Wireless Personal Communications (2005) 34: 321–331 DOI: 10.1007/s11277-005-4827-9 C Springer 2005 Optimization of Half-Rate Codec Assignment in GERAN M. TORIL1,R.FERRER2,S.PEDRAZA2,V.WILLE3 and J.J. ESCOBAR2 1Dpt. Ingenier´ıa de Comunicaciones, ETSIT, University of Malaga,´ 29071 Malaga,´ Spain E-mail: [email protected] 2Tartessos Technologies, Edif. Inst. Universitarios, PTA, 29590 Malaga,´ Spain 3Nokia Network Performance Services, Ermine Business Park, Huntingdon, Cambs. PE29 6YJ, UK Abstract. Half-Rate (HR) channel coding can be used to deal with temporary traffic peaks in Global System for Mobile Communications (GSM)/Enhanced Data Rates for Global Evolution (EDGE) Radio Access Networks. Since operators have to pay for the use of HR codecs, the number of transceivers on which HR can be used is normally limited. An algorithm that optimizes the assignment of a limited number of HR codecs in a network is presented. The final solution obtained with the greedy algorithm proposed has proved to be optimal. Subsequent application of the algorithm in a real environment shows significant performance benefits in terms of network congestion reduction in comparison to the current approach used by network operators. Keywords: mobile, network, optimization, traffic, codec Abbreviations: HR: Half-Rate; GSM: Global System for Mobile Communications; EDGE: Enhanced Data Rates for Global Evolution; GERAN: GSM/EDGE Radio Access Network, TRX: Transceiver; KP: Knapsack Problem; TSL: Time Slot; LP: Linear Programming; ILP: Integer Linear Programming; FR: Full Rate; BH: Busy Hour. Introduction GSM/EDGE Radio Access Networks (GERAN) faces the challenge of providing capacity for existing and new services with a limited amount of spectrum. Several solutions have been proposed to improve network capacity in a cost-effective manner. During the planning stage, frequency reuse tightening is targeted through the use of features such as frequency hopping, discontinuous transmission, power control and adaptive multi-rate coding [1, 2]. In subsequent network operation, intelligent traffic management algorithms ensure optimum load balancing among cells of different size, layer and frequency band [3]. As a last resort, congestion relief mechanisms such as Directed Retry [4] and Half-Rate coding [5] can be used to minimize call blocking in the system. GSM specifications describe two kinds of traffic channels: full-rate (FR) and half-rate (HR) [6–8]. When a traffic channel is in HR mode, one timeslot, which normally serves one connection in FR mode, may be shared by two connections, thus doubling the number of connections that can be handled by a transceiver (TRX). In the context of circuit switched traffic, the HR feature allows operators to accommodate up to twice the number of users with the same hardware resources but at the expense of a slight call-quality reduction. Although it might seem that permanent application of HR coding might provide an overall capacity enhancement, this is not actually the case. The underlying reason is the higher C/I requirement for HR users compared to FR users when offering equal voice quality, which is translated into alower frequency load permitted in the frequency hopping layers of the network [2]. Hence, 322 M. Toril et al. HR mode does only provide a capacity benefit from its dynamic allocation as a blocking relief strategy during peak traffic periods. The Codec Assignment Problem OUTLINE OF PROBLEM In current networks, HR codecs are allocated on a per-TRX basis. Since operators have to pay for the use of these codecs, the number of TRXs on which HR can be used is normally limited. The codec allocation process is performed statically (i.e. dynamic share of a codec is not possible). Even though this process can be completed remotely, there might be a need to re-start the cell (or even site) to activate the changes. Since this action temporarily prevents traffic from being carried, this re-allocation process is a night activity, what makes dynamic codec allocation unfeasible. Thus, optimum assignment of a limited pool of HR codecs is key to reduce network congestion. Traditionally, both the initial prediction of the required number of codecs and its subsequent assignment to suitable TRXs during network planning stages have been carried out manually. This approach proves tedious, time-consuming and does not guarantee optimum results. Fur- thermore, subsequent variations of traffic spatial distribution in the network over the course of time necessitate periodic assignment revision if optimum performance is targeted. It can thus be concluded that an automatic method is crucial to obtain maximum performance benefit from the use of HR codecs. MATHEMATICAL FORMULATION The problem of codec ascription can be considered as a special case of the combinatorial optimization problem known as the 0/1 Knapsack