Mobility models and biased sampling problem

In studies of cellular networks, such as the performance analysis of handoff or location update, mobility models for mobile terminals play a very important role. Several mobility models have been proposed in the previous studies, each of them depicts the terminal mobility by a simple method. In this paper, the authors studied Thomas's, Hong's and Guerin's mobility models. They find that Thomas's formula for outgoing terminals can be extended to the other two models. Thus, some system performance information derived from Thomas' model can also be used in the other two models. In the next analysis of a mobility model, the probability density function (PDF) of terminal speeds is a very important condition. For a given PDF for total terminals, a subset of terminals, such as the boundary-crossing terminals of the speed-renewing terminals (if the model requires speed-renewing), may have a different PDF, which follows the "Biased Sampling" formula. The PDF of moving directions at boundaries is also biased. The proposed formulas, boundary conditions and renewal conditions can be used as the basic components for the future studies of cellular systems.