Insensitive light traffic in a cellular system with mobile subscribers

We consider the problem of finding a light traffic limit for the stationary state distribution of a single cell, called the tagged cell, in a cellular system with mobile subscribers (customers). The number of channels in the tagged cell is finite. Customers in the adjacent cells move to this cell according to a Poisson process whose rate may depend on the number of customers in the tagged cell. The sojourn times of customers in the tagged cell have an exponential distribution. Each customer in the system is characterized as active (having a call in progress) or inactive. Each inactive customer in the tagged cell generates a call according to an exponential distribution. The duration time (service time) of each call in the system has a general distribution. Yamazaki and Toshimitsu derived a light traffic limit for stationary distribution of the two-state stochastic process denoting the total number of customers and the number of active customers in the tagged cell when the service time distribution is exponential. In this paper, we show that the light traffic limit is insensitive with respect to the service time distribution.