Priority queues with setup times

Queueing analysis is conducted for M/G/1-type systems with multiple classes of service requests that need a setup time prior to each busy period. The paper considers a variety of service disciplines: FCFS (first-come, first-served), LCFS (last-come, first-served), nonpreemptive priority, preemptive resume priority, and gated batch priority. This study has been motivated by the performance evaluation of multiprocessor bus arbitration protocols. The Laplace-Stieltjes transform of the distribution function, the mean, and the second moment of the waiting time for each class are derived explicitly. As a limit of continuous priorities, the shortest-job-first discipline with setup times is also considered.