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Adaptive Genetic Algorithms for Dynamic Channel Assignment in Mobile Cellular Communication Systems Marcos A. C. Lima, Aluízio F. R. Araújo, and Amílcar C. César, Member, IEEE
Abstract—Two adaptive genetic algorithms (GAs), namely GA for locking channel (GALC) and GA for switching channel (GASC), are proposed for a dynamic channel assignment in mobile cellular communication systems. The algorithms aim to minimize the blocking probability of new calls and the dropping probability of handoff calls in channelized systems, simultaneously considering three types of electromagnetic compatibility (EMC) constraints: 1) the cochannel; 2) the adjacent channel; and 3) the cosite. The proposed algorithms add a number of mechanisms to the canonical GA in order to increase their efficiency and velocity of convergence. Such mechanisms are adaptive parameters, random immigrants, a greedy policy, a reservoir to assist the initial population, a truncation selection scheme, and a three-point crossover. The GASC allows call switching between channels during the call holding time, whereas the GALC does not allow it. Computer simulations evaluated the performance of the proposed models considering a benchmark cellular environment formed by 49 cells with 70 channels and nonuniform traffic load characteristics. The impact of EMC constraints on the blocking probability of new calls and on the dropping probability of handoff calls was assessed, and the proposed models reached suitable performance. Equipment failure tests showed robust performance of the two adaptive GA schemes during the fault occurrence and recovery capability after the fault ends. The results suggest that the GASC has lower overall blocking probability of new calls than the GALC; however, the GALC may do better than the GASC in a number of combinations of handoff requests and EMC restrictions. Index Terms—Dynamic channel assignment (DCA), electromagnetic compatibility (EMC), genetic algorithm (GA) with adaptive parameters, mobile communication.
I. I NTRODUCTION
I
N RECENT years, mobile communication systems have experienced remarkable technological progress. New requirements from multimedia services and a huge expansion of the number of users increased the demand for bandwidth and multiple accesses to the transmission medium significantly. Manuscript received August 8, 2002; revised March 31, 2005, July 31, 2006, and September 19, 2006. This work was supported in part by the São Paulo State Research Funding Agency (FAPESP) under Grant 00/09180-1. This paper was presented in part at the 13th IEEE International Symposium on Personal, Indoor, and Mobile Radio Communications, Lisbon, Portugal, September 2002. The review of this paper was coordinated by Dr. T. Wong. M. A. C. Lima and A. C. César are with the Department of Electrical Engineering, School of Engineering of São Carlos, University of São Paulo, 13566-590 São Carlos-SP, Brazil (e-mail:
[email protected]). A. F. R. Araújo is with the Center of Informatics, Federal University of Pernambuco, 50740-540 Recife-PE, Brazil (e-mail:
[email protected]). Digital Object Identifier 10.1109/TVT.2007.898411
Hence, efforts have been made to improve the efficiency of channel reuse, which is widely employed as the key strategy to manage the limited electromagnetic spectrum allocated to mobile cellular communication systems. A channel reuse technique considers that any geographic coverage area is divided into cells in such a way that identical channels can be simultaneously assigned to calls in distinct cells. However, a channel reuse scheme might generate interferences that degrade the quality of a transmission. Such interferences are divided into the cochannel and the adjacent channel types. Cochannel interference occurs due to simultaneous use of the same channel in neighboring cells, whereas adjacent channel interference is caused by simultaneous use of adjacent channels in the same cell (cosite) or in neighboring cells (adjacent channel) [1]. Blocking probability of new call requests and dropping probability of handoff call requests are criteria often employed to evaluate the performance of mobile cellular communication systems. In such systems, high percentages of handoff failure severely affect the overall system performance; thus, the efficiency of channel reuse is improved by using proper procedures to give priority to handoff calls [2]. Hence, a channel can be simultaneously used by a number of cells, attaining desired standards of quality of service, if a particular traffic demand and some electromagnetic compatibility (EMC) constraints are satisfied. Therefore, a channel allocation problem (CAP) presently plays an important role in mobile cellular communication systems. The CAP can be understood as a large-scale dynamic optimization task to be carried out in stochastic environments, considering multiple goals and constraints. Such a problem is solved by algorithms grouped into three major categories, namely a fixed channel allocation (FCA), a dynamic channel allocation (DCA), and a hybrid channel allocation (HCA), which is a combination of the FCA and the DCA schemes. A number of such algorithms have been investigated, and a good review concerning the CAP can be found in [3]. So far, authors have 1) proposed heuristic algorithms to solve the FCA [1], [4]–[7] and DCA [8], [9]; 2) investigated the impact of some EMC constraints upon system performance [1], [6], [7], [10]; and 3) included system capability to deal with handoff calls [2], [4]. The CAP may be efficiently solved by computational intelligence approaches, such as reinforcement learning [11], [12], heuristically oriented search, neural networks, and evolutionary algorithms (EAs). In particular, EAs may be useful for solving optimization problems in which heuristic solutions are neither
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available nor viable. EAs are stochastic search methods that mimic the metaphor of natural biological evolution and include genetic algorithms (GAs). GAs are heuristic methods with the capability to effectively explore and exploit spaces of solutions. GAs can be used to solve many complex optimization tasks [13] such as multiconstrained [14] and NP-complete problems [15]. The use of GAs simply demands mapping between the search and the chromosome spaces, a set of operators, and an evaluation function. The optimal or suboptimal solutions of a problem are expected to be encoded in the descendants of the best fit individuals over a number of generations, and their attributes tend to be preserved for the next generations. Furthermore, GAs are robust, do not require previous knowledge concerning the solution of a problem, are appropriate for parameter adaptation, may learn changes in the environment dynamics, and can generate a number of concomitant solutions. Such features are adequate to solve the CAP because it shows complex