A simple approach to the map/d/s queue

Abstract

We provide a simple approach to analyze the stationary MAP/D/s queue, where customers are served under the FCFS discipline. Assuming a cyclic assignment of customers to servers, we first characterize the sojourn time distribution, and with this, the queue length distribution immediately after departures is obtained. Further, utilizing the relationship between the time-average queue length distribution and the customer-average queue length distribution at departures, we obtain a numerically feasible formula for the stationary queue length mass function