How many servers are best in a dual-priority system?

We ask the question, “for minimizing mean response time (sojourn time), which is preferable: one fast server of speed 1, or k slow servers each of speed 1 / k ?” Our setting is the M / PH / k system with two priority classes of customers, high priority and low priority, where PH is a phase-type distribution. We find that multiple slow servers are often preferable, and we demonstrate exactly how many servers are preferable as a function of the load and service time distribution. In addition, we find that the optimal number of servers with respect to the high priority jobs may be very different from that preferred by low priority jobs, and we characterize these preferences. We also study the optimal number of servers with respect to overall mean response time, averaged over high and low priority jobs. Lastly, we ascertain the effect of the service demand variability of high priority jobs on low priority jobs.