Optimization of scheduling in wireless ad-hoc networks using matrix games

In this paper, we present a novel application of matrix game theory for optimization of link scheduling in wireless ad-hoc networks. Optimum scheduling is achieved by soft coloring of network graphs. Conventional coloring schemes are based on assignment of one color to each region or equivalently each link is member of just one partial topology. These algorithms based on coloring are not optimal when links are not activated with the same rate. Soft coloring, introduced in this paper, solves this problem and provide optimal solution for any requested link usage rate. To define the game model for optimum scheduling, first all possible components of the graph are identified. Components are defined as sets of the wireless links can be activated simultaneously without suffering from mutual interference. Then by switching between components with appropriate frequencies (usage rate) optimum scheduling is achieved. We call this kind of scheduling as soft coloring because any links can be member of more than one partial topology, in different time segments. To simplify this problem, we model relationship between link rates and components selection frequencies by a matrix game which provides a simple and helpful tool to simplify and solve the problem. This proposed game theoretic model is solved by fictitious playing method. Simulation results prove the efficiency of the proposed technique compared to conventional scheduling based on coloring.