Mobile relay deployment based on Markov chains in WiMAX networks

In WiMAX networks with fixed relay stations (FRSs), mobile users move in and out of the coverage area of FRS in different periods of a day. Frequent handover requests generated by population mobility lead to load imbalances among FRSs and low data rate. Mobile relay stations (MRSs), which can shift between FRSs, can share part of the users´ requests, then reduce the burden of FRSs. In this paper, we define and study the Minimum Mobile Relay Path selection problem (MMRP), whose objective is to deploy minimum MRSs to patrol FRSs according to their busy durations. To reflect the FRSs´ real situation, Markov chains are adopted to predict FRSs´ busy durations which are then represented as a weighted graph. Based on this graph, the original problem is transformed into a Minimum Vertex-disjoint Path Cover problem. After analyzing properties of the weighted graph, we propose the algorithms based on the principles of graph searching, maximum matching and the maximum flow, respectively. Theoretical analysis and simulation results show that, compared with traditional search algorithms, solutions based on maximum matching and the maximum flow have lower complexity, yet better performance on the number of paths and system overhead, and the solution using predicted busy durations is superior to those in paths gains whose busy duration is presupposed.