TY - GEN

T1 - On cycle time approximations for the failure prone G/G/m queue

AU - Kim, Woo Sung

AU - Morrison, James R.

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

KW - Absorbing Markov chain

KW - Failure prone tool

KW - Performance evaluation

KW - Queueing approximation formula

UR - http://www.scopus.com/inward/record.url?scp=84856545812&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84856545812

SN - 9781457708350

T3 - International Conference on Control, Automation and Systems

SP - 1558

EP - 1563

BT - ICCAS 2011 - 2011 11th International Conference on Control, Automation and Systems

Y2 - 26 October 2011 through 29 October 2011

ER -