Optimal Admission Control in Damper-Based Networks: Branch-and-Price Algorithm

This paper presents a study of the optimal Admission Control in Damper-based Networks (ACDN) problem. The use of dampers in large-scale networks is becoming increasingly beneficial for a wide range of applications as it provides a reliable means of achieving deterministic delay guarantees without the need for synchronization between routers. In this context, optimal admission control solutions are required to fully utilize capacity. The problem being studied is a variant of the Unsplittable Multi-Commodity Flow (UMCF) problem, with additional constraints related to forwarding and shaping. This paper proposes two Integer Linear Programming (ILP) formulations to address the ACDN problem. The former is a compact formulation, which is solved using the CPLEX solver. The latter is an extended path formulation, for which a Branch-and-Price algorithm is developed, including a column generation procedure, an efficient branching scheme, and reinforced by a primal heuristic. Tests on realistic instances show that solving the path formulation using the Branch-and-Price algorithm is better than solving the compact formulation using CPLEX. Our algorithm divides by 14 the average running time given by CPLEX, and the path formulation gives a stronger linear relaxation with an average optimally gap of 0.3%. This work builds upon previous research [1] that developed a heuristic for finding near-optimal solutions, and instead aims to find exact optimal solutions for ACDN.