Korean Management Science Review (경영과학)

The Korean Operations Research and Management Science Society (한국경영과학회)
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Determining the Optimal Buffer Sizes in Poisson Driven 3-node Tandem Queues using (Max, +)-algebra

(Max, +)-대수를 이용한 3-노드 유한 버퍼 일렬대기행렬 망에서 최적 버퍼 크기 결정

  • 서동원 (경희대학교 경영학부) ;
  • 황승준 (한양대학교 경상대학 경영학부)
  • Published : 2007.05.31
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Abstract

In this study, we consider stationary waiting times in finite-buffer 3-node single-server queues in series with a Poisson arrival process and with either constant or non-overlapping service times. We assume that each node has a finite buffer except for the first node. The explicit expressions of waiting times in all areas of the stochastic system were driven as functions of finite buffer capacities. These explicit forms show that a system sojourn time does not depend on the finite buffer sizes, and also allow one to compute and compare characteristics of stationary waiting times at all areas under two blocking rules communication and manufacturing blocking. The goal of this study is to apply these results to an optimization problem which determines the smallest buffer capacities satisfying predetermined probabilistic constraints on stationary waiting times at all nodes. Numerical examples are also provided.

Keywords

References

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