Problem (KP), which has been extensively covered in the literature (for a survey, see [9, 10]). The conventional KP originally gets its name from the common situation where a hitch-hiker has to select among various objects to fill up his knapsack, maximizing the profit. The 0/1 prefix emphasizes that a fraction or multiple instances of an object are not selectable. In the case considered here, the KP is defined by a finite set T ={t1, t2,...,tn} of TRXs that are potential candidates for codec ascription. Each TRX ti has a positive integer penalty wi (in terms of codecs seized) and profit pi (in terms of blocked traffic relieved) derived from the assignment of a codec. Let C be the number of codecs in the pool owned by the network operator. Then, the problem calls for selecting the set of TRXs with a maximum profit among those sets that do not exceed the pool capacity. The integer linear programming (ILP) model of the problem can be formulated as the search of a vector X of binary (decision) variables xi (i = 1,...,n) with the meaning 1, if TRX is selected x = (1) i 0, otherwise that maximizes the objective function P (profit) n P = pi xi (2) i=1 Optimization of Half-Rate Codec Assignment in GERAN 323 subject to the constraint n wi xi ≤ C (3) i=1 In the particular case analyzed, the benefit from the assignment of a codec to a certain TRX is not fixed, but depends on the existence of other TRX in the same cell. Hence, profit values pi are dependent on the decision variables xi , converting P into a non-linear objective function. Thus, the problem can be classified as a 0/1 non-linear KP. Finally, the search of an optimal solution may be simplified taking into account that the assignment of a codec have a constant penalty, regardless of the TRX being considered, i.e. the reduction in the number of codecs in the pool by one unit (wi = 1). Thus, the constraint expressed in Eq. (3) converts into n xi ≤ C (4) i=1 The Optimization Process OPTIMIZATION TECHNIQUE A large number of algorithms have been proposed in the literature for exact and approximate solutions to the KP problem [11–13]. Among them, the greedy algorithm, the branch and bound algorithm and the dynamic programming algorithm are most popular. For the problem under study, the classical greedy algorithm used to solve the continuous relaxation of the 0/1 KP problem [13–15] has been chosen because of its simplicity. In essence, a greedy algorithm finds a solution to a small part of a problem and extends it to the final solution, assuming that a local optimal solution is part of the global optimal solution. In the context of selection problems, the greediness property refers to the fact that, once a can- didate has been included in the final selection list, its appropriateness is never evaluated again. The main advantage of greedy algorithms is that they are easy to understand and easy to implement. However, unlike other algorithms, there is no guarantee that the optimal global solution is obtained. Nonetheless, when optimum is obtained, they are usually the most efficient option available. Thus, time complexity of greedy algorithm compares favorably with that of other approaches (i.e. greedy algorithm has polynomial time complexity O(n)incontrast to exponential O(nn2) and pseudo-polynomial O(nW) time complexities of branch and bound and dynamic programming algorithms, respectively). Hence, whenever optimality of greedy algorithms is proved, no gain will be achieved by using more complicated algorithms. OPTIMIZATION ALGORITHM The optimization criterion in the codec-assignment problem is to maximize the overall traffic congestion relief with a given number of HR codecs. To achieve this goal, the following procedure is applied: 1) Sort of TRXs in the network based on their HR capabilities on a cell basis: For that purpose, TRXs are first grouped by the cell to which they belong. TRXs in a cell are ranked by the 324 M. Toril et al. number of HR capable time slots (TSLs), since some TSLs on a TRX might be devoted to signaling or packet data purposes and hence can not be used to carry voice traffic. This figure of merit may differ from TRX to TRX, due to the uneven distribution of non HR capable TSLs in the TRXs of a cell. Obviously, TRXs with more HR capable TSLs will be preferred within a cell, as they would provide higher congestion relief if a HR codec was used. 2) Estimation of profit from codec assignment to TRXs (pi ): The benefit from every codec ascription is defined as the increase of carried traffic during the busy hour (BH) due to the extension of traffic resources in the cell considered. Thus, the profit values pi can be calculated from the difference between carried traffic with and without codec assignment as = = − pi Ac Ac Ac (5) where Ac ≡ BH carried traffic in Erlangs, and (’) will denote values after codec assign- ment henceforth.