dynamic behavior with a high degree of correlation between the channels, and the CAP solution demands adaptation capability to respond suitably to parametric changes in the environment. GAs present an implicit parallelism, that is, at each time step, GAs simultaneously take into account a number of solutions, whereas other computational intelligence methods, such as reinforcement learning [11], [12], consider a unique solution. The use of the canonical GA to solve the CAP has been investigated by several authors who proposed algorithms to handle the FCA [16]–[19], the DCA [20], and the effects of the EMC constraints regarding the blocking probability of new calls and the dropping probability of handoff calls [16], [17]. The usual approach, that is, the canonical GA, may yield unsuitable solutions when the environment changes. GAs with the capacity to change their own parameters to respond adequately to environmental modifications, to handle multiple constraints (all EMC constraints), and to consider a second objective (the handoff requests) should be used to solve this more realistic version of the CAP. In this paper, two adaptive GAs are proposed to solve the CAP in mobile cellular communication systems, which are dynamic environments. The algorithms aim to minimize the blocking probability of new calls and the dropping probability of handoff requests in channelized systems, simultaneously considering three types of EMC constraints: 1) the cochannel constraint (CCC); 2) the adjacent channel constraint (ACC); and 3) the cosite constraint (CSC). The first algorithm, which is hereafter called GA for locking channel (GALC), locks in the channel assigned throughout the call holding time. The second algorithm, which is hereafter called GA for switching channel (GASC), can switch the assigned call from a channel to another one within the same cell during its call holding time. The GALC and GASC find a new optimal or suboptimal solution at each time step of the mobile system operation. Both the GALC and GASC need to respond quickly; thus, they need to include some features to increase the efficiency of former solutions. In comparison with previous approaches, the main contributions of this paper are 1) the proposal of algorithms to solve the DCA according to a more up-to-date and actual view;
Fig. 1. Cellular environment with two nonuniform traffic distributions with averages of (a) 91.83 calls per hour and (b) 106.53 calls per hour (values indicated within parentheses) [11]. Thick-line cells represent a seven-cell pattern. Marked cells represent a set of cells using channel k. Cells located in the two tiers around cell i represent the cochannel interfering cells.
2) the introduction of an adaptive GA to respond to environmental changes; 3) the robustness of the GALC and GASC when submitted to simultaneous disturbance caused by the three EMC constraints; 4) the short time interval required by the proposed GAs to provide a number of solutions; 5) the significant success of the system allocation concerning new and handoff calls; and 6) the possibility of extending the procedures to manage resources in nonchannelized systems in a simple way. The performance of the GALC and GASC were evaluated by means of computer simulations considering a benchmark cellular environment subject to a nonuniform traffic load. Numerical results showed promising performance of the proposed algorithms. We emphasize that the proposed GAs establish one request call within 136 ms, on average, considering a population of 75 individuals evolved by a maximum of 100 generations. Furthermore, the proposed GAs present lower blocking probability than both FCA based on borrowing with directional channel locking (FCA-BDCL) [5] and DCA based on Q-learning [11], which are two of the most efficient models. The remainder of this paper is organized as follows. Section II briefly presents the cellular environment. Section III introduces the GA for the locking channel and the GA for the switching channel and their chosen parameters. Section IV describes the evaluation of the GAs performance and presents a discussion about the proposed models. Finally, Section V concludes this paper. II. C ELLULAR E NVIRONMENT The cellular environment has its coverage area divided into cells of hexagonal shape, in which a reference cell i and its surrounding cells compose a compact pattern. The P cells use a set of channels, and the same channel (or a subset of channels) may be reused in another cell with distance sufficient to provide a minimum acceptable carrier-to-interference ratio. Fig. 1 shows the cellular environment composed of 49 cells with 70 channels available and two nonuniform traffic distributions [11] of our simulations.
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A. EMC Constraints 1) CCC: The cells satisfying the minimum acceptable carrier-to-interference ratio are the cochannel cells, and the corresponding minimum distance between cochannel cells is the cochannel reuse distance. For P = 7, the cells satisfying the cochannel reuse distance are located on the third tier [21] (Fig. 1). 2) ACC: Adjacent channels cannot be simultaneously assigned to adjacent cells. Therefore, channels assigned to adjacent cells must keep a minimum distance of channels. The distance for ACC is usually larger than that for CCC [10]. 3) CSC: Any pair of channels in the same cell must keep a minimum distance of channels. The distance for CSC is usually larger than that for ACC [10]. The EMC constraints are denoted as ccc, acc, and csc = n, meaning that a particular channel assigned to a reference cell prohibits the allocation of the same channel and its (n − 1) right and left neighbors. For example, assuming acc = 3, any channel within two channels apart from the reference cell cannot be assigned to other cells. Detailed uses concerning the EMC can be found in [10].
Fig. 2. GA representation of one individual. Allocation channel solution.
of individuals (each one represents a possible solution) from generation to generation, which is based on a weighted fitness selection process. To efficiently reach solutions within a short period of time, the proposed models include additional mechanisms to the canonical GA scheme to simultaneously increase the efficiency of the exploration and exploitation processes. Hence, the random immigrant mechanism increases the diversity of the population, adding new individuals to an existing generation, whereas the greedy policy guarantees the survival of the fittest individual. The truncation selection scheme chooses the percentage of the best individuals to produce the offspring, whereas a reservoir stores the best fit individuals of previous generations in order to assist the formation of the next population. Furthermore, the proposed GA models employ adaptive mechanisms to adjust the mutation, crossover, and reproduction rates according to the diversity of the selected parents of each generation.
