Multi-period Channel Assignment

Transcription

1 Multi-eriod Channel Assignment Hakim Mabed, Alexandre Caminada and Jin-Kao Hao 2 France Télécom R&D, 6 Avenue des Usines, BP 382, 97 Belfort, France {hakim.mabed,alexandre.caminada}@francetelecm.com Tel: (+33) , Fax (+33) University of Angers, 2 Bd Lavoisier, 4945 Angers Cedex, France jin-kao.hao@univ-angers.fr Abstract. The well-known fixed channel assignment scheme for cellular networks is not flexible enough to follow the evolution of traffic. This aer introduces a multi-eriod channel assignment model. In addition to the usual objective of minimizing the interference, the model integrates another requirement to minimize the transition cost from a frequency lan to another one. Several heuristic solution aroaches are also roosed. Exerimental results on real data are resented to comare the multi-eriod model and the fixed model, and to assess the effectiveness of the roosed solution algorithms. Keywords: Multi-eriod channel assignment, otimization, genetic search, tabu search. Introduction In a GSM network [9], the geograhical area is artitioned into cells, each one served by a single base station. To ensure communications occurring on their cells, stations require a certain number of frequencies deending on the exected traffic load. In other words, lightly loaded cells are assigned fewer channels than heavily loaded ones. The mobile network oerators disose of a very limited number of frequencies to cover all the network area. For this reason, frequencies reusing is indisensable to increase the network caacity. Channel assignment consists in assigning the available frequency sectrum to the stations of the network in order to satisfy their demands and to minimize the interference. Interference is caused by the resence of overlaing areas between cells where several signals of good quality are received. The quality of communications in cellular networks deends closely on how the available frequency sectrum is managed. Because of its imlementation simlicity, fixed channel assignment (FCA) is largely used in today s GSM mobile networks. In this case, a subset of nominal frequencies is definitively allocated to each base station. However, the main inconvenient of FCA is that it is not adative to traffic variation. In fact, usually frequency lan dimensioning is based on an over-sizing of traffic data [][6][7] and unused channels in lightly loaded cell are not reassigned to heavily loaded ones. To overcome this handica, many alternative strategies have been adoted as dynamic channel assignment [][3], hybrid channel assignment [5] and channel borrowing [6]. Usually those techniques erform badly in heavy traffic or require additional signaling loads to ensure channel readjustment [8]. M. Conti et al. (Eds.): PWC 23, LNCS 2775, , 23. IFIP International Federation for Information Processing 23

2 542 H. Mabed, A. Caminada and J.-K. Hao This aer resents a channel assignment model noted MCA for Multi-eriod Channel Assignment [2], which associates simlicity and adatability. In this case, the frequency-lanning roblem consists in finding a sequence of frequency lans following the traffic evolution for a number of time eriods. Each frequency lan is conceived to fit the traffic situation at the eriod in which it is oerational. Two reasons make the roblem more comlicated. First, in addition to the classical criteria dealing with interference, the transition cost caused by frequency lan change must be minimized. Second, the multi-eriod character of the roblem increases its combinatorial comlexity. To coe with this comlexity, we roose several otimization techniques based on a genetic tabu search algorithm and we comare their erformances against the FCA scheme in terms of lost traffic. The aer is organized as follows. In next section we formally describe the MCA model and we give a set of definitions used in the remainder of the aer. Section 3 describes in details the basic genetic tabu search algorithm used to solve the FCA roblem. Section 4 resents how genetic tabu search algorithm is readated to MCA model. Section 5 is dedicated to the exerimental tests carried out in order to assess the MCA model. 2 Multi-eriod Channel Assignment Problem In fixed channel assignment, a single frequency lan is built in order to be ermanently oerational even if the traffic evolves in time. The key word is then the robustness of the frequency lan over time. To that end, modelers use an aggregation of traffic data, for examle traffic at second busy hour to evaluate the quality of frequency lans []. In the case of multi-eriod channel assignment, we assume that traffic evolution follows a cyclical scheme. According to the desired scale level, one cycle is divided into eriods of equal duration (hours, days...). We assume also that the traffic load is known on every cell for each eriod. The objective is then to find a sequence of frequency lans. Each frequency lan is built with the objective to minimize the interference recorded at the associated eriod. In addition, the frequency lan must meet another requirement to minimize transition costs between frequency lans. Transition cost measures the required effort or damage caused by the frequency lan changes. Several asects can be taken into account to measure the transition cost between two frequency lans: (a) Minimizing the number of changed frequencies between two frequency lans; (b) minimizing the number of stations affected by the changes or (c) minimizing the traffic load affected by the changes. In this work, the number of changed frequency is taken as the transition criterion. 2. Basic Notations We introduce here the basic notations and definitions, which will be used in the continuation of the aer: N: The number of stations. {S,, S N }: The set of stations comosing the network. m i / i [..N]: The number of frequencies required by the station S i.

