A MAP/G/1 Queue With Cyclic Service Times

This paper studies a queueing system with a Markov arrival process and cyclic service times. When customers are distinguished by the types of their service times, the queueing processes experienced by different types of customers are different. First, a computational approach is developed to find the distributions of the queue length and waiting time of each type of customer. The results are useful in comparing the queueing processes experienced by different types of customers. Second, since a number of servers is utilized cyclically, the issue of how to sequence these servers is addressed. Algorithms are proposed for computing the best and worst sequences of servers in terms of the mean queue length or the mean waiting time. Numerical examples are presented to show in which sequence (of servers) the mean queue length or the mean waiting time is minimized or maximized for queueing systems with bursty and nonbursty input processes.