In this paper, we explore the Mobile Investment Strategy (MIS) problem within the French telecommunications market, which includes four Mobile Network Operators (MNOs): Bouygues Telecom, SFR, Free, and Orange France (OFR). We adopt the perspective of OFR, the incumbent operator, focusing on its critical network investment decisions related to the deployment of the latest mobile network technologies. Additionally, we examine user responses to the investment choices made by each MNO, a dynamic significantly shaped by competitive forces. To model and address the MIS problem, we propose a Mixed-Integer Non-Linear Program (MINLP), which we linearize and enhance by incorporating historical data from various datasets to empirically evaluate its performance.

Virtual Network Embedding (VNE) is an optimization problem at the core of many modern network telecommunication technologies related to the implementation of virtual networks, such as Network Slicing. The VNE problem consists in finding an optimal assignment of virtual demands to physical resources, encompassing simultaneous placement and routing decisions.We study the offline version of the VNE, which arises in the context of decision-making for resource allocation and network slice planning. For large networks, the heuristics of the literature often struggle to find solutions, especially when available resources (on nodes and edges) are sparse.To address these challenges, we explore mathematical programming approaches. Since the classical Flow Formulation provides a weak linear relaxation, we consider a novel formulation, based on a partition of the virtual graph into smaller virtual subgraphs. Since this formulation has an exponential number of variable, its linear relaxation can be solved with Column Generation. We devise a Price-Branch heuristic able to solve large instances, while providing optimality gap. The resulting computational experiments indicate our Price-Branch heuristic is often the only algorithm able to find a solution from a certain instance size, largely outperforming the Flow Formulation or literature heuristics.

In this paper, we consider the Unsplittable Shortest Path Routing (USPR) problem which arises in the field of traffic engineering for IP networks. This problem consists, given a bidirected graph and a set of commodities, to compute a set of routing paths and the associated link weights such that each commodity is routed along the unique shortest path between its origin and its destination, according to these weights. In this paper, we propose a novel extended formulation based on routing variables that is solved using a column generation procedure, further enriched by primal heuristics allowing to build of an efficient matheuristic. We show through a set of experiments that our algorithm allows to quickly identify good feasible solutions when compared to the results obtained by the state-of-the-art local search algorithm.

When adopting a novel mobile technology, a mobile network operator faces the dilemma of determining which is the best time to start the installation of next generation equipment onto the existing infrastructure. In a strategic context, the best possible time for deployment is also the best response to competitors’ actions, subject to normative and material constraints and to the customer’s adoption curve. We formulate in this paper a finite discrete-time game which captures the main features of the problem for a two-player game played over a prescribed finite horizon. Our numerical results provide insights on the possible optimal tradeoffs for an operator between fixed costs and installation strategies.

We model the network slice provisioning as an optimization problem including novel mapping and provisioning requirements rising with new radio and core function placement policies. We propose an open-access framework based on an MILP formulation that encompasses flexible functional splitting, with possibly different splitting for different slices and slice subnets, while taking into account different network sharing policies from 5G specifications. We also consider novel mapping and continuity constraints specific to the 5G architectures and beyond. We show by numerical simulations the impact of taking into full and partial consideration these peculiar novel technical constraints.

In this work, we model the network slice provisioning as an optimization problem including novel mapping and provisioning requirements rising with new 5G radio and core function placement policies. We propose an MILP-based formulation that joins different functional splitting strategies with different network function sharing policies and novel mapping continuity constraints from 5G specifications. We show by numerical simulations the impact of taking into full and partial consideration these peculiar sets of novel technical constraints.

International audience