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. We consider 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.