B. Handoff For each handoff request originated in cell i, the destination cell probability is estimated, considering the traffic demand of cells in the neighborhood of i. Then, cell j, which is a neighbor of cell i, with traffic load Tj will have the following probability of being the destination cell: Pj =
Tj Q
(1) Tk
k=i=j
A. Representation of Cellular Environment Consider a system with N cells and M channels. A cell can use any available channel if such a choice satisfies the EMC constraints. Each gene represents a channel state (on or off), and M genes form a chromosome representing the state of a particular cell. An individual, which is formed by N chromosomes, represents an option of channel assignment. Hence, each individual is denoted by a vector of dimension V = N × M , as shown in Fig. 2, where
where Q is the total number of cell-i neighbors. cij =
1, 0,
if channel j is in use in cell i . otherwise
C. Blocking Probability of New Calls and Dropping Probability of Handoff Calls A new call means a channel request arriving to the set of cells, whereas a handoff call means a request for a channel originated by a call in progress (assigned call). For a particular traffic load, the blocking probability of new calls (Pbn ) and the dropping probability of handoff calls (Pdh ) can be evaluated as follows: Pbn =
Bbn Aan
(2a)
Pdh =
Bdh Arh
(2b)
where Bbn is the number of new calls that are blocked, Bdh is the number of handoff calls that are dropped, Aan is the number of new call arrivals, and Arh is the number of handoff requests. III. GA S The solution of optimization problems solved by means of GAs results from the artificial evolution of a population
B. Genetic Operators and Their Parameters The values of the GA control parameters, in particular, the number of individuals that may suffer mutation, crossover, and selection rates, may be modified at each generation or whenever necessary, depending on some features of the population. These are called adaptive control parameters, and their use aims to accelerate the algorithm convergence and to avoid local optimum solutions. A suitable range for each adaptive control parameter, as usual in the optimization area, was heuristically determined after many simulations. 1) Size, Initialization, and Diversity of a Population: Both size and diversity of a population and its initial set of individuals are crucial when allowing any GA to find an appropriate balance between exploration and exploitation. Therefore, in order to find an optimal or suboptimal solution, within a viable amount of time, a GA needs the following: 1) a suitable population size; 2) a number of promising individuals in the initial population; and 3) an adequate amount of diversity in the population.
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Fig. 3. GALC scheme. Blocking probability of new calls versus time for different numbers of individuals. Nonuniform traffic distribution with an average of 91.83 calls per hour and an 80% traffic increase is assumed. The GASC showed very similar results.
request to be about 0.2 s (when ran on a Pentium-IV 2.2-GHz 512-MB PC) for 75 individuals, which is compatible with an actual operation. The results suggest that the population size yields a suitable compromise between performance and convergence time. The formation of each initial population is assisted by a reservoir in which the best fit individuals of previous solutions were stored. Therefore, the initial population at each time interval (in which a new solution must be evolved) is composed of 75 individuals, which are divided into three groups: 20 are randomly chosen from the reservoir; 50 are randomly generated; and five are the fittest individuals from previous solutions. To produce the five fittest individuals when the evolutionary process starts, the allocations of a seven-cell pattern are considered. Initially, the reservoir is empty, and it will be filled up with the best element of each generation until its full capacity is reached. The proposed GAs update the number of mutant individuals, crossover, and selection rates as a function of the parent diversity Pdiv , which is calculated as a function of the repeated parents among the selected ones, according to Pdiv = 1 −
Fig. 4. Simulation time per call request versus number of individuals for GALC and GASC schemes (new calls). Nonuniform traffic distribution with an average of 91.83 calls per hour and an 80% traffic increase is assumed.
Hesser et al. [22] argued that in GA, the most important feature is the amount of variability in the individual chromosomes, and it was noted that the highest increase in variability often occurs with populations ranging from 30 to 110 individuals. Preliminary experiments for GALC and GASC schemes, within that population range, evaluated the blocking probability of new calls as a function of time for five different population sizes. The results (Fig. 3) suggest 75 individuals as the minimum population size within the best performance group when the chosen options were considered. The option for 75 individuals is justified because there is a tendency of marginal performance growth for population sizes higher than this value. This does not guarantee the best number of individuals; however, it provides an alternative to fulfill the objectives of the algorithms. Furthermore, the simulation time per call request as a function of population sizes for the GALC and GASC algorithms is shown in Fig. 4. Both algorithms show the time per call
number of repeated parents . number of selected parents
The values of the adaptive parameters, reproduction, crossover, and mutation rates are related to the parent diversity. The parametric adaptation of the proposed GAs is guided by the diversity, which should not be very low or very high, avoiding convergence to local optimum or random search, respectively. To do this, first, the number of mutations must be reduced, and the crossover and reproduction rates must be increased when the parent diversity grows toward one. This reduces the exploration for new solutions and increases the exploitation of the fit individuals. Second, when the parent diversity falls, growth of the number of mutations and simultaneous fall of two other rates must occur to increase exploration of the solution space. Note that the three parameters must decrease or increase within boundaries. Moreover, the variation of such parameters should slow down for low or high diversities and should speed up for intermediate values. Sigmoid functions were chosen to fulfill the stated features: parent diversities as a function of parameter values. A sigmoid function produces a curve having an “S” shape, and it is often used to assure that certain parameters remain within a specified range and have mostly linear variation. 2) Selection of Parents and Crossover: The crossover operator is applied to two parents by means of cuts at the same point (randomly chosen) and recombination of the parts of each individual to form the offspring. The truncation selection mechanism chooses the 10% best fit individuals of the population to be potential parents. Then, the actual parents are randomly chosen to produce their offspring, according to the crossover rate exp(6Pdiv − 3) − 1 . (3) ρc = 0.25 + 0.10 exp(6Pdiv − 3) + 1 An often task-dependent determination is the number of crossover points. To determine the most efficient option for the
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GALC and GASC, some cases were exhaustively tested, and the results have highlighted the three-point crossover as the best alternative. 3) Mutation: The number of individuals in the current generation that undergo mutation, and hence will be included in the next generation, is determined by ηm = 0.30 − 0.15
exp(6Pdiv − 3) − 1 . exp(6Pdiv − 3) + 1
(4)
The number of individuals that experience mutation depends on the parent diversity; then, an adaptive mutation probability was used to keep an adequate level of diversity during evolution. Considering that the performance of an individual can be improved with the increase of the variability of the chromosomes, each chromosome can be associated with a particular mutation probability in accordance with its fitness. Thus, each chromosome has one mutation probability in accordance with its blocking probability of a new call and the dropping probability of a handoff call. The use of an adaptive probability for a mutation rate increases the possibility of finding the global optimum and accelerates the convergence time. 4) Random Immigrants: The random immigrant mechanism [23] aims to increase the diversity of the population, including new individuals into the existing generation to act in response to changes that occur in the environment and to avoid premature convergence. 5) Selection of Survivors: To increase the probability of the existence of fit individuals in the next generation, a percentage of the remaining population is selected through the roulette wheel mechanism, according to the reproduction rate
Fig. 5. Genetic operators as a function of the parent diversity obeying the relation ρc + ηm + ρr = 0.7.
