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ON THE TIME-DEPENDENT BEHAVIOR OF A MARKOVIAN REENTRANT-LINE MODEL

Published online by Cambridge University Press:  03 August 2018

Brian Fralix
Brian Fralix*
Affiliation:
Department of Mathematical Sciences Clemson University, Clemson, SC, USA E-mail: bfralix@clemson.edu
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Abstract

We use the random-product technique from [5] to study both the steady-state and time-dependent behavior of a Markovian reentrant-line model, which is a generalization of the preemptive reentrant-line model studied in the work of Adan and Weiss [2]. Our results/observations yield additional insight into why the stationary distribution of the reentrant-line model from [2] exhibits an almost-geometric product-form structure: indeed, our generalized reentrant-line model, when stable, admits a stationary distribution with a similar product-form representation as well. Not only that, the Laplace transforms of the transition functions of our reentrant-line model also have a product-form structure if it is further assumed that both Buffers 2 and 3 are empty at time zero.

Keywords

random-product representationreentrant-line modeltime-dependent behavior
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 33 , Issue 3 , July 2019 , pp. 367 - 386
Copyright
Copyright © Cambridge University Press 2018 

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