A compact normal walk model for PCS networks

Abstract

Model-based movement patterns play a crucial role in evaluating the performance of mobility-dependent Personal Communication Service (PCS) strategies. This study proposes a new normal walk model to represent more closely the daily movement patterns of a mobile station (MS) in PCS networks than a conventional random walk model. The proposed walk model uses a drift angle θ to determine the direction in which an MS leaves a hexagonal cell in the next one step. The angle θ is assumed to approach the normal distribution with the parameters: μ = 0° and σ is on the interval [5°; 90°], based on the concept that most trips follow the shortest path, to make the movement patterns more realistic. A compact classification that types cells with side indices is further developed to partition an n-layer cluster of PCS networks into 12 mirror regions; consequently, the number of states can be reduced significantly, and the computational complexity is also reduced in the probability derivation. Two metrics are formulated in experiments to measure the expected and average numbers of steps taken by an MS to move out of an n-layer cluster. Experimental results confirm that for σ = 10°, 30°, 60°, and 90°, the discrepancies between the analytical computations and the simulated values are all within ±0.46%, and most are even within ±0.35%. Moreover, when σ is set to 71°, a normal walk can almost represent, and even replace, a conventional random walk, since the discrepancies between them are all within ±0.71%.