한국경영과학회지 (Journal of the Korean Operations Research and Management Science Society)

  • 제40권1호
  • /
  • Pages.1-4
  • /
  • 2015
  • /
  • 1225-1119(pISSN)
  • /
  • 2733-4759(eISSN)
한국경영과학회 (The Korean Operations Research and Management Science Society)
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GI/G/1 대기행렬 대기시간 분포의 새로운 유도방법

A Heuristic Derivation of the Waiting Time Distribution of a GI/G/1 Queue

  • 임대은 (백석대학교 경상학부) ;
  • 김보근 (삼성SDS SCM컨설팅그룹2) ;
  • 김남기 (전남대학교 산업공학과) ;
  • 채경철 (KAIST 산업 및 시스템공학과)
  • Lim, Dae Eun (Division of Business and Commerce, Baekseok University) ;
  • Kim, Bokeun (SCM Consulting Group 2, Samsung SDS) ;
  • Kim, Nam K. (Department of Industrial Engineering, Chonnam National University) ;
  • Chae, Kyung C. (Department of Industrial and Systems Engineering, KAIST)
  • 투고 : 2014.09.18
  • 심사 : 2014.11.03
  • 발행 : 2015.02.28
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초록

This paper presents a heuristic approach to derive the Laplace-Stieltjes transform (LST) and the probability generating function (PGF) of the waiting time distributions of a continuous- and a discrete-time GI/G/1 queue, respectively. This is a new idea to derive the well-known results, the waiting time distribution of GI/G/1 queue, in a different way.

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참고문헌

  1. Hunter, J.J., Mathematical techniques of applied probability, Discrete time models:techniques and applications, Academic Press, Vol.2(1983).
  2. Lindley, D.V., "The Theory of Queues with a Single Server," Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 48(1952), pp.277-289. https://doi.org/10.1017/S0305004100027638
  3. Marshal, K.T., "Some Relationships between the distributions of waiting time, idle time and interoutput time in the GI/G/1 queue," SIAM Journal on Applied Mathematics, Vol. 16(1968), pp.324-327. https://doi.org/10.1137/0116026
  4. Medhi, J., Stochastic Models in Queueing Theory, Academic Press, 2002.