3 Multi-eriod Channel Assignment 543 F: The number of available frequencies. n: The number of studied time eriods. 2B i : The eriod on which the traffic load on the station S i reaches its second greatest value. Interference damage between stations deends on several factors such as interchannel searation between used frequencies, signal owers It is also largely deending on traffic intensity on these stations. The imact of traffic on interference is twofold. As interferer station, traffic load describes the utilization rate of frequencies and hence imacts on the quantity of generated interference. As interfered station, traffic intensity reflects the imortance of the area covered by the station and consequently the interest of interference reduction on this area. Let us note by: I i,j,d : The interference damage between S i and S j caused by a air of frequencies distanced by d channels. 2B I i, j, d: The interference damage between S i and S j measured according to traffic load on station S i at the eriod 2B i and on station S j at the eriod 2B j. I i, j, d: The interference damage between S i and S j measured according to traffic situation at the eriod. Assignment f i,k [..F] corresonds to the k th "ermanent" frequency assigned to the station S i. Assignment f [..F] corresonds to the k th frequency assigned to the station S i at the eriod. A frequency lan is either a vector of "ermanent" assignments < f,,, f,m,, f, m,, f N N, m > (for FCA) or a vector of "temorary" N assignments < f,,, f,, f,, f > (for MCA)., m N, NmN, A sequence is a vector of temorary frequency lans n n n f,.., f,.., f,.., f,.., f,.., f.,, m N, mn,, m N, mn 2.2 Problem Formulation In the fixed channel scheme, a single frequency lan is constructed on the basis of 2 I B i, j, d values. The objective of the otimization is to find the vector < f,,, f,m,, f, m,, f N N, m > which minimizes the total interference deicted by the N function F 2B. N, N mi, mj 2 B = 2 B i, j, fik, fjl, i=, j= k=, l= F I Where the double sum in the formula measures the total of interference over the network, caused by used frequencies. The frequency lan thus worked out will be ermanently oerational. ()

4 544 H. Mabed, A. Caminada and J.-K. Hao By oosition, in multi-eriod channel assignment, the objective is to find a sequence of frequency lans corresonding to f values, which minimizes the two functions: F n N, N mi, mj = Σ = i=, j= k=, l= I i, j, f f jl, (2) n N m i C = IND f f Σ = i= k + ( ) if condition is true IND( condition) = otherwise The function F reresents the sum of interference recorded over all the time eriods whereas the function C deicts the transition cost between frequency lans comosing the sequence. (3) 3 Genetic Tabu Search for Fixed Channel Assignment The multi-eriod frequency assignment roblem can be seen as an extension of the fixed channel assignment, requiring the generation of a sequence of frequency lans instead of a single frequency lan. For this reason, we describe first the algorithm serving to generate a single frequency lan. This algorithm is also used in Section 5 to comare the fixed channel assignment model and the multi-eriod frequency assignment model. Many algorithms based on metaheuristics have been roosed for the fixed channel assignment roblem [4][7][][5]. We resent here a hybrid genetic tabu search algorithm that is described in details in []. This article doesn t aim to study the erformance of such algorithm but tries to show the relevance of MCA scheme and how the FCA algorithms can be readated to this model. The FCA algorithm starts from a oulation of individuals corresonding to frequency lans. The algorithm makes evolve the frequency lans iteratively. At each generation, the algorithm selects two frequency lans from the oulation and alies a crossover oerator to them. The two new generated frequency lans are then imroved using a Tabu Search based mutation. 3. Crossover Oerator As crossover oerator, we adot the geograhical crossover described in [][3]. The rincile is this one: we randomly choose a reference station S R and we build the set of its neighbors V(S R ) comosed of interfering stations S i (i.e. d/ I Rid > ). The,, arts of the frequency lans corresonding to V(S R ) {S R } are then exchanged between the two arents.

