State probabilities for an M/M/1 queuing system with two capacity levels

Alexander Hübl, Klaus Altendorfer

Research output: Chapter in Book/Report/Conference proceedingsConference contributionpeer-review

5 Citations (Scopus)


Flexible capacity of production system gets in times of short-time working and economic crisis an increasingly important status. Therefore, models to handle flexible capacity of production systems are necessary. In production planning queuing theory is a widely applied modeling approach. Since classical M/M/1 queuing models neglect flexible capacity this work implements two production rates in an M/M/1 queuing model. Whenever the queue length is more than k, the system runs at high speed otherwise low speed is used. The aim of this paper is the calculation of the state probabilities of the Markov chain. The state probabilities are the basis for developing an approximation for the production lead time which is dedicated to further research. Finally, a simulation study for the evaluation of state probabilities for flexible capacity with one and two switching points is conducted.
Original languageEnglish
Title of host publication2015 Winter Simulation Conference, WSC 2015
Number of pages8
ISBN (Electronic)9781467397438
Publication statusPublished - 16 Feb 2016
Event2015 Wintersim Conference - Huntington Beach, United States
Duration: 6 Dec 20159 Dec 2015

Publication series

NameProceedings - Winter Simulation Conference
ISSN (Print)0891-7736


Conference2015 Wintersim Conference
Country/TerritoryUnited States
CityHuntington Beach
Internet address


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