Optimal Capacity Planning in Multi-Radio Multi-Channel Wireless Networks

In this paper, we study how to compute the optimal capacity planning in a multi-radio multi-channel (MR-MC) wireless network, that is, to find solutions for a set of coupled problems including channel assignment, scheduling, and routing, with the objective to optimize network capacity. The current state of the art mainly resorts to formulation of a mixed integer programming problem, which is NP-hard in general, and then computes an approximate solution to such a problem. We develop a novel concept of multi-dimensional conflict graph (MDCG) in this paper. Based on MDCG, the optimal capacity planning can be modeled as a linear programming (LP) multi-commodity flow (MCF) problem, augmented with constraints derived from the MDCG. The MDCG-based MCF solution will provide not only the maximum throughput or utility, but also the optimal channel assignment, scheduling and routing to achieve it. Moreover, the MDCG-based optimal capacity planning can exploit dynamic channel swapping, which is difficult to achieve for those existing heuristic algorithms. Numerical results are presented to demonstrate the efficiency of the MDCG-based capacity planning, with comparison to the well-known heuristic algorithm presented in [1].