In this paper a priority M/D/k queue is analyzed. The arrival process of the queue is assumed to be Poisson and the service is assumed to be deterministic. Customers are served on a first-come-first-served basis. The queue uses nonpreemptive head-of-the-line priority discipline. An analytical expression for the mean waiting time of customers belonging to different priority classes is obtained. This is an approximate result that uses the heavy traffic assumption and the steady-state probability result for an M/M/k queue as applied to an M/D/k queue. Extensive numerical results are reported that illustrate the variation of the mean waiting time with the system parameters.
