Wireless mobile backhaul networks have been proposed as a substitute in cases in which wired alternatives are not available due to economical or geographical reasons. In this work, we study the location problem of base stations in a given region where mobile terminals are distributed according to a certain probability density function and the base stations communicate through microwave backhaul links. Using results of optimal transport theory, we provide the optimal asymptotic distribution of base stations in the considered setting by minimizing the total power over the whole network.
Location games have been introduced by Hotelling @cite_0 , who modeled the spatial competition along a street between two firms for persuading the largest number of customers which are uniformly distributed. Problems similar to location games, as for example the maximum capture problem, have been analyzed by @cite_4 @cite_5 and references therein.
@cite_0 @cite_5 @cite_4
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After the work of the late Professor F. Y. Edgeworth one may doubt that anything further can be said on the theory of competition among a small number of entrepreneurs. However, one important feature of actual business seems until recently to have escaped scrutiny. This is the fact that of all the purchasers of a commodity, some buy from one seller, some from another, in spite of moderate differences of price. If the purveyor of an article gradually increases his price while his rivals keep theirs fixed, the diminution in volume of his sales will in general take place continuously rather than in the abrupt way which has tacitly been assumed. Abstract We give an overview of the research, models and literature about optimisation approaches to the problem of optimally locating one or more new facilities in an environment where competing facilities are already established.