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We propose a model of incentives for data pricing in large mobile networks,in which an operator wishes to balance the number of connections (active users)of different classes of users in the different cells and at different timeinstants, in order to ensure them a sufficient quality of service. We assumethat each user has a given total demand per day for different types ofapplications, which he may assign to different time slots and locations,depending on his own mobility, on his preferences and on price discountsproposed by the operator. We show that this can be cast as a bilevelprogramming problem with a special structure allowing us to develop apolynomial time decomposition algorithm suitable for large networks. First, wedetermine the optimal number of connections (which maximizes a measure ofbalance); next, we solve an inverse problem and determine the prices generatingthis traffic. Our results exploit a recently developed application of tropicalgeometry methods to mixed auction problems, as well as algorithms in discreteconvexity (minimization of discrete convex functions in the sense of Murota).We finally present an application on real data provided by Orange and we showthe efficiency of the model to reduce the peaks of congestion.

A bilevel optimization model for load balancing in mobile networks through price incentives