C. Fitness Function The fitness function evaluates the capability of an individual to adapt itself to survive in an environment. For the cellular environment, each individual represents an option of channel assignment for all cells. Hence, the fitness function aims to evaluate each channel assignment for requested calls, considering the current state of the system concerning new calls, handoff calls, and EMC constraints. The total fitness function uses the function proposed by Nie and Haykin [11], [12], adding to it new terms to take into consideration the simultaneous effect of the three EMC constraints and the handoff, as follows:
exp(6Pdiv − 3) − 1 . ρr = 0.15 + 0.05 exp(6Pdiv − 3) + 1
f ittot =
N =49 M =70 i=1
(5)
k=1
f it(i, k) +
N
n5 (i)r5
(6)
i=1
where Each generation of the proposed models is composed of the following individuals: 10% are potential parents; 20% are random immigrants; and 70% are individuals derived from the use of genetic operators. 6) Adaptation of Parameters: The reproduction, crossover, and mutation rates as a function of parent diversity are shown in Fig. 5. The lower and upper boundaries of the curves, as well as the parameters of (3)–(5), were heuristically found through trial and error. In this paper, the number of mutations and the rates of crossover and reproduction were chosen in such a way that they obey the relation ρc + ηm + ρr = 0.7 to reach a low blocking probability of new calls and a low dropping probability of handoff calls within a suitable time interval. Considering that the performance of an individual can be improved with the increase of the chromosome variability, the mutation probability of each chromosome can be indirectly associated with a particular fitness. Thus, in the proposed GAs, each chromosome has a mutation probability in accordance with its blocking probability of new calls and the dropping probability of handoff calls.
f it(i, k) = n1 (k)r1 + n2 (k)r2 + n3 (k)r3 + n4 (k)r4
(7)
is the fitness function of cell i for each channel k; n1 (k) is the number of cochannel cells located in the third tier referring to cell i, in which channel k is in use (Fig. 1); n2 (k) is the number of cochannel cells located in the third tier referring to cell i, in which channel k is not in use; n3 (k) is the number of other cochannel cells using channel k; n4 (k) is the number of channels to be blocked due to EMC constraints if channel k is assigned; n5 (k) is the number of dropped handoff calls referring to cell i; and the coefficients ordered as ri > r2 > r3 > r4 > r5 were heuristically established as r1 = 5, r2 = 1, r3 = −1, r4 = −15, and r5 = −60. The positive values of r1 and r2 reward proper assignments, and the negative values of r3 , r4 , and r5 penalize unsuitable assignments. The coefficient r4 is significantly higher (the absolute value) than coefficients r1 and r2 ; thus, a solution with a constraint violation usually has fitness that is much lower than any viable solution. Therefore, any unacceptable solution has low fitness, making it very unlikely that the algorithms
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converge to nonviable solutions. The same reasoning, with tougher penalties (r5 is higher, in absolute value, than r4 ), is valid to consider handoff calls. The values of the coefficients r1 to r5 were established after many simulations to reach the lowest blocking probability of new calls and the lowest dropping probability of handoff calls within an acceptable time interval. The values of the penalty term for EMC in (7) for the solutions were checked during the simulations to assure the inexistence of violated constraints. D. Procedure for the Proposed Algorithms The procedure for the proposed algorithms to search for the solution of the DCA is as follows, obeying the maximum number of generations or the convergence as the stop criterion. a) Initialize the following variables and parameters: population size, maximum number of generations, number of channels per cell, traffic load, handoff rate, and EMC constraints; b) While the time criterion does not end; b.1 Present the request calls (new and handoff) for time instant t; b.2 Create the initial population for the evolutionary process to find a near-optimum solution to the time instant t, as discussed in Section III-B; b.3 Repeat until the termination criterion is reached; b.3.1 Compute the global fitness function for each individual in (6); b.3.2 Choose the parents according to the truncation selection mechanism; b.3.3 Update the genetic operators according to (3)–(5); b.3.4 Apply the genetic operators to the population; b.3.5 Select the individuals to the next generation; b.4 End Repeat; b.5 Assign channels for the call requests (new and handoff); b.6 Free ending calls; b.7 Add one to the time instant t; c) End of the While. E. How GALC and GASC Schemes Work Both the GALC and GASC aim to find a channel allocation policy to reach the lowest blocking probability of new calls and the lowest dropping probability of handoff calls. In the GALC scheme, a channel once assigned remains locked during the call holding, that is, the GALC only considers idle channels to allocate call requests. Alternatively, in the GASC scheme, the calls can be switched to different channels during the connection time, that is, the GASC looks for the most suitable option to allocate all channel requests. In the GALC, the mutation is only allowed for the genes representing unlocked channels, whereas in the GASC, any gene can experience mutation. The GASC uses a memory system in addition to the strategies utilized to compose the initial population. Thus, while the GALC search starts each in-
Fig. 6. Comparison of the blocking probability of new calls as a function of the traffic load increase for the GALC and GASC, the Q-learning-based DCA [11], and the BDCL [5] schemes. EMC constraint included: CCC.