5 Multi-eriod Channel Assignment 545 Geograhic crossover allows the conservation of the building blocs resent in the arent chromosomes. This is made by swaing information related to the local resolution of interference between stations. This oerator is generalized later to multieriod assignment (see 4..3). 3.2 Tabu Search Based Mutation After crossover, the two new frequency lans are imroved by a tabu search based mutation. The idea is to aly a cycle of local search to the new frequency lans. More concretely, we associate to each assignment f i,k of the individual, a value called violation score measuring the contribution of that assignment to the recorded interference. Equation 4 gives the function serving to calculate the violation score of the assignment f i,k. At each cycle of the local search oerator, one assignment is chosen on the basis of the violation scores and its value is changed. The new frequency value corresonds to the best one which is not tabu. After the change, the new and the old value are considered tabu for this assignment. N m j 2 B SCORE = Ii, j, fik, fjl, j= l= (4) Notice that such a tabu management contributes to two different roles. The element (i, k, f old ) avoids the recurrence of visited solutions, whereas the element (i, k, f new ) revents the remainder individuals from re-exloring the same search area since the tabu list is shared by all oulation individuals. After mutation the new frequency lan are inserted in the oulation in relacement of another one. The relaced frequency lan is chosen on the basis of its fitness. More recisely, individuals of bad fitness have more chance to be relaced. The algorithms below describe the main rocedure of the genetic tabu search algorithm as well as the tabu based mutation rocedure. TabuSearchOerator(Frequency lan f) Begin Best_f:=f; CalculateScores(f); for iter:= to TSML {Tabu Search based mutation length} (i,k):=selectassignment(f);{on the basis of violation scores} f_old:= f[i,k]; f_new := SelectBestFrequency(f, i, k); {which is not tabu} AddToTabuList(i,k,f_old); AddToTabuList(i,k,f_new); f[i,k]:= f_new; UdateScores(f); If BetterThan(f,Best_f) then Best_f=f; End if End for End.

6 546 H. Mabed, A. Caminada and J.-K. Hao Genetic Tabu Search Begin P:=RandomInitPoulation(Po_size); For g:= to NbGenerations (,2):=SelectParents(P) with a Pc robability do (f,f2):=crossover(,2) otherwise f:=; f2:=2; f:=tabusearchoerator(f); f2:=tabusearchoerator(f2); (v,v2):=selectvictims(p); RelaceBy(v,f); RelaceBy(v2,f2); End for End. 4 Genetic Tabu Search for Multi-eriod Channel Assignment For the urose of finding multi-eriod channel assignment, we have designed and exerimented different otimization techniques. Each technique resents a articular manner to readat FCA algorithms (in our case the Genetic Tabu Search) for the resolution of the MCA roblem. These techniques can be roughly classified into two classes: direct otimization and decomosed otimization. 4. Direct Otimization The multi-eriod character of the roblem increases its combinatorial comlexity. In direct otimization, the roblem is considered in its totality without restriction on search sace. In other words, search sace will corresond to all the sequences of the form: n n n f,.., f,.., f,.., f,.., f,.., f,, m N, mn,, m N, mn The otimization algorithm generates the different frequency lans comosing the otimal sequence in a cometing way. It is then necessary to readat search oerators of the basic algorithm. 4.. Objective Function To assess the fitness of a sequence, two criteria are considered: the total of interference recorded over time eriods F Σ and the total of transition cost C Σ. The quality of each frequency lan in the sequence is calculated regarding to the other lans. Therefore, choices made on a art of the sequence may lead to other changes in the entire sequence. The interference and transition criteria ( 2.2) are aggregated into a single objective function. A threshold value S is defined as the maximal tolerated number of changes in the sequence. Exceeding this threshold the sequence quality is enalized with a very high value M. The objective function takes then the following form:

