An M/G/1 queueing system with multiple priority classes

We consider anM/G/1 queueing system with multiple priority classes of jobs. Considered preemptive rules are the preemptiveresume, preemptive-repeat-identical, and preemptive-repeat-different policies. These three preemptive rules will be analyzed in parallel. The key idea of analysis is based on the consideration of a busy period as a composite of delay cycle. As results, we present the exact Laplace-Stieltjes (L.S.) transforms of residence time and completion time in the system.