Classical coverage models, adopted for second-generation cellular systems, are not suited for planning universal mobile telecommunication system (UMTS) base station (BS) location because they are only based on signal predictions and do not consider the traffic distribution, the signal quality requirements, and the power control (PC) mechanism. In this paper, we propose discrete optimization models and algorithms aimed at supporting the decisions in the process of planning where to locate new BSs. These models consider the signal-to-interference ratio as quality measure and capture at different levels of detail the signal quality requirements and the specific PC mechanism of the wideband CDMA air interface. Given that these UMTS BS location models are nonpolynomial (NP)-hard, we propose two randomized greedy procedures and a tabu search algorithm for the uplink (mobile to BS) direction which is the most stringent one from the traffic point of view in the presence of balanced connections such as voice calls. The different models, which take into account installation costs, signal quality and traffic coverage, and the corresponding algorithms, are compared on families of small to large-size instances generated by using classical propagation models.Index Terms-Code-division multiple access (CDMA), optimization algorithms, optimization models, planning, power control (PC), universal mobile telecommunication system (UMTS).
Radio planning and coverage optimization are critical issues for service providers and vendors that are deploying third generation mobile networks and need to control coverage as well as the huge costs involved. Due to the peculiarities of the Code Division Multiple Access (CDMA) scheme used in 3G cellular systems like UMTS and CDMA2000, network planning cannot be based only on signal predictions, and the approach relying on classical set covering formulations adopted for second generation systems is not appropriate.In this paper we investigate mathematical programming models for supporting the decisions on where to install new base stations and how to select their configuration (antenna height and tilt, sector orientations, maximum emission power, pilot signal, etc.) so as to find a trade-off between maximizing coverage and minimizing costs. The overall model takes into account signal-quality constraints in both uplink and downlink directions, as well as the power control mechanism and the pilot signal.Preliminary results have been presented in [5,7,8].Since even small and simplified instances of this NP-hard problem are beyond the reach of state-of-the-art techniques for mixed integer programming, we propose a Tabu Search algorithm which provides good solutions within a reasonable computing time. Computational results obtained for realistic instances, generated according to classical propagation models, with different traffic scenarios (voice and data) are reported and discussed.
We consider two approaches for solving the classical minimum vertex coloring problem, that is the problem of coloring the vertices of a graph so that adjacent vertices have different colors, minimizing the number of used colors, namely Constraint Programming and Column Generation. Constraint Programming is able to solve very efficiently many of the benchmarks, but suffers from the lack of effective bounding methods.On the contrary, Column Generation provides tight lower bounds by solving the fractional vertex coloring problem exploited in a Branch-and-Price algorithm, as already proposed in the literature. The Column Generation approach is here enhanced by using Constraint Programming to solve the pricing subproblem and to compute heuristic solutions. Moreover new techniques are introduced to improve the performance of the Column Generation approach in solving both the linear relaxation and the integer problem. We report extensive computational results applied to the benchmark instances: we are able to prove optimality of 11 new instances, and to improve the best known lower bounds on other 17 instances. Moreover we extend the solution approaches to a generalization of the problem known as Minimum Vertex Graph Multicoloring Problem where a given number of colors has to be assigned to each vertex.
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