A multi-server queueing-inventory system with stock-dependent demand

Gabi Hanukov; Tal Avinadav; Tatyana Chernonog; Uri Yechiali

doi:10.1016/j.ifacol.2019.11.124

A multi-server queueing-inventory system with stock-dependent demand

Gabi Hanukov, Tal Avinadav, Tatyana Chernonog, Uri Yechiali

Department of Management

Tel Aviv University

Research output: Contribution to journal › Conference article › peer-review

14 Scopus citations

Abstract

We consider a two-server service system in which idle servers produce and store preliminary services for reducing the sojourn time of incoming customers and increasing customers arrival rate. We model the system as a Markovian process and provide a method, based on matrix geometric (MG) analysis, to obtain closed-form solutions to the steady state probabilities and relevant performance measures. We show the relation of the elements in the rate matrix of the MG to Catalan numbers, and prove that the stability condition remains as is in the traditional M/M/2 queue, although the expected sojourn time of customers has been reduced. We provide an economic analysis for a system in which the PS capacity and the investment to increase customers' arrival rate are decision variables.

Original language	English
Pages (from-to)	671-676
Number of pages	6
Journal	IFAC-PapersOnLine
Volume	52
Issue number	13
DOIs	https://doi.org/10.1016/j.ifacol.2019.11.124
State	Published - Sep 2019
Event	9th IFAC Conference on Manufacturing Modelling, Management and Control, MIM 2019 - Berlin, Germany Duration: 28 Aug 2019 → 30 Aug 2019

Bibliographical note

Publisher Copyright:
© 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Funding

This research was supported by the Israel SCIENCE FOUNDATION (grant No. 1448/17).

Funders	Funder number
Israel Science Foundation	1448/17

Keywords

Economic analysis
Markov process
Matrix geometric analysis
Queueing-inventory system
Stock-dependent demand

Access to Document

10.1016/j.ifacol.2019.11.124

Cite this

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abstract = "We consider a two-server service system in which idle servers produce and store preliminary services for reducing the sojourn time of incoming customers and increasing customers arrival rate. We model the system as a Markovian process and provide a method, based on matrix geometric (MG) analysis, to obtain closed-form solutions to the steady state probabilities and relevant performance measures. We show the relation of the elements in the rate matrix of the MG to Catalan numbers, and prove that the stability condition remains as is in the traditional M/M/2 queue, although the expected sojourn time of customers has been reduced. We provide an economic analysis for a system in which the PS capacity and the investment to increase customers' arrival rate are decision variables.",

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A multi-server queueing-inventory system with stock-dependent demand

Abstract

Bibliographical note

Funding

Keywords

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