7 Multi-eriod Channel Assignment 547 F = F + M IND( C > S ) where M is a very high value (5) Σ Σ Σ 4..2 Initial Poulation Generation of the initial oulation asses through a re-otimization hase. For each sequence of the initial oulation, we choose iteratively one eriod. An otimization hase is launched to generate a frequency lan, f, well adated to that eriod with the objective function given in equation 6. Then the frequency lan f is fixed during all eriods forming a sequence <f,..,f> which is inserted in the initial oulation. This rocess is reiterated for the other individuals of the initial oulation. mi, mj N, N i, j, fik, fjl, i=, j= k=, l= [ ] F = I /.. n (6) 4..3 Crossover Oerator Considering the effectiveness of the geograhical crossover, a multi-eriod version of this oerator should be interesting. The objective is to allow both satial and temoral configuration exchange between sequences. In other words, the frequency lan evolution in a art of the network is grafted into another sequence. To that end, a reference station is randomly selected and the set of its neighbors is built. Then the corresonding arts in the two arent sequences are exchanged. The crossover working is schematized in the following figure. Interfering stations Reference station Interfering stations Sequence Frequency lan Periods Network Parent Parent 2 Offsring Offsring 2 Fig.. Crossover oerator for multi-eriod channel assignment 4..4 Mutation Oerator Two variants of the revious tabu search based mutation oerator are imlemented. The first variant (M) changes the value of a single assignment f. First, a eriod is randomly chosen and the violation score of each assignment of the considered eriod is calculated using the formula 7. Then an assignment f is selected with a robability roortional to its violation score and the best not tabu value is attributed to it.

8 548 H. Mabed, A. Caminada and J.-K. Hao SCORE n N m j = = j= l= I i, j, f f jl, (7) The second variant (M2) resets to the same value all the assignments ( [..n]). The working scheme is the same as in mutation (M) excet that the new value is attributed to all assignments of the same osition as f. These two variants are used in a cometing way with robabilities Pm, -Pm. The algorithm below deicts the Tabu Search based mutation of direct otimization. The main rocedure is the same as in fixed assignment excet that maniulated individuals are sequences. TabuSearchOerator(Sequence seq) Begin Best_seq:=seq; =Random(n); CalculateScores(Seq[eriod]); {seq(eriod) corresonds to the frequency lan of the eriod } for iter:= to TSML {Tabu Search based mutation length} (i,k):=selectassignment(f);{on the basis of violation scores} f_old:= seq[,i,k]; f_new := SelectBestFrequency(seq,, i, k); {which is not tabu} with a Pm robability, do AddToTabuList(,i,k,f_old); AddToTabuList(,i,k,f_new); seq[,i,k]:= f_new; else do AddToTabuList(,i,k,f_old); AddToTabuList(TOUT,i,k,f_new); for each er=..n do seq[er,i,k]:= f_new; end with UdateScores(seq); If BetterThan(seq,Best_f) then Best_seq=seq; End if End for End. f 4.2 Decomosed Otimization In decomosed methods, the initial roblem is decomosed into several sub-roblems of lower comlexity, leading to reduced search sace. On each sub-roblem, an otimization hase is launched to generate a art of the final sequence of frequency lans. Each otimization hase handles individuals of frequency lan tye. Three decomosed algorithms are imlemented. Details of their imlementation are given here below Ste by Ste Otimization The otimal sequence of frequency lans is built in an iterative manner. At each iteration, one eriod is considered according to its chronological order. A frequency lan is then generated (by otimization) to fit the traffic situation at this eriod and to minimize transition cost from revious frequency lan. The final solution corresonds then to the set of those frequency lans. Note that the art of the otimal sequence already built can t be readjusted in further iterations. We give hereafter the different stes followed by the method. The value S designates the maximal tolerated change

