity regions with equal service mix in the subsystems.

In general, the resource consumption of different users is dependent on each other and on the number of users in the system. This is the case, e.g., for interference limited systems, where the resource consumption of a user is dependent on the interference level is has to overcome, which in turn depends on the individual resource consumption of other users and the number of users. It is assumed 2) that the dependencies may be bounded as follows:

(30) Further assume 3) that poor quality occurs when the total re. The system-level quality source consumption exceeds may then be expressed as

it is shown that under certain conditions the variance of , and thereby also the combining gain, approaches zero as the relative resource consumption per user approaches zero. The variance is given by of

(35) This expression is difficult to simplify further. Using the bounds of (30), it may, however, be limited by

(31) For reasonably high system-level qualities, the expected number of users is limited. Specifically assume that (32) for some constant (it is later seen that in fact in the cases of interest). The system capacity is as previously defined as the maximum expected number of users for which the quality exceeds its minimum acceptable value

(33) A necessary requirement for achieving a combining gain is that at the capacity limit, the systems sometimes have some free resources, i.e., for

(36) Using (32) and reordering the second and third terms, the variis limited by ance of

(37) thus approaches zero, as , provided The variance of that all the below conditions hold, where is has been used that also since as (38)

(34)

(39)

If this is valid, a combining gain from combining subsystems may be achieved by evening out the total resource consumption between the subsystems. If this is not valid, no combining gain can be achieved. Using Chebyshev’s inequality, it can be shown that for (34) to be valid requires that the variance of is greater for ). In what follows, than zero (since

(40) (41) Note that if conditions (39) and (41) are valid, so is the condition in (40).

FURUSKÄR AND ZANDER: MULTISERVICE ALLOCATION FOR MULTIACCESS WIRELESS SYSTEMS

To conclude, for systems where assumptions 1)-3) apply, the combining gain from (27) thus approaches zero, provided that the conditions in (38), (39), and (41) hold. This can be shown to be the case for many blocking and interference limited systems. For subsystems with around 100 users, combining gain in the order of a few percent may be achieved.

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correspond to single-service endpoints, In our case, and and is a simple function of the service mix . A two-access system with linear subsystem capacity regions, and equal service mixes in the two subsystems, will thus have a combined capacity region delimited by

A. Comments 1) It may be noted that if faster than , users may still be reallocated between subsystems. The relative and thus combining gain is, however, proportional to represents an uplink interference diminishes. 2) In the case budget, no external interference is included. This should not, however, affect the conclusions provided that the external inter. ference approaches a constant as APPENDIX B EFFECT OF REQUIRING EQUAL SUBSYSTEM QUALITIES The combined capacity definitions of (10) and (13) differ must in whether the system-level quality requirements be fulfilled individually by all subsystems. Higher capacities may be achieved if the requirement as in (10) is relaxed to require acceptable system-level qualities averaged over all subsystems. This may be simply illustrated for a single-service two-access system. Around the balanced capacity limit, the averaged quality is given by the first-order Taylor-series expansion

(42) where corresponds to a number of users that are moved to subsystem 1 from subsystem 2. Obviously, if the loss in quality in subsystem 1 is smaller than the gain in subsystem 2, a quality improvement can be achieved. can be traded into The above average quality gain a capacity gain by adding more users until the average quality . The resulting capacity again reaches its minimum level gain again depends on the slopes of the quality versus load behavior. When the quality falls very rapidly with the expected number of users around the capacity limit, this means that the potential gain in average quality can only be traded to a small capacity increase. This is typically the case for large user populations. In fact, under the assumptions used in Appendix A1, approaches zero, approaches a negative step when function, and no capacity gain can be achieved.

