A queueing model in an alternating random environment

In this paper, we consider a single server queueing model with alternately varying Poisson arrival rates. Such arrival processes are usually modelled using the Doubly Stochastic Poisson (DSP) processes whose Poisson rates vary alternately and remains the same during an exponential time duration called a switching time. Queues with the DSP arrival processes are often employed to describe production, computer and communication systems. A DSP process includes both renewal and nonrenewal point processes. Since performance measures of a single server queue with a DSP input are difficult to evaluate, we approximate a DSP arrival process by a renewal process. We then use parameters so developed in an expression for the expected waiting time in a GI/G/1. To demonstrate the quality of our approximations, we also present exact results. Our approximations have applications in production, inventory, insurance and maintenance systems.