New random walk model for PCS networks

This paper proposes a new approach to simplify the two-dimensional random walk models capturing the movement of mobile users in Personal Communications Services (PCS) networks. Analytical models are proposed for the new random walks. For a PCS network with hexagonal configuration, our approach reduces the states of the two-dimensional random walk from (3n² + 3n - 5) to n(n + 1)/2, where n is the layers of a cluster. For a mesh configuration, our approach reduces the states from (2n² - 2n + 1) to (n² + 2n + 4)/4 if n is even and to (n² + 2n + 5)/4 if n is odd. Simulation experiments are conducted to validate the analytical models. The results indicate that the errors between the analytical and simulation models are within 1%. There applications (i.e., microcell/macrocell configuration, distance-based location update, and GPRS mobility management for data routing) are used to show how our new model can be used to investigate the performance of PCS networks.