2010-10-01
On the probability distribution of join queue length in a fork-join model
Publication
Publication
Probability in the Engineering and Informational Sciences , Volume 24 - Issue 4 p. 473- 483
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. Copyright
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dx.doi.org/10.1017/S0269964810000112 | |
Probability in the Engineering and Informational Sciences | |
Organisation | School of Mathematics and Statistics |
Li, J. (Jun), & Zhao, Y. (2010). On the probability distribution of join queue length in a fork-join model. Probability in the Engineering and Informational Sciences, 24(4), 473–483. doi:10.1017/S0269964810000112
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