Queuing model-based optimal traffic flow in a grid network

A transportation network describes a network structure to allow flow of some commodity. Flow maximization is a classical problem in this domain. In this paper, we address the problem of flow maximization in a transportation network with fix sources and a fixed sink. For simplicity to find an analytical solution, we start with a grid structured road network. The goal is to find a traffic distribution over the road network such that the total average time of travel from source to sink is minimized. The theoretical result obtained was verified using linear programming problem solving tool in MATLAB.