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

Content Provider	IEEE Xplore Digital Library
Author	Woo-sung Kim Morrison, J.R.
Copyright Year	2011
Description	Author affiliation: Department of Industrial and Systems Engineering, KAIST, Daejeon, Korea (Woo-sung Kim; Morrison, J.R.)
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.
Starting Page	1558
Ending Page	1563
File Size	740362
Page Count	6
File Format	PDF
ISBN	9781457708350
ISSN	20937121
e-ISBN	9788993215038
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-10-26
Publisher Place	Korea (South)
Access Restriction	Subscribed
Rights Holder	ICROS
Subject Keyword	Performance evaluation Queueing approximation formula Absorbing Markov chain Absorption Loading Markov processes Maintenance engineering Servers Approximation methods Failure prone tool Load modeling
Content Type	Text
Resource Type	Article

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