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

Gabi Hanukov, Tal Avinadav, Tatyana Chernonog, Uri Yechiali

Research output: Contribution to journalConference articlepeer-review

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 languageEnglish
Pages (from-to)671-676
Number of pages6
JournalIFAC-PapersOnLine
Volume52
Issue number13
DOIs
StatePublished - Sep 2019
Event9th IFAC Conference on Manufacturing Modelling, Management and Control, MIM 2019 - Berlin, Germany
Duration: 28 Aug 201930 Aug 2019

Keywords

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

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