Mean waiting times in nonpreemptive priority queues with Markovian Arrival and i.i.d. service Processes

Abstract

This paper considers nonpreemptive priority queues with P (>=2) classes of customers. Customers in each class arrive to the system according to a Markovian Arrival Process (MAP). MAP is a class of non-renewal arrival processes and includes the Markov Modulated Poisson Process (MMPP). The service times of customers in all classes are independent and identically distributed according to a common distribution function. Using both generating function techniques and matrix analytic methods, we derive the mean waiting time for each customer class. The algorithmic implementation of the analytical results is also discussed along with numerical examples.