9 Multi-eriod Channel Assignment 549 threshold between two consecutive frequency lans in the sequence. This threshold serves to aggregate the two artial functions F (equation 6) and C (described in the algorithm). Find the values f, which minimize: F For each eriod [2..n] Find the values f, which minimize: N m i F + M IND( C >S), where C = IND( f f ) i, k i, k i= k The final solution will corresond to the sequence f,.., f,.., f,.., f,.., f,.., f. n n n,, m N, mn,, m N, mn Sequential Otimization The idea is to use the robust frequency lan generated by fixed channel assignment method as a starting oint for search. More recisely, an initial otimization hase using the function F 2B is erformed roducing a robust frequency lan. The different frequency lans comosing the sequence are constructed iteratively in chronological order of eriods exactly as in ste-by-ste otimization. The first frequency lan corresonding to the initial eriod is generated starting from the robust frequency lan (with resect to the transition cost criterion). We give hereafter the details of sequential otimization algorithm. Find the value f, which minimize F 2B For each eriod [..n] Find the values f, which minimize: F + M IND( C > S) Parallel (or Simultaneous) Otimization The iterative asect of sequential otimization makes it slow. To overcome this inconvenient, a arallel variant of this technique is roosed. In this case, the frequency lans associated with the different eriods are constructed starting from the robust lan in arallel. To exlain this difference we give the working scheme of this arallel otimization, the arallel algorithm being imlemented under PVM (Parallel Virtual Machine) system. Find the value f, which minimize F 2B For each eriod [..n] do simultaneously Find the values f, which minimize: N m i + > = i, k i, k i= k F M IND( C S), where C IND( f f )

10 5 H. Mabed, A. Caminada and J.-K. Hao 5 Exerimental Tests The objective of this section is twofold. On the one hand, we comare the erformance of the imlemented multi-eriod otimization techniques. On the other hand, we comare the quality of solutions generated by the multi-eriod model with those roduced by the FCA model. Results of multi-eriod and fixed channel assignment are comared from two oints of view. The first is based on objective functions (Formulas to 3). The second adots oerator s oint of view and comares the solutions according to the lost traffic. 5. Benchmark Problems Tests are carried out on both fictitious and real data. The first roblem, B-63, reresents a fictitious roblem instance with 63 stations, 3 available frequencies and 6 eriods. The second instance, D-639, corresonds to a real world roblem. The network is comosed of 639 stations with 62 frequencies and traffic data during 3 hours (eriods). The third instance, BM-2, is another real world roblem with 2 stations and 62 available frequencies. BM-2 is dedicated to study the erformance of MCA for large-scale traffic data. Traffic evolution is thus studied over one week, day by day. 5.2 Comarison between Multi-eriod Channel Assignment Techniques Four multi-eriod otimization algorithms, described before, are comared. Those algorithms corresond to direct otimization, ste by ste otimization, sequential otimization and arallel otimization. Table gives the results obtained by each technique for the two roblems B-63 and D-639. We run each algorithm 5 times on every roblem. Only the best solution is reorted for each algorithm. Two imlementations of the direct otimization technique are resented. The first uses only the mutation oerator M. The second uses in a simultaneous way the two mutation oerators M and M2. For each technique we give the name, the objective and eventually the mutation oerator used. Obtained solutions are comared according to interference (F ) and transition (C ) cost at each eriod as well as their sum over time. From columns (2) and (3) we remark the effectiveness of using the two mutation oerators in cooerative way. By using only the M oerator, the transition cost reaches quickly the threshold S and hence slows down the algorithm evolution. Ste-by-ste technique gives bad results. This can be exlained by the absence of a global vision. In fact, at each hase, ste-by-ste algorithm otimizes the frequency lan according to the traffic situation at the associated eriod without taking into account the future evolution of traffic. However, the main observation is that decomosed aroaches, reresented in table by columns (4) and (5), give the best results. We notice also that results of sequential and arallel-decomosed otimization are very close. By fictitious data, we mean a real network whose traffic data are artificially modified.

