Asymptotic-Diffusion Analysis for Retrial Queue with Batch Poisson Input and Multiple Types of Outgoing Calls

Abstract

In this paper, we consider a retrial queue with batch Poisson input process, arbitrarily distributed service times and arbitrarily distributed number of calls in the batch. Upon arrival, a call from the batch occupies the server if it is idle. The other calls from the batch join the orbit. If the server is busy, all calls from the batch go to the orbit. In the orbit, incoming calls stay for an exponentially distributed random delay and repeat their request for service. Besides incoming calls, the server can also make outgoing calls when idle. We assume that there are several types of outgoing calls in the system. The aim of the current research is to obtain asymptotic probability distribution of the number of incoming calls in the system using an asymptotic-diffusion analysis method.