teraction with many randomly generated individuals, the GASC search may start evolution close to the optimal solution by using individuals with the best fitness stored in memory. Moreover, the immigrants in the GALC do have fixed values for their genes representing the call in progress. IV. E VALUATION OF THE P ERFORMANCE OF THE GA S The performance of the GALC and GASC schemes were evaluated by simulating the cellular mobile communication system that is described in Fig. 1. Based on [11] and [12], the following system characteristics are considered: 1) The blocked new and dropped handoff calls are cleared according to the Erlang-B formula; 2) the arrivals of new call and handoff requests follow Poisson distribution with uniform or nonuniform mean interarrival times; 3) the mean arrival rate is λ, which ranges from 20 to 200 calls per hour (Fig. 1); 4) the call holding time for all new and handoff call requests obeys an exponential distribution with mean call duration T = 180 s; and 5) the offered traffic in each cell is ρ = T λ. For each handoff request that originates in cell i, the destination cell probability was estimated using (1). The blocking probability of new calls and the dropping probability of the handoff were calculated using (2a) and (2b), respectively. Computer simulations produced numerical results to be compared with FCA-BDCL and DCA based on Q-learning schemes. In the simulations, the call arrival rates were increased from 0% to 100%. Comparisons with fixed assignment algorithms were not done since their performance was worse than that of the DCA based on Q-learning [11]. The obtained results are shown in Fig. 6 for two traffic load conditions. The results suggest that the GASC strategy reaches the best performance: the lowest blocking probability in both light (average of 91.83 calls per hour) and heavy (average of 106.53 calls per hour) traffic load conditions. For example, if traffic load increases by 40% in both light and heavy demands, the blocking probabilities for the GASC scheme are, respectively, 0.62% and 6.17% lower than those obtained by
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Fig. 7. Blocking probability of new calls versus traffic load increase for the GALC and GASC schemes. This simulation assumes a nonuniform traffic distribution with an average of 91.83 calls per hour. EMC constraint included: CCC.
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Fig. 8. Dropping probability of handoff calls versus traffic load increase for the GALC and GASC schemes. This simulation assumes a nonuniform traffic distribution with an average of 91.83 calls per hour. EMC constraint included: CCC.
the BDCL scheme. Moreover, the performances of the GALC and BDCL are very similar in the whole light demand. The performance of each of the proposed algorithms is always better than that of the Q-learning DCA. It is worth noting that the performances of the BDCL and GASC are nearly the same for high increases in heavy demand, which is a situation in which there are very few assignment options. From this point onward, the simulations will consider the GALC and GASC because the other algorithms did not execute the next tests. A. Handoff In this paper, two handoff rates, namely 20% and 40%, were tested. The handoff rate means the percentage of ongoing calls requesting handoff. The obtained results for blocking probability of new calls as a function of the traffic load increase are shown in Fig. 7. The no handoff case (0% rate) was included for comparison. The GASC scheme does not vary performance independently of the handoff requests when the traffic load ranges from low to moderate levels. In this case, the GASC scheme can find more resources to assign channels than GALC because the latter, having locked channels, exhausts system resources faster than GASC. Note that when the increase in traffic load is higher than 40% for GALC or 50% for GASC, the blocking probability exceeds its recommendable operational value of 2%. As the GASC scheme shows higher exploration capability because it has more options available than the GALC, the blocking probability of new calls for the GASC is lower than that of the GALC (Fig. 7). Therefore, the GASC usually handles more assigned calls than the GALC. The dropping probability of handoff calls for the GALC and GASC is shown in Fig. 8. The results for the 20% and 40% handoff rates are very similar, and only the results for 40% were plotted for the sake of clarity. Blocking probability of new calls and dropping probability of handoff calls tend to increase
Fig. 9. Number of generations versus traffic load increase of the new calls for GALC and GASC schemes. Nonuniform traffic distribution with an average of 91.83 calls per hour. EMC constraint included: CCC.
significantly when the traffic overload is very severe due to the exhaustion of system resources. Regardless of the high levels of traffic load increase, both GALC and GASC schemes keep the dropping probability under acceptable levels. Although the GASC has lower blocking probability than the GALC, the difference in performance in Fig. 7 is not the same for all traffic loads. The blocking probability of the GASC is more affected than that of the GALC when the handoff rate increases. Moreover, the dropping probability of the GASC tends to deteriorate its performance faster than that of the GALC for high load increase (Fig. 8). To learn about the convergence velocity of the GASC and GALC, the average number of generations due to the traffic load increase of new calls is shown in Fig. 9. Note that the GASC scheme has better performance than the GALC scheme within a shorter time interval (expressed by the number of generations) for operation under low to moderate traffic load, and this occurs
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Fig. 10. Blocking probability of new calls versus traffic load increase for (dashed line) GALC and (solid line) GASC schemes. EMC constraints included ACC and CSC. Cochannel constraint (ccc = 1) is included in all cases. Nonuniform traffic distribution with an average of 91.83 calls per hour is assumed.
because the GASC has more options to find the optimum (or near optimum) during the evolutionary process. In contrast, under high traffic load conditions, there are few or no resources available for both the GALC and GASC, and the call requests tend to be blocked. As the handoff rate increases, both the GALC and GASC need more generations to reach the optimum (or near optimum). The time interval required by the GASC increases faster, giving rise to situations in which the GALC converges in fewer generations since it assigns fewer channels than the GASC. Another significant difference between the two strategies is that the GASC scheme needs a similar average number of generations to handle the 20% or 40% handoff rate, which is a useful characteristic of the proposed scheme. B. Electromagnetic Constraints The next tests evaluate the impact of the three EMC constraints upon the system performance. All experiments in this section employed a nonuniform traffic distribution with an average of 91.83 calls per hour and a 20% handoff rate. The performances in terms of the blocking probability of new calls and the dropping probability of handoff calls are shown in Figs. 10 and 11. While the CSC excludes only (n − 1) channels of the reference cell, the ACC makes the (n − 1) channels of cells within the neighborhood of the reference cell unavailable. Hence, the degradation caused by the ACC is significantly more severe than that caused by the CSC. The GALC and GASC keep their consistency in the presence of EMC. Such restrictions diminish the number of channels available. Therefore, the GALC and GASC degrade their performance proportionally to the increase of the constraint severity (compare Figs. 7 and 10 with Figs. 8 and 11, respectively). For example, considering the constraint values (csc = 3 and acc = 1) and a 40% traffic increase, the blocking probabilities of new calls for the GALC and GASC are 4.35% and 2.95% (Fig. 10), whereas the results for the dropping probability of
Fig. 11. Dropping probability of handoff calls versus traffic load increase for (dashed line) GALC and (solid line) GASC schemes. EMC constraints included ACC and CSC. Cochannel constraint (ccc = 1) is included in all cases. Nonuniform traffic distribution with an average of 91.83 calls per hour is assumed.