11 Multi-eriod Channel Assignment 55 Table. Comarison between the different multi-eriod channel assignment techniques () (2) (3) (4) (5) Name Ste by ste decomosed Direct Direct Sequential decomosed Parallel decomosed Objective F +IND(C >S), S=3, F +IND(C >S ), S=3, 6 F +IND(C >S ), S=3, 6 F +IND(C >S), S=3, F +IND(C >S), S=3, Mutation M M+M2 Cost F C F C F C F C F C B-63 D-639 P P P2 P3 P4 P Total : 8: 9: : : 2: 3: 4: 5: 6: 7: 8: 9: Total Comarison between Fixed and Multi-eriod Solutions for D-639 Problem To comare fixed and multi-eriod channel assignment, we have run the fixed channel assignment algorithm (Section 3) five times on the D-639 roblem. In the tables 2 and 3, we comare the best solution found by the FCA with the multi-eriod solution found by the arallel decomosed otimization (column 5 in table ). This comarison is made on the basis of objective function (table 2) and lost traffic (table 3). In table 3, we give the lost traffic (in Erlang) at each eriod as well as the total of lost traffic for the two comared solutions. We use for that, the quality evaluator of PARCELL 2. Results show a reduction of lost traffic reaching sometime 8% by using the MCA model. Notice that in table 2, transition cost for fixed solution is usually zero since there is a single frequency lan. 2 Engineering tool for design of mobile radio network, ORANGE society all rights reserved.

12 552 H. Mabed, A. Caminada and J.-K. Hao Table 2. Comarison between fixed and multi-eriod channel assignment in terms of objective function Table 3. Comarison between fixed and multi-eriod channel assignment in terms of lost traffic for the D-639 roblem Name Fixed Parallel decomosed Objective F 2B F +IND(C >) Cost F C F C 7: : : : : : : : : : : : : Total D-639 Periods Traffic Fixed Multi-eriod Gain 7h-8h % 8h-9h % 9h-h % h-h h-2h % 2h-3h h-4h % 4h-5h % 5h-6h % 6h-7h % 7h-8h % 8h-9h % 9h-2h % Total Table 4. Comarison between fixed and multi-eriod channel assignment for BM-2 instance Days Fixed solution F 2B Multi-eriod solution F +IND(C >) F C F C June, Monday June, Tuesday June, Wednesday June, Thursday June, Friday June, Saturday June, Sunday Comarison between Fixed and Multi-eriod Solutions for Large-Scale Traffic Data (BM-2 Problem) In tables 4 and 5, we comare two solutions generated for the BM-2 instance. The first solution is generated using the FCA model, and the second using the arallel decomosed algorithm for the multi-eriod model. As for D-639 roblem, we comare these two solutions in terms of objective function (table 4) and lost traffic quantity (table 5). The first observation is that, during the weekend, frequency lan adatation requires more changes. For both Saturday and Sunday, the change threshold is reached. This can be exlained by the great difference between the traffic situation during the weekend and the remainder days. This observation results in table 4, where we note a great quality imrovement during the weekend (the gain is of 8% and.4%) in the MCA model.

