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International audience; 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.

This chapter gives an insight into some challenging combinatorial optimization problems that have to be tackled to deliver efficient and appropriate decision algorithms to manage future networks. The first part of the chapter is dedicated to variants of routing optimization problems in future IP networks, and the second part is dedicated to two optimization problems related to network virtualization and 5G network slicing, the virtual network embedding problem and the service function chaining problem. Each of these optimization problems is described along with the main challenges to overcome, and a recent and extensive related state of the art is given, so as to highlight the most recent and promising approaches to solve them.

We consider the Capacitated Multi-Layer Network Design with Unsplittable demands (CMLND-U) problem. Given a two-layer network and a set of traffic demands, this problem consists in installing minimum cost capacities on the upper layer so that each demand is routed along a unique “virtual” path (even using a unique capacity on each link) in this layer, and each installed capacity is in turn associated a “physical” path in the lower layer. This particular hierarchical and unsplittable requirement for routing arises in the design of optical networks, including optical OFDM based networks. In this paper, we give an ILP formulation to the CMLND-U problem and we take advantage of its sub-problems to provide a partial characterization of the CMLND-U polytope including several families of facets. Based on this polyhedral study, we develop a Branch-and-Cut algorithm for the problem and show its effectiveness though a set of experiments, conducted on SNDlib-derived instances and also on real instances.

We consider a mobile market driven by two Mobile Network Operators (MNOs) and a new competitor Mobile Virtual Network Operator (MVNO). The MNOs can partner with the entrant MVNO by leasing network resources; however, the MVNO can also rely on other technologies such as free WiFi access points. Moreover, in addition to its connectivity offer, the MVNO can also draw indirect revenues from services due to its brand. In that framework including many access technologies and several revenue sources, a possible partner MNO will then have to decide which wholesale price to charge the MVNO for its resources. This multi-actor context, added to the need to consider both wholesale and retail markets, represents a new challenge for the underlying decision-making process. In this paper, the optimal price setting is formulated as a multi-level optimization problem which enables us to derive closed-form expressions for the optimal MNOs wholesale prices and the optimal MVNO retail price. The price attractivity of the MVNO is also evaluated in terms of its indirect revenues and the proportion of resources leased from possible partner MNOs. Finally, through a game-theoretical approach, we characterize the scenario where both MNOs partner with the MVNO as the unique Nash equilibrium under appropriate conditions., Accepted in IFIP Networking 2018. Key words: Network Economics, Strategic Partnership, Multi-Level Optimization, Non-Cooperative Game Theory

We investigate a variant of the Multi-Layer Network Design problem where minimum cost capacities have to be installed upon a virtual layer in such a way that (i) a set of traffic demands can be routed AND (ii) each capacity (subband) is assigned a route in the physical layer. The traffic demands cannot be splitted along several paths (nor even several capacities installed on the same link), which makes the problem even more difficult. In this paper, we present new non-compact ILP formulations to model the problem and provide column generation procedures, based on different Dantzig-Wolfe decomposition schemes to solve it. More precisely, an arc-flow formulation is given for the problem and used to derive two different paths formulations: non-aggregated and aggregated. The former contains two families of path variables and requires a double column generation procedure to solve it, while the latter relies on a single path variable with a specific structure. These alternative modeling approaches induce two Branch-and-Price algorithms that allow to solve the problem efficiently for several classes of instances.

In this paper we consider the traffic Grooming, Routing and Wavelength Assignment problem in optical WDM mesh networks. This is a network design problem which consists in grooming the demands in lightpaths, assigning a wavelength to each lightpath and routing the traffic on these lightpaths so that the total cost is minimum. We first give an Integer Linear Programming formulation for the problem. Then we discuss a preprocessing procedure for efficiently managing the existing resources of the network. We then propose a fast and effective heuristic for solving large and real instances of the problem. We finally provide an illustrative application of the proposed heuristic for a real backhaul network instance.