handoff calls are 0.04% and 0.06%, respectively (Fig. 11). For an 80% traffic increase, the blocking probabilities of new calls for the GALC and GASC are 14.79% and 13.95%, whereas the handoff figures move toward 0.42% and 0.84%, respectively. Considering the worst constraint case that was shown (csc = 3 and acc = 2) and a 40% traffic increase, the blocking probabilities of new calls for the GALC and GASC are 25.37% and 23.64%, whereas the results for the dropping probability of handoff calls are 1.97% and 1.75%, respectively. For an 80% traffic increase, the blocking probabilities of new calls for the GALC and GASC are 39.51% and 35.76%, and the handoff values grow to 3.69% and 3.64%, respectively. In all analyzed cases considering EMC with handoff, the GASC obtains better overall performance than the GALC in terms of blocking probability. However, Fig. 11 shows that the dropping probability of the handoff for the GALC is lower than that of the GASC for less-severe constrains and tends to be very similar to more acute restrictions. C. Equipment Failure The next results involve an ordinary occurrence in mobile communication systems during operating hours: equipment failure. A typical example of equipment failure is the temporary unavailability of channels, causing an important impact on the performance of new and handoff calls. Fig. 12 illustrates how the GALC and GASC adaptive schemes respond to this kind of situation. High values of traffic load increase were assumed to test the robustness under a faulty operational state and a high load demand. Initially, there were 70 channels available, and during the failure period, seven channels, which were randomly chosen, became temporarily unavailable for use [11]. After the time interval of 5 h, the unavailable channels started to operate again. Note that the performance of the GALC and GASC degraded after the faulty state, even if they kept on adapting themselves to allocate the new calls. After the faulty period, the
LIMA et al.: ADAPTIVE GAs FOR DCA IN MOBILE CELLULAR COMMUNICATION SYSTEMS
Fig. 12. Robustness of the GALC and GASC schemes to channel failure: normal operation and failure of seven channels. The time interval of the failure ranges from 10:00 to 15:00. Nonuniform traffic distribution of new calls with an average of 91.83 calls per hour, an 80% traffic load increase, and a 20% handoff rate. EMC constraint included: CCC.
GALC and GASC continued to adapt, and they showed a clear tendency to recover the best levels reached under nonfaulty conditions. It is worth noting that the results suggest that the GALC is more robust than the GASC because the GASC deals with a higher number of requests than the GALC, that is, the GALC presents a lower variation of performance. Operating at a high traffic load increase (80%) and at a handoff rate of 20%, both schemes need a similar number of generations (Fig. 9) to assign call requests. As the GASC always deals with more call requests, it would tend to need more generations to recover the best level. Regardless of its apparent incapability to manage faults in a shorter time interval, the GASC makes effective use of all the available resources; therefore, its blocking probability is always lower than that of the GALC scheme. Equipment failures were also employed to test the role played by adaptive parameters. As the GASC reaches smaller overall blocking probability than the GALC, only the results for GASC are shown. For a single period of fault, two cases of GASC were compared: with and without the mechanism to adapt GA parameters. Hereafter, the GASC with adaptive parameters (employed in all previous experiments) will continue to be called GASC, whereas the version with nonadaptive parameters will be called nonadaptive GASC. The results for the blocking probability of new calls and the dropping probability of handoff calls are shown in Figs. 13 and 14, respectively. Nonuniform traffic characteristics are assumed. The nonadaptive GASC parameters were fixed in the best options. Concerning new calls (Fig. 13), although the two schemes perform well before and after the fault occurrence, the GASC always does better than its nonadaptive version. After the fault occurrence, the GASC responds better to it than the nonadaptive scheme for the two traffic conditions, that is, the blocking probability increase is smaller for the adaptive version. Moreover,
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Fig. 13. Blocking probability of new calls for the GASC and the nonadaptive GASC tested to channel failure. The time interval of a seven-channel failure is from 10:00 to 15:00. Two nonuniform traffic distribution cases are investigated. (a) With an average of 103.53 calls per hour, a 60% traffic load increase, and a 20% handoff rate. (b) With an average of 91.83 calls per hour, an 80% traffic load increase, and a 20% handoff rate. EMC constraint included: CCC.
Fig. 14. Performance of adaptive and nonadaptive GASC schemes to channel failure. The dropping probability of handoff calls as a function of time is evaluated. The time interval of a seven-channel failure is from 10:00 to 15:00. See Fig. 13 for cases (a) and (b) of nonuniform traffic distribution. EMC constraint included: CCC.
