On Overflow Processes of Trunk Groups with Poisson Inputs and Exponential Service Times

Abstract

Recurrence formulas for the Laplace transforms and the moments of the interoverflow distributions are obtained under the assumptions that the traffic offered is random (Poissonian) and that the service times are independent of each other and have a common negative exponential law. Under the same assumptions, it is also shown that the distribution of the nonbusy period of a group of c trunks is identical to the interoverflow distribution of a group of c — 1 trunks and that the distribution of the number of consecutive successful calls is essentially a mixture of geometric distributions. Processes obtained by superposing two or more overflow processes from independent trunk groups are not of the renewal type because interoverflow intervals are no longer independent. It is shown here that the correlation between two consecutive interoverflow intervals of a composite overflow process is always positive.