An explicit solution for the value function of a priority queue (Q1878851)

For an \(N\)-class preemptive-resume priority queue with Poisson arrivals, general class-dependent service time distributions, and holding and switching costs, the authors derive closed-form expressions for the total expected discounted holding and switching costs for any initial state. They calculate the long-run average holding and switching costs and the bias function. This paper generalizes the results of the authors [Queueing Syst. 34, No. 1--4, 199--214 (2000; Zbl 0942.90016)] and \textit{C. Buyukkoc, P. Varaiya} and \textit{J. Walrand} [Adv. Appl. Probab. 17, 237--238 (1985; Zbl 0557.60082)] where the case of two customer classes and exponential service times is treated, for the discounted and the average cost criterion, respectively.