the GASC tends to return to its optimum performance faster than the nonadaptive GASC. Concerning handoff calls (Fig. 14), the two schemes show low values of dropping probabilities before and after the fault occurrence. In contrast with the performance shown by the GASC for new calls (Fig. 13), the dropping probabilities for handoff calls for the adaptive scheme are higher than the corresponding values for the nonadaptive scheme. As the adaptive parameters were adjusted to reach the best performance, low blocking probability of new calls is achieved with a slight increase in the dropping probability of handoff calls since fewer resources remain to assign them. As a last comment on these results, note that the overall performance of the GASC, adding the blocking probability
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TABLE I AVERAGE NUMBER OF GENERATIONS AS A FUNCTION OF TRAFFIC LOAD INCREASE FOR GALC AND GASC SCHEMES
of new calls and the dropping probability of handoff calls, is always better than that of the nonadaptive GASC. D. Algorithm Convergence Evaluation To estimate the velocity of the algorithms to perform each optimization process (occurring at each sample interval of the telecommunication system), the average number of generations to each traffic load increase is presented in Table I. Nonuniform traffic distribution with an average of 91.83 calls per hour, a 20% handoff rate, and 75 individuals is assumed. The cochannel constraint (ccc = 1) is included in all cases. For the slowest case (an 80% traffic increase, csc = 2, acc = 2, and a 20% handoff rate), the GASC takes, on average, 110.38 generations to allocate new and handoff call requests. The average number of generations ranges from 15.40 to 110.38, which is an appropriate range of values for a dynamic operation. The results shown in Table I suggest that a maximum number of 100 generations is good enough for the GALC and GASC to produce a solution. Furthermore, such a solution can be produced within a time interval that is compatible with the real operation: For instance, on a Pentium-IV 2.2-GHz 512-MB PC, the convergence of the GASC for the slowest case took about 136 ms. V. C ONCLUSION In this paper, two strategies using adaptive GAs were proposed to solve the DCA problem in mobile cellular communi-
cation systems. Given the environment behavior and the traffic load demand, the optimal channel assignment involved the dynamic determination of the way to distribute the channels among the cells in order to minimize the blocking probability of new calls and the dropping probability of handoff calls while simultaneously satisfying the three electromagnetic constraints CCC, ACC, and CSC. The GALC and GASC present one main difference between themselves: The former does not reallocate channels for calls in progress, whereas the latter does. Both models included a number of mechanisms to increase the efficiency and the convergence speed of the GAs to use them in online real-world applications. Computer simulations of nonuniform load traffic in a benchmark cellular environment showed that the performance of the proposed algorithms was good. The parameters and adaptive functions of the GAs were chosen after many simulations pursuing the lowest blocking probabilities of new calls and low dropping probability of handoff calls under a number of traffic load conditions. This adaptation strategy yields suitable levels of blocking and dropping probabilities. The overall performances of the GALC and GASC were better than those of the DCA strategies based on Q-learning and FCA based on BDCL schemes, which were both better than the FCA schemes that were previously reported in the literature. It is worth mentioning that the canonical GA, which is characterized by roulette parent selection, pairwise tournament selection, one-point crossover, standard mutation, and the current fitness function, was initially attempted to solve this DCA problem. As expected, this option was discarded because it showed poor performance due to the features of the DCA problem: 1) changes in the network load and demands characterizing a new optimization problem at each time step; 2) presence of simultaneous disturbance caused by the three EMC constraints; 3) priority necessary to handoff calls; and 4) short time interval to provide a solution. To achieve optimal or suboptimal solutions, the proposed GAs included the ability to adapt their own parameters [24], [25] to respond to different characteristics of the DCA problem at each time step. The strategy to adapt the GA parameters aimed to vary them as a function of diversity to balance exploration and exploitation. Hence, the parameters of (3)–(5) might need a new setup for a different cellular configuration; however, the consistent results suggest that the strategy to adapt the GA parameters remains valid for any arrangement. Furthermore, auxiliary mechanisms such as immigration and elitism schemes were considered to accelerate the convergence of the GAs. The impact of EMC constraints on the blocking probability of new calls and the dropping probability of handoff calls was investigated, showing that adjacent channel interference can strongly decrease the performance of both strategies. Tests for equipment failures, which were carried out, showed robust performance of the two adaptive GA schemes and the ability to return to the best performance levels following the fault cessation. The overall performance of the GASC is better than that of the GALC, except for some particular situations. The GALC
LIMA et al.: ADAPTIVE GAs FOR DCA IN MOBILE CELLULAR COMMUNICATION SYSTEMS
showed similar performance to the BDCL strategy for moderate traffic load, as confirmed in Fig. 6. Its performance for both new and handoff calls is adequate (2% of blocking probability of new calls and dropping probability of handoff calls), considering moderate traffic load, nonsevere EMC, and long range of traffic load increase, as shown in Figs. 10 and 12. Also, the GALC showed robustness in operation under channel faults, as shown in Fig. 12, in spite of its higher blocking probability than the GASC. Moreover, the GALC can be useful in such cases in which a system cannot operate properly under a large number of channel switching as the GASC demands. In particular, we are reminded that switching can demand time to be executed, and the call can be dropped due to hardware failure. In this paper, we used the conventional model of cellular systems in which the location of the mobile station is considered anywhere within the cell. However, techniques of channel assignment based on signal strength measurement, minimum interference, or power control can be implemented, exploring the GAs capacity to handle impairments through strategies to solve constrained optimization problems. Moreover, if the number of cells and channels increase, the desired optimum or suboptimum can still be reached at the expense of the growth of the population size and/or the number of generations that the GA takes to converge. Hence, different environment characteristics can demand distinct GA parameters, as usual. Considering future work, we could suggest the extension of the algorithms for resource management as time slots in time-division multiple access or pseudonoise code in codedivision multiple access. Particularly, the bandwidth is a limited resource, and its efficient management is of great importance, wherein different levels of quality of service must be attained. A number of constraints and objectives are added to the procedures, increasing their suitability for GA solutions.
ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for their valuable comments and suggestions.
