Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 3, Pages 339-354

Analysis of a multi-server queueing model of ABR

R. Núñez-Queija and O. J. Boxma

CWI, P.O. Box 94079, Amsterdam 1090 GB, The Netherlands

Received 1 October 1997; Revised 1 May 1998

Copyright © 1998 R. Núñez-Queija and O. J. Boxma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we present a queueing model for the performance analysis of Available Bit Rate (ABR) traffic in Asynchronous Transfer Mode (ATM) networks. We consider a multi-channel service station with two types of customers, denoted by high priority and low priority customers. In principle, high priority customers have preemptive priority over low priority customers, except on a fixed number of channels that are reserved for low priority traffic. The arrivals occur according to two independent Poisson processes, and service times are assumed to be exponentially distributed. Each high priority customer requires a single server, whereas low priority customers are served in processor sharing fashion. We derive the joint distribution of the numbers of customers (of both types) in the system in steady state. Numerical results illustrate the effect of high priority traffic on the service performance of low priority traffic.