Stochastics and Statistics Waiting time analysis of the multiple priority dual queue with a preemptive priority service discipline P. Zeephongsekul * , A. Bedford School of Mathematical and Geospatial Sciences, RMIT University, GPO Box 2476V, Melbourne, Victoria 3001, Australia Received 22 August 2003; accepted 15 October 2004 Available online 21 December 2004 Abstract The dual queue consists of two queues, called the primary queue and the secondary queue. There is a single server in the primary queue but the secondary queue has no service facility and only serves as a holding queue for the overloaded primary queue. The dual queue has the additional feature of a priority scheme to help reduce congestion. Two classes of customers, class 1 and 2, arrive to the dual queue as two independent Poisson processes and the single server in the primary queue dispenses an exponentially distributed service time at the rate which is dependent on the customerÕs class. The service discipline is preemptive priority with priority given to class 1 over class 2 customers. In this paper, we use matrix-analytic method to construct the infinitesimal generator of the system and also to provide a detailed analysis of the expected waiting time of each class of customers in both queues. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Queueing; Multi-priority dual queue; Waiting time analysis; Matrix-analytic method; Preemptive priority 1. Introduction The dual queue was introduced in [7] as a device to improve the quality of service (QoS) of customers in communication networks. The dual queue consists of two sub-queues, denoted by queue 1 (the primary queue) and queue 2 (the secondary queue). Both queues have finite capacity, i.e. the amount of waiting rooms in each queue including that in service, is finite. When the primary queue is full, an arriving customer waits in the secondary queue. There is a single server in the primary queue but the secondary queue has no service facility and only serves as a holding queue for the overloaded primary queue. If both queues are full, 0377-2217/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2004.10.013 * Corresponding author. Tel.: +61 3 99253224; fax: +61 3 99251748. E-mail address: panlopz@rmit.edu.au (P. Zeephongsekul). European Journal of Operational Research 172 (2006) 886–908 www.elsevier.com/locate/ejor