A Finite Population Model and Product-Form Approximation for Cellular Mobile Systems with Traveling Users

We propose a new finite population model for cellular mobile systems with traveling users. In this model, mobile users arrive according to a Poisson process from outside the system, independently travel in the system, and leave the system in due time. A mobile user is either in call (active) or out of call (inactive). We find that if two minor modifications are made to the model, the joint distribution of the number of calls in progress in each cell has the product form. Making the two modifications is referred to as product-form approximation in this paper. Under the product-form approximation, the call blocking probability or the hand-off blocking probability is given by the Erlang-loss formula. We evaluate the accuracy of the product-form approximation through several simulation experiments, and find that the Erlang-loss formula gives accurate estimates of call-blocking probability in most of cases. Our work would give theoretical justification for applying the Erlang-loss formula to the performance analysis or channel provisioning of cellular mobile systems.