산업경영시스템학회지 (Journal of Korean Society of Industrial and Systems Engineering)

  • 제39권2호
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  • Pages.1-10
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  • 2016
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  • 2005-0461(pISSN)
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  • 2287-7975(eISSN)
한국산업경영시스템학회 (Society of Korea Industrial and System Engineering)
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낮은 교통밀도 하에서 서버 고장을 고려한 복수 서버 대기행렬 모형의 체제시간에 대한 분석

On the Exact Cycle Time of Failure Prone Multiserver Queueing Model Operating in Low Loading

  • 김우성 (한동대학교 경영경제학부) ;
  • 임대은 (강원대학교 시스템경영공학과)
  • Kim, Woo-Sung (School of Management and Economics, Handong Global University) ;
  • Lim, Dae-Eun (Dept. of System and Management Engineering, Kangwon National University)
  • 투고 : 2015.11.26
  • 심사 : 2016.01.13
  • 발행 : 2016.06.30
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초록

In this paper, we present a new way to derive the mean cycle time of the G/G/m failure prone queue when the loading of the system approaches to zero. The loading is the relative ratio of the arrival rate to the service rate multiplied by the number of servers. The system with low loading means the busy fraction of the system is low. The queueing system with low loading can be found in the semiconductor manufacturing process. Cluster tools in semiconductor manufacturing need a setup whenever the types of two successive lots are different. To setup a cluster tool, all wafers of preceding lot should be removed. Then, the waiting time of the next lot is zero excluding the setup time. This kind of situation can be regarded as the system with low loading. By employing absorbing Markov chain model and renewal theory, we propose a new way to derive the exact mean cycle time. In addition, using the proposed method, we present the cycle times of other types of queueing systems. For a queueing model with phase type service time distribution, we can obtain a two dimensional Markov chain model, which leads us to calculate the exact cycle time. The results also can be applied to a queueing model with batch arrivals. Our results can be employed to test the accuracy of existing or newly developed approximation methods. Furthermore, we provide intuitive interpretations to the results regarding the expected waiting time. The intuitive interpretations can be used to understand logically the characteristics of systems with low loading.

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참고문헌

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