Average waiting time of customers in a priority M/D/k queue with finite buffers

Abstract

Analysis of priority multiserver queues is known to be a difficult problem. In this paper, a priority M/D/k queue with finite buffers is analyzed and an approximate closed-form expression for the average waiting time of customers belonging to different priority classes is obtained. The key assumption is the presence of heavy traffic in the network leading to loss of customers from the service stations. Several interesting numerical results are reported that show the interplay between arrival and service rate of customers, capacity of the buffer, proportion of traffic belonging to each class and probability of loss as experienced by incoming customers. Priority queues with finite buffers are used to model various types of telecommunications and manufacturing situations. These queues are specially useful for modelling high-speed asynchronous transfer mode (ATM) networks that are subject to loss due to overfilling of the buffers. In general, it is difficult to obtain close-form solutions of the various performance measures for these queues. Analysis of such queues with the deterministic service discipline can help provide useful guidelines for designers and developers of telecommunication and manufacturing networks. © 2001 Elsevier Science Ltd. All rights reserved.