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A QUEUEING MODEL WITH RANDOMIZED DEPLETION OF INVENTORY

Published online by Cambridge University Press:  13 September 2016

Hansjörg Albrecher ,
Onno Boxma ,
Rim Essifi  and
Richard Kuijstermans
Hansjörg Albrecher
Affiliation:
Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne and Swiss Financial Institute, UNIL-Dorigny, CH-1015 Lausanne, Switzerland
Onno Boxma
Affiliation:
Department of Mathematics and Computer Science, Eindhoven University of Technology and EURANDOM, P.O. Box 513, 5600 MB Eindhoven, The Netherlands E-mail: o.j.boxma@tue.nl
Rim Essifi
Affiliation:
Department of Mathematics and Computer Science, Eindhoven University of Technology and EURANDOM, P.O. Box 513, 5600 MB Eindhoven, The Netherlands E-mail: o.j.boxma@tue.nl
Richard Kuijstermans
Affiliation:
Department of Mathematics and Computer Science, Eindhoven University of Technology and EURANDOM, P.O. Box 513, 5600 MB Eindhoven, The Netherlands E-mail: o.j.boxma@tue.nl
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Abstract

In this paper, we study an M/M/1 queue, where the server continues to work during idle periods and builds up inventory. This inventory is used for new arriving service requirements, but it is completely emptied at random epochs of a non-homogeneous Poisson process, whose rate depends on the current level of the acquired inventory. For several shapes of depletion rates, we derive differential equations for the stationary density of the workload and the inventory level and solve them explicitly. Finally, numerical illustrations are given for some particular examples, and the effects of this depletion mechanism are discussed.

Keywords

applied probabilityinventory theoryqueueing theorystochastic modelling
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 31 , Issue 1 , January 2017 , pp. 43 - 59
Copyright
Copyright © Cambridge University Press 2016 

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