(44) From testing, this appears to yield concave capacity regions unand , for which case a linear capacity less region is achieved. Two examples are given in Fig. 8. REFERENCES [1] R. H. Katz and E. A. Brewer, “The case for wireless overlay networks,” in Proc. SPIE Multimedia Networking Conf., San Jose, CA, Jan. 1996, pp. 77–88. [2] M. Frodigh, S. Parkvall, C. Roobol, P. Johansson, and P. Larsson, “Future-generation wireless networks,” IEEE Personal Commun., vol. 8, pp. 10–17, Oct. 2001. [3] R. Keller, T. Lohmar, R. Tönjes, and J. Thielecke, “Convergence of cellular and broadcast networks from a multi-radio perspective,” IEEE Personal Commun., vol. 8, pp. 51–56, Apr. 2001. [4] A. Tölli, P. Hakalin, and H. Holma, “Performance of common radio resource management (CRRM),” in Proc. IEEE Int. Conf. Communications 2002 (ICC 2002), vol. 5, Apr.-May 2002, pp. 3429–3433. [5] K. Pahlavan, P. Krishnamurthy, A. Hatami, M. Ylianttila, J.-P. Makela, R. Pincha, and J. Vallström, “Handoff in hybrid mobile data networks,” IEEE Personal Commun., vol. 7, pp. 34–47, Apr. 2000. [6] H. J. Wang, R. H. Katz, and J. Giese, “Policy-enabled handoffs across heterogeneous wireless networks,” in Proc. Mobile Computing Systems and Applications 1999 (WMSCA’99), Feb. 1999, pp. 51–60. [7] “Improvement of RRM across RNS and RNS/BSS (Release 5),” 3rd Generation Partnership Project, Technical Specification Group Radio Access Network, 3GPP TR 25.881 V5.0.0 (2001-12). [8] “Improvement of RRM Across RNS and RNS/BSS (Post Rel-5); (Release 6),” 3rd Generation Partnership Project, Technical Specification Group Radio Access Network, 3GPP TR 25.891 V0.1.0 (2002-08). [9] J. Kalliokulju, P. Meche, M. J. Rinne, J. Vallström, P. Varshney, and S.-G. Häggman, “Radio access selection for multistandard terminals,” IEEE Commun. Mag., vol. 39, no. 10, pp. 116–124, Oct. 2001. [10] R. S. Pindyck and D. L. Rubinfeld, Microeconomics, 4th ed. Englewood Cliffs, NJ: Prentice-Hall, 1998, pp. 579–615. [11] F. S. Hillier and G. J. Lieberman, Introduction to Operations Research, 7th ed. New York: McGraw-Hill, 2002, pp. 381–390. [12] A. Furuskär, “Allocation of multiple services in multiaccess wireless systems,” in Proc. IEEE Mobile and Wireless Communication Networks (MWCN) Conf. 2002, Sept. 2002, pp. 261–265. , “Radio resource sharing and bearer service allocation for multi[13] bearer service, multiaccess wireless networks,” Ph.D. dissertation, Royal Inst. Technol., Stockholm, Sweden, 2003. [14] L. Råde and B. Westergren, Beta Mathematics Handbook, 2nd ed: Studentlitteratur. [15] A. M. Viterbi and A. J. Viterbi, “Erlang capacity of a power controlled CDMA system,” IEEE J. Select. Areas Commun., vol. 11, pp. 892–900, Aug. 1993.

APPENDIX C PERFORMANCE WITH EQUAL SERVICE MIXES IN SUBSYSTEMS In this appendix, the combined capacity region for a two-service two-access case with linear subsystem capacity regions, for which an equal service mix service allocation strategy is used, and is derived. A straight line between the points may be represented in polar form by the radius and angle as (43)

Anders Furuskär received the M.Sc. degree in electrical engineering and Ph.D. degree in radio communications systems from the Royal Institute of Technology, Stockholm, Sweden, in 1996 and 2003, respectively. He joined the Corporate Unit of Ericsson Research in 1997, working mainly with standardization of third generation cellular systems. He currently is a Senior Research Engineer whose research interests include radio resource management in multiservice multiaccess wireless networks.

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Jens Zander (S’82-M’85) received the M.S degree in electrical engineering and the Ph.D degree in datatransmission from Linköping University, Linköping, Sweden, in 1979 and 1985, respectively. From 1985 to 1989, he was a Partner and Vice President of SECTRA, a high-tech company in telecommunications systems and applications. In 1989, he was appointed Professor and Head of the Radio Communication Systems Laboratory, Royal Institute of Technology, Stockholm, Sweden. Since 1992, he has also served as Senior Scientific Advisor to the Swedish Defence Research Institute (FOI). He is Cofounder of Wireless@KTH, Center for Wireless Systems, Royal Institute of Technology, Stockholm. He served as its Scientific Director from 2000 2002 and since 2003 as Director of that center. He is also on the board of directors of several Swedish companies in the wireless systems area. He has published numerous papers in the field of radio communication, in particular on resource management aspects of personal communication systems. He has also coauthored four textbooks, including the English textbooks Principles of Wireless Communications and Radio Resource Management for Wireless Networks. His current research interests include architectures, resource management regimes, and business models for future wireless infrastructures. He is frequently invited as a speaker and panelist at international conferences on the subject of the future of wireless communications. Dr. Zander is a member of the Royal Academy of Engineering Sciences. He is the chairman of the IEEE VT/COM Swedish Chapter and the local organization chair of the IEEE Vehicular Technology Conference 2005, Stockholm. He is an Associate Editor of the ACM Wireless Networks journal and Area Editor of Wireless Personal Communications. He was the recipient of the IEEE Vehicle Technology Society’s Jack Neubauer Award for best systems paper in 1992.