Scaling analysis of an extended machine-repair model

L.R. van Kreveld, O. J. Boxma, J. L. Dorsman, M. R.H. Mandjes

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

1 Citation (Scopus)

Abstract

We consider an extension of the classic machine-repair model, where we explicitly model the fact that machines, apart from requiring service from a single repairer, also supply service themselves to products. Due to this dual role of the machines, the system exhibits an intricate relation between the processing rate of products and the performance of the repairer. To characterize this relation, we analyze this model under a Halfin-Whitt inspired scaling regime, where we amplify the arrival rate of products, the repair speed of the repairer and the number of machines appropriately. The resulting limiting stationary distribution is elegant, allows for a closed-form expression and provides intuition on the system's behavior resulting from the machines' dual role. With numerical results we illustrate the convergence, and assess under which conditions the limiting distributions lead to accurate approximations. Next to this valuable insight, the analysis in this paper can be viewed as a first step towards a unifying scaling analysis for general closed queueing networks.

Original languageEnglish
Title of host publicationProceedings of the 13th EAI International Conference on Performance Evaluation Methodologies and Tools, VALUETOOLS 2020
PublisherAssociation for Computing Machinery, Inc
Pages172-179
Number of pages8
ISBN (Electronic)9781450376464
DOIs
Publication statusPublished - 18 May 2020
Event13th EAI International Conference on Performance Evaluation Methodologies and Tools, VALUETOOLS 2020 - Tsukuba, Japan
Duration: 18 May 202020 May 2020

Publication series

NameACM International Conference Proceeding Series

Conference

Conference13th EAI International Conference on Performance Evaluation Methodologies and Tools, VALUETOOLS 2020
Country/TerritoryJapan
CityTsukuba
Period18/05/2020/05/20

Fingerprint

Dive into the research topics of 'Scaling analysis of an extended machine-repair model'. Together they form a unique fingerprint.

Cite this