Heuristic Approach to the Mean Waiting Time of $Geo^x/G/1$ Vacation Queues with N-policy and Setup Time

휴리스틱 방법을 이용한 N정책과 준비기간을 갖는 휴가형 $Geo^x/G/1$ 모형의 평균대기시간 분석

  • Published : 2007.03.31

Abstract

We consider the discrete-time $Geo^x/G/1$ queues under N-policy with multiple vacations (a single vacation) and setup time. In this queueing system, the server takes multiple vacations (a single vacation) whenever the system becomes empty, and he begins to serve the customers after setup time only if the queue length is at least a predetermined threshold value N. Using the heuristic approach, we derive the mean waiting time for both vacation models. We demonstrate that the heuristic approach is also useful for the discrete-time queues.

Keywords

References

  1. 이성희, 김성진, 채경철, '휴리스틱 방법을 이용한 준비기간을 갖는 휴가형 $Geo^X/G/1$ 모형의 평균대기시간 분석', 2006 대한산업공학회/한국경영과학회 춘계공동학술대회
  2. Bruneel, H. and B.G. Kim, Discrete-Time Models for Communication System Including ATM, Kluwer Academic Publishers, Boston, 1993
  3. Chae, K.C. and H.W. Lee, '$M^X/G/1$ Vacation Models with N-Policy : Heuristic Interpretation of the Mean Waiting Time,' Journal of the Operational Research Society, Vol.46, No.2(1995), pp.258-264 https://doi.org/10.1057/jors.1995.31
  4. Medhi, Stochastic Models in Queueing Theory, second edition, Academic Press, 2003
  5. Hur, S. and S. Ahn, 'Batch Arrival Queues with Vacations and Server Setup,' Applied Mathematical Modeling, Vol.29(2005), pp. 1164-1181 https://doi.org/10.1016/j.apm.2005.03.002
  6. Takagi, H., Queueing Analysis, Vol 3 : Discrete-Time Systems, North-Holland, Amsterdam, 1993