Queueing Systems

40 (4): 355-382, May 2002

Copyright © 2002 Kluwer Academic Publishers

All rights reserved

Two-Class Priority Queueing System with State-Dependent Arrivals

Gabriel Bitran

Sloan School of Management, MIT, Cambridge, MA 02139, USA gbitran@mit.edu

René Caldentey

Stern School of Business, New York University, New York 10012, USA rcaldent@stern.nyu.edu

Abstract

In this paper, we present a performance analysis of a 2-dimensional preemptive priority queueing system with state-dependent arrivals. Using a Markovian formulation we first compute the steady state distribution for the queue length of both classes. Then, waiting times and busy periods are characterized through (i) first and second moments and (ii) the approximation of their cumulative distribution functions (cdf) and Laplace–Stieltjes transforms (LST). We derive these approximations connecting bounds in the Laplace domain with bounds on the original time domain. We also, study the behavior of the inter-departure time for each class. Finally, we conclude the paper with a set of computational experiments testing our results.

Keywords

birth–death queue, priority queue, waiting time and output process approximations