13 Multi-eriod Channel Assignment 553 Table 5. Lost traffic recorded for fixed and multi-eriod solution for the BM-2 instance Days Traffic Fixed Multi-eriod Gain June, Monday % June, Tuesday % June, Wednesday % June, Thursday % June, Friday % June, Saturday % June, Sunday % Total Conclusion In this aer we have roosed a multi-eriod channel assignment (MCA) model for GSM mobile networks. In addition to the classical minimization interference criterion, we introduced another otimization criterion based on the transition cost from the frequency lan of a eriod to the lan of another one. Comared with the fixed channel assignment model, the roosed model has the advantage of being flexible and adative to traffic evolution. Based on the MCA model, we have develoed several otimization techniques to find a sequence of frequency lans for a given time eriods. These solution techniques are adated from a hybrid Genetic Tabu Search algorithm for fixed channel assignment. We roosed two ways of generating a solution for the MCA model: direct otimization in which the best sequence of frequency lans is sought directly; and decomosed otimization in which the whole solution is built by finding frequency lans for each individual eriods. Several exeriments on three realistic data sets have been carried out. These data sets include both fine grained (hour by hour) and large scale (day by day) time stes. Exerimental results have led to the following observations. First, comaring the different otimization techniques for the MCA model on these data sets shows that the sequential and arallel imlementation of the decomosed otimization give frequency lans of better quality in terms of the two otimization criteria (global interference and transition cost between frequency lans). Second, when comaring solutions obtained using the MCA model and the FCA model, one observes that the multi-eriod model leads to frequency lans of lower interference. Third and most imortantly, thanks to the multi-eriod model, the lost traffic is always reduced, reaching sometimes a gain of communications u to.4%. This last oint is esecially beneficial from an oerator s oerational oint of view. Finally, let us mention two ossible imrovements for multi-eriod frequency assignment. As to the model itself, other otimization objectives may be taken into consideration (as mentioned in Section 2). As to solution techniques, an interesting alternative to the enalty-based aggregation aroach used in this study is a true multi-criteria otimization aroach that would be certainly worth of investigation.

14 554 H. Mabed, A. Caminada and J.-K. Hao References. Baier, K. Bandelow "Traffic engineering and realistic network caacity in cellular radio networks with inhomogeneous traffic distribution" Proc. of IEEE VTC, 997, P T. H Chan, M. Palaniswani, D. Everitt "Neural network-based dynamic channel assignment for cellular mobile communication systems" IEEE Transaction on Vehicular Technology, Vol 43, N 2, 994, P L. Chen, S. Yoshida, H. Murata "A dynamic channel assignment algorithm for voice and data integrated TDMA mobile radio" Proc. of IEEE VTC, 996, P R. Dorne, J-K. Hao "An evolutionary aroach for frequency assignment in cellular radio networks" IEEE International Conference on Evolutionary Comutation, 995, P M. Duque-Anton, D. Kunz, B. Rüber "Channel assignment for cellular radio using simulated annealing" IEEE Transaction on Vehicular Technology, Vol 42, N, 993, P D. Grillo, R. A. Skoog, S. Chia, K. K. Leung. "Teletraffic Engenieering for Mobile Personal Communications in ITU-T Work: The Need to Match Practice and Theory" IEEE Personal Communications, Vol 2, 998, P J-K. Hao, R. Dorne, P. Galinier "Tabu search for frequency assignment in mobile radio networks" Journal of Heuristics 4, 998, P Katzela,M. Naghshineh "Channel assignment schemes for cellular mobile telecommunication systems: A Comrehensive Survey" IEEE Personal Communications, June 996, P W. Lee, "Mobile communications design fundamentals" Wiley Series in Telecommunications: H. Mabed, A. Caminada, J-K. Hao "A dynamic traffic model for frequency assignment" Parallel Problem Solving from Nature PPSN VII, Lecture Notes in Comuter Science 2439, 22, P S. Matsui, I. Watanabe, H. Tokoro "A arameter-free genetic algorithm for fixed channel assignment roblem with limeted bandwidth" Parallel Problem Solving from Nature PPSN VII, L Lecture Notes in Comuter Science 2439, 22, P K. Murray, D. Pesch "Adative radio resource management for GSM/GPRS networks" First joint IEI/IEE Symosium on Telecommunications Systems Research, 27 Nov D. Renaud, A. Caminada "Evolutionary Methods and Oerators for Frequency Assignment Problem" SeedU Journal (2), 997, P P. Reininger, S. Iksal, A. Caminada, J. Korczak "Multi-stage otimization for mobile radio network lanning" Proc. IEEE Vehicular Technology Conference, 999, P J. Tajima, K. Imamura "A strategy for flexible channel assignment in mobile communication systems" IEEE Transaction on Vehicular Technology, Vol 37, N 2, 988, P V. Wille, H. Multimaki, S. Irons "A ractical aroach to channel borrowing for microcells in GSM systems" Proc. IEEE VTC, 998, P J. Zander. "Radio Resource Management in Future Wireless Networks: Requirements and Limitations" IEEE Communications Magazine, 997, P 3 36.