On cycle time approximations for the failure prone G/G/m queue: Theoretical justification of a practical approximation

Woo Sung Kim, James R. Morrison

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

Abstract

As high tech manufacturing systems are very expensive, it is especially important to operate them efficiently. To determine if a system is operating efficiently, one must evaluate its performance. One efficiency issue in practical systems is that tools are not perfectly reliable; tools may fail. Approximate queueing formulae are often used to model system performance such as mean cycle time. While many approximations for failure prone tools have been proposed, the theoretical justification for such formulae is sometimes insufficient. There are few solutions for the failure prone queue, so it can be hard to justify approximation formulae theoretically. In particular, approximation formulae can have significant error in low loading because most focus on heavy traffic. By studying the G/G/m failure prone queue in low loading, we can determine if approximation formulae work well. Assuming Poisson arrivals, exponential service and low loading, we can model the system as an absorbing Markov chain. Using renewal theory, we derive an exact solution for mean cycle time of the system in low loading. Based on our results, we can test common mean cycle time approximations and compare them in low loading. In this paper, we test two common approximations. The result is that one is more accurate than the other. As the number of servers increases, there is greater accuracy difference between the two.

Original languageEnglish
Title of host publicationICCAS 2011 - 2011 11th International Conference on Control, Automation and Systems
Pages1558-1563
Number of pages6
StatePublished - 2011
Event2011 11th International Conference on Control, Automation and Systems, ICCAS 2011 - Gyeonggi-do, Korea, Republic of
Duration: Oct 26 2011Oct 29 2011

Publication series

NameInternational Conference on Control, Automation and Systems
ISSN (Print)1598-7833

Conference

Conference2011 11th International Conference on Control, Automation and Systems, ICCAS 2011
Country/TerritoryKorea, Republic of
CityGyeonggi-do
Period10/26/1110/29/11

Keywords

  • Absorbing Markov chain
  • Failure prone tool
  • Performance evaluation
  • Queueing approximation formula

Fingerprint

Dive into the research topics of 'On cycle time approximations for the failure prone G/G/m queue: Theoretical justification of a practical approximation'. Together they form a unique fingerprint.

Cite this