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[8] S. Anand, A. Sridharan, and K. N. Sivarajan, “Performance analysis of channelized cellular systems with dynamic channel allocation,” IEEE Trans. Veh. Technol., vol. 52, no. 4, pp. 847–859, Jul. 2003. [9] S. Borst and P. Whiting, “Achievable performance of dynamic channel assignment schemes under varying reuse constraints,” IEEE Trans. Veh. Technol., vol. 49, no. 4, pp. 1248–1254, Jul. 2000. [10] N. Funabiki, T. Nakanishi, T. Yokohira, S. Tajima, and T. Higashino, “A quasi-solution state evolution algorithm for channel assignment problems,” IEICE Trans. Fundam., vol. E85-A, no. 5, pp. 977–987, May 2002. [11] J. Nie and S. Haykin, “A Q-learning dynamic channel assignment technique for mobile communication systems,” IEEE Trans. Veh. Technol., vol. 48, no. 5, pp. 1676–1687, Sep. 1999. [12] J. Nie and S. Haykin, “A dynamic channel assignment policy through Q-learning,” IEEE Trans. Neural Netw., vol. 10, no. 6, pp. 1443–1455, Nov. 1999. [13] A. Quintero and S. Pierre, “Sequential and multi-population mimetic algorithms for assigning cells to switches in mobile networks,” Comput. Netw.—Int. J. Comput. Telecommun. Netw., vol. 43, no. 3, pp. 247–261, Oct. 22, 2003. [14] B. Ombuki, B. J. Ross, and F. Hanshar, “Multi-objective genetic algorithms for vehicle routing problem with time windows,” Appl. Intell., vol. 24, no. 1, pp. 17–30, Feb. 2006. [15] J. P. B. Leite and B. H. V. Topping, “Improved genetic operators for structural engineering optimization,” Adv. Eng. Softw., vol. 29, no. 7–9, pp. 529–562, Aug./Nov. 1998. [16] W. K. Lai and G. G. Coghill, “Channel assignment through evolutionary optimization,” IEEE Trans. Veh. Technol., vol. 45, no. 1, pp. 91–96, Feb. 1996. [17] Y. Ngo and V. O. K. Li, “Fixed channel assignment in cellular radio networks using a modified genetic algorithm,” IEEE Trans. Veh. Technol., vol. 47, no. 1, pp. 163–172, Feb. 1998. [18] A. Yener and C. Rose, “Genetic algorithms applied to cellular call admission: Local policies,” IEEE Trans. Veh. Technol., vol. 46, no. 1, pp. 72–79, Feb. 1997. [19] J. Yoshino and I. Ohtomo, “Study on efficient channel assignment method using the genetic algorithm for mobile communication systems,” Soft Comput., vol. 9, no. 2, pp. 143–148, Feb. 2005. [20] C. Y. Lee, H. G. Kang, and T. Park, “Dynamic sectorization of microcells for balanced traffic in CDMA: Genetic algorithms approach,” IEEE Trans. Veh. Technol., vol. 51, no. 1, pp. 63–72, Jan. 2002. [21] W. C. Y. Lee, Mobile Cellular Telecommunications Systems. New York: McGraw-Hill, 1990. [22] J. Hesser, R. Manner, and O. Stucky, “Optimization of Steiner trees using genetic algorithms,” in Proc. 3rd ICGA, Arlington, VA, Jun. 1989, pp. 231–232. [23] K. F. Man, K. S. Tang, and S. Kwong, “Genetic algorithms: Concepts and designs,” IEEE Trans. Ind. Electron., vol. 43, no. 5, pp. 519–534, Oct. 1996. [24] A. E. Eiben, R. Hinterding, and Z. Michalewicz, “Parameter control in evolutionary algorithms,” IEEE Trans. Evol. Comput., vol. 3, no. 2, pp. 124–141, Jul. 1999. [25] C. W. Ahn and R. S. Ramakrishna, “A genetic algorithm for shortest path routing problem and the sizing of populations,” IEEE Trans. Evol. Comput., vol. 6, no. 6, pp. 566–579, Dec. 2002.
R EFERENCES [1] K.-N. Chang and S. Kim, “Channel allocation in cellular radio networks,” Comput. Oper. Res., vol. 24, no. 9, pp. 849–860, Sep. 1997. [2] R. Fantacci, “Performance evaluation of prioritized handoff schemes in mobile cellular networks,” IEEE Trans. Veh. Technol., vol. 49, no. 2, pp. 485–493, Mar. 2000. [3] I. Katzela and M. Naghshineh, “Channel assignment schemes for cellular mobile telecommunication systems: A comprehensive survey,” IEEE Pers. Commun., vol. 3, no. 3, pp. 10–31, Jun. 1996. [4] S. Yamanaka, H. Kawano, and Y. Takahashi, “Modeling and performance analysis of cellular networks with channel borrowing,” IEICE Trans. Commun., vol. E85-B, no. 5, pp. 929–937, 2002. [5] M. Zhang and T. S. P. Yum, “Comparisons of channel-assignment strategies in cellular mobile telephone systems,” IEEE Trans. Veh. Technol., vol. 38, no. 4, pp. 211–215, Nov. 1989. [6] A. A. Bertossi, C. M. Pinotti, and R. B. Tan, “Channel assignment with separation for interference avoidance in wireless networks,” IEEE Trans. Parallel Distrib. Syst., vol. 14, no. 3, pp. 222–235, Mar. 2003. [7] S. Sakar and K. N. Sivarajan, “Channel assignment algorithms satisfying cochannel and adjacent channel reuse constraints in cellular mobile networks,” IEEE Trans. Veh. Technol., vol. 51, no. 5, pp. 954–967, Sep. 2002.
Marcos A. C. Lima received the B.Sc. degree in electrical engineering from the Federal University of Goiás, Goiânia, Brazil, in 1996, the M.Sc. degree in electrical engineering from the Federal University of Santa Catarina, Florianópolis, Brazil, in 1999, and the Ph.D. degree in electrical engineering from the University of São Paulo, São Carlos, Brazil, in 2005. He is currently with the University of São Paulo. His areas of interest include evolutionary computation and its application for resource allocation problems in wireless and optical networks, design of microwaves, and optical devices.
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Aluízio F. R. Araújo was born in Recife, Brazil, in 1957. He received the B.S. degree in electrical engineering from Federal University of Pernambuco, Recife, in 1980, the M.S. degree in electrical engineering from the State University of Campinas, Campinas, Brazil, in 1988, and the D.Phil. degree in computer science and artificial intelligence from the University of Sussex, Brighton, U.K., in 1994. He was with the São Francisco Hidroelectrical Company for five years, and in 1998, he became an Assistant Professor with the University of São Paulo, São Carlos, Brazil, where, in 1994, he was promoted to Adjunct Professor. Since 2003, he has been with the Federal University of Pernambuco. He has published 23 papers in international or national journals and more than 80 papers in international or national conferences. His research interests are in the areas of neural networks, machine learning, robotics, dynamic systems theory, and cognitive science.
Amílcar C. César (M’07) received the B.S. degree in electrical engineering from the University of São Paulo, São Carlos, Brazil, in 1976 and the M.S. and Ph.D. degrees in electrical engineering from the State University of Campinas, Campinas, Brazil, in 1982 and 1990, respectively. Since 1977, he has been with the Department of Electrical Engineering, School of Engineering of São Carlos, University of São Paulo, where he is currently an Associate Professor. His areas of interest include algorithms for resource allocation in wireless and optical networks and computational modeling of waveguides for microwaves, millimeter waves, and optical applications.
