A solution to mean delay in the ∑ Mc/ Gck/1 cyclic priority queue with cycle ( k) and class ( c) dependent feedback and service times

Abstract

In this paper we develop an original solution to mean delay in a general ∑ M c / G ck /1 cyclic priority queue with class ( c) and cycle ( k)-dependent service time and feedback. Each class has its priority assigned. There may be one or more classes with the same priority. This model is suitable for performance analysis of round robin processor sharing policies. The analysis may be used to examine the effects of quantum sizes in round robin scheduling used in operating systems. Each customer, upon entering the system, requires a number of service cycles before it leaves the system. Each service cycle is characterized by its service-time distribution, and the probability of having at least one more cycle before the customer leaves the system. These characteristics of cycles may be different for different cycles of a service process. The solution is represented as a system of linear equations. It may be efficiently solved using the Gauss–Seidel iterative procedure. A general solution is developed of which, the two special cases are a non-priority (single-priority) and a one-class-per-priority non-preemptive queues. Computational complexity of the numerical procedure is between computational complexity of the two special cases, O( C 3 K 3) and O( CK 3), respectively. C stands for the number of classes, and K stands for the maximum number of cycles being numerically considered.