Switched poisson process/g/1 queue with service interruptions

Abstract

In this paper, we develop an expression for the expected waiting time in a single server queueing system subject to interruptions with alternately varying Poisson arrival and renewal service rates. This queueing system is useful to model situations in production, computer and telecommunication systems in which customer arrivals and service requirements differ depending on whether the server is working or not. We develop an expression for the expected waiting time by approximating the virtual delay process by a Brownian motion. Our approximation for the expected waiting time involves only the means and variances and does not depend on any assumptions regarding the interarrival, service or switching time distributions. We present simulation results to illustrate the quality of our approximations.