Advances in Operations Research
Volume 2013 (2013), Article ID 680539, 21 pages
Research Article

On the Nonsymmetric Longer Queue Model: Joint Distribution, Asymptotic Properties, and Heavy Traffic Limits

1Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL 60607-7045, USA
2Department of Mathematics and Computer Science, QCC, The City University of New York, 222-05 56th Avenue, Bayside, NY 11364, USA

Received 28 January 2013; Accepted 8 April 2013

Academic Editor: Khosrow Moshirvaziri

Copyright © 2013 Charles Knessl and Haishen Yao. 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.


We consider two parallel queues, each with independent Poisson arrival rates, that are tended by a single server. The exponential server devotes all of its capacity to the longer of the queues. If both queues are of equal length, the server devotes of its capacity to the first queue and the remaining to the second. We obtain exact integral representations for the joint probability distribution of the number of customers in this two-node network. Then we evaluate this distribution in various asymptotic limits, such as large numbers of customers in either/both of the queues, light traffic where arrivals are infrequent, and heavy traffic where the system is nearly unstable.