Light traffic in a cellular system with mobile subscribers and its applications

This paper is concerned with a cellular system with mobile subscribers (customers). This system consists of a cell, called the tagged cell, and its adjacent cells. Each cell has some finite number of channels. The sojourn times of customers in the tagged cell have an exponential distribution. Customers in the adjacent cells move to the tagged cell according to a Poisson process whose rate depends on the number of customers in the tagged cell. Each customer without call in progress generates his call according to an exponential distribution and the channel holding times of calls at each cell have a common exponential distribution. We first show that under some restriction, the light traffic limit for the stationary state distribution in the tagged cell is given by a mixture of a Poisson and binominal distributions. Based on the limit, we develop formulae for evaluating the hand-off and blocking probabilities and the mean number of busy channels in the tagged cell. Several numerical examples are presented that demonstrate the practical usefulness of the formulae.