Journal of Korean Institute of Industrial Engineers (대한산업공학회지)

Korean Institute of Industrial Engineers (대한산업공학회)
권호 표지

An Analysis of M/G/1 Vacation Systems with Restriction to the Waiting Time of the First Customer

첫 고객의 대기시간에 제약이 있는 M/G/1 휴가모형의 분석

  • Hur, Sun (Department of Industrial Engineering, Hanyang University) ;
  • Lee, Jeong Kyoo (Department of Industrial Engineering, Hanyang University) ;
  • Ahn, Suneung (Department of Industrial Engineering, Hanyang University)
  • 허선 (한양대학교 산업공학과) ;
  • 이정규 (한양대학교 산업공학과) ;
  • 안선웅 (한양대학교 산업공학과)
  • Published : 2002.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we consider an M/G/1 queueing system with vacation. The length of vacation period may be controlled by the waiting time of the first customer. The server goes on vacation as soon as the system is empty, and resumes service either when the waiting time of the leading customer reaches a predetermined value, or when the vacation period is expired, whichever comes first. We consider two types of vacation, say, multiple vacation type and N-policy type. We derive the steady-state distributions of the number of customers at arbitrary time and arbitrary customer's waiting time by means of decomposition property. Also, the mean lengths of busy period, idle period and a cycle time are given.

Keywords

References

  1. Alfa, A. S. and Frigui, I. (1996), Discrete NT-policy single server queue with Markovian arrival process and phase type service, European Journal of Operational Research, 88, 599-613
  2. Doganata, Y. N. (1990), NT-vacation policy for M/G/I queue with starter, Communication, Control, and Signal Processing, E. Arikan (ed.),1663-1669, Elsevier Science, Amsterdam
  3. Doshi, B. T. (1986), Queueing Systems with vacations : Survey, Queueing Systems, 1, 29-66
  4. Fuhrmann, S. W. and Cooper, R (1985), Stochastic Decompositions in the M/G/l Queue with Generalized Vacations, Opns Res, 33(5), 1117-1129 https://doi.org/10.1287/opre.33.5.1117
  5. Heyman, D. P. (1977), T-policy for the M/G/I queue, Management Science, 23, 775-778
  6. Hur, S., Lee, H. and Kim, J. S. (2000), An analysis of M/G/I system with N and T-policy, Journal of the Korean Institute of Industrial Engineers, 26, 81-87
  7. Lee, H. W. (1998), Queueing Theory, Sigma Press, Seoul, Korea