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ON THE PROBABILITY DISTRIBUTION OF JOIN QUEUE LENGTH IN A FORK-JOIN MODEL

Published online by Cambridge University Press:  19 August 2010

Jun Li  and
Yiqiang Q. Zhao
Jun Li
Affiliation:
Communications Research Centre (CRC) Canada, Ottawa, ON, CanadaK2H 8S2 E-mail: jun.li@crc.gc.ca
Yiqiang Q. Zhao
Affiliation:
School of Mathematics and Statistics, Carleton University, Ottawa, ON, CanadaK1S 5B6 E-mail: zhao@math.carleton.ca
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Abstract

In this article, we consider the two-node fork-join model with a Poisson arrival process and exponential service times of heterogeneous service rates. Using a mapping from the queue lengths in the parallel nodes to the join queue length, we first derive the probability distribution function of the join queue length in terms of joint probabilities in the parallel nodes and then study the exact tail asymptotics of the join queue length distribution. Although the asymptotics of the joint distribution of the queue lengths in the parallel nodes have three types of characterizations, our results show that the asymptotics of the join queue length distribution are characterized by two scenarios: (1) an exact geometric decay and (2) a geometric decay with the prefactor n−1/2.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 24 , Issue 4 , October 2010 , pp. 473 - 483
Copyright
Copyright © Cambridge University Press 2010

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