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STEADY-STATE OPTIMIZATION OF AN EXHAUSTIVE LÉVY STORAGE PROCESS WITH INTERMITTENT OUTPUT AND RANDOM OUTPUT RATE

Published online by Cambridge University Press:  17 April 2020

Royi Jacobovic Open the ORCID record for Royi Jacobovic [Opens in a new window]  and
Offer Kella
Royi Jacobovic
Affiliation:
Department of Statistics and Data Science, The Hebrew University of Jerusalem, Jerusalem 9190501, Israel E-mail: royi.jacobovic@mail.huji.ac.il; offer.kella@gmail.com
Offer Kella
Affiliation:
Department of Statistics and Data Science, The Hebrew University of Jerusalem, Jerusalem 9190501, Israel E-mail: royi.jacobovic@mail.huji.ac.il; offer.kella@gmail.com
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Abstract

Consider a regenerative storage process with a nondecreasing Lévy input (subordinator) such that every cycle may be split into two periods. In the first (off), the output is shut off and the workload accumulates. This continues until some stopping time. In the second (on), the process evolves like a subordinator minus a positive drift (output rate) until it hits the origin. In addition, we assume that the output rate of every on period is a random variable, which is determined at the beginning of this period. For example, at each period, the output rate may depend on the workload level at the beginning of the corresponding busy period. We derive the Laplace–Stieltjes transform of the steady-state distribution of the workload process and then apply this result to solve a steady-state cost minimization problem with holding, setup and output capacity costs. It is shown that the optimal output rate is a nondecreasing deterministic function of the workload level at the beginning of the corresponding on period.

Keywords

Lévy driven queuesoptimization with partial informationoutput rate controlqueues with server vacations
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 3 , July 2021 , pp. 730 - 744
Copyright
© Cambridge University Press 2020

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