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

## TL;DR

This paper introduces a bilevel optimization model using price incentives to balance load in mobile networks, employing advanced mathematical techniques and demonstrating effectiveness with real data to reduce congestion peaks.

## Contribution

It develops a polynomial-time decomposition algorithm for a bilevel pricing model in mobile networks, integrating tropical geometry and discrete convexity methods.

## Key findings

- Efficient load balancing reduces network congestion peaks.
- The model performs well on real Orange network data.
- The approach is scalable to large networks.

## Abstract

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 time instants, in order to ensure them a sufficient quality of service. We assume that each user has a given total demand per day for different types of applications, which he may assign to different time slots and locations, depending on his own mobility, on his preferences and on price discounts proposed by the operator. We show that this can be cast as a bilevel programming problem with a special structure allowing us to develop a polynomial time decomposition algorithm suitable for large networks. First, we determine the optimal number of connections (which maximizes a measure of balance); next, we solve an inverse problem and determine the prices generating this traffic. Our results exploit a recently developed application of tropical geometry methods to mixed auction problems, as well as algorithms in discrete convexity (minimization of discrete convex functions in the sense of Murota). We finally present an application on real data provided by Orange and we show the efficiency of the model to reduce the peaks of congestion.