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Stochastic comparisons of density profiles for the road-hog process

Published online by Cambridge University Press:  14 July 2016

Rengarajan Srinivasan
Rengarajan Srinivasan*
Affiliation:
University of Saskatchewan
*
∗ Postal address: Department of Mathematics, University of Saskatchewan, Saskatoon, Canada S7N 0W0.
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Abstract

We consider the asymmetric simple exclusion process which starts from a product measure such that all the sites to the left of zero (including zero) are occupied and the right of 0 (excluding 0) are empty. We label the particle initially at 0 as the leading particle. We study the long-term behaviour of this process near large sites when the leading particle's holding time is different from that of the other particles. In particular, we assume that the leading particle moves at a slower rate than the other particles. We call this modified asymmetric simple exclusion process the road-hog process. Coupling and stochastic ordering techniques are used to derive the density profile of this process. Road-hog processes are useful in modelling series of exponential queues with Poisson and non-Poisson input process. The density profiles dramatically illustrate the flow of customers through the queues.

Keywords

SIMPLE EXCLUSION PROCESSHYDRODYNAMIC LIMITSERIAL NETWORK
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 4 , December 1991 , pp. 852 - 863
Copyright
Copyright © Applied Probability Trust 1991 

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