A SIMPLE APPROACH TO THE WORKLOAD ANALYSIS OF M/G/1 VACATION QUEUES

  • Kim, Nam-Ki (Department of Industrial Engineering, Chonnam National University) ;
  • Park, Yon-Il (National Library of Medicine, Bethesd) ;
  • Chae, Kyung-Chul (Department of Industrial Engineering, KAIST)
  • Published : 2004.06.01

Abstract

We present a simple approach to finding the stationary workload of M/G/1 queues having generalized vacations and exhaustive service discipline. The approach is based on the level crossing technique. According to the approach, all that we need is the workload at the beginning of a busy period. An example system to which we apply the approach is the M/G/1 queue with both multiple vacations and D-policy.

Keywords

References

  1. Journal of Applied Probability v.38 The queue length distribution for the M/G/1 queue under the D-policy CHAE,K.C.;PARK,Y.I. https://doi.org/10.1239/jap/996986663
  2. Journal of Applied Probability v.14 On up- and downcrossings COHEN,J.W. https://doi.org/10.2307/3213014
  3. Journal of Applied Probability v.35 Queueing processes in bulk systems under the D-policy DSHALALOW,J.H. https://doi.org/10.1239/jap/1032438392
  4. Journal of the Korean Statistical Society v.31 A level crossing approach to the analysis of finite dam KIM,S.;LEE,E.Y.
  5. Journal of Applied Probability v.35 $P_{\lambda}^M$-policy for a dam with input formed by a compound Poisson process LEE,E.Y.;AHN,S.K. https://doi.org/10.1239/jap/1032192863
  6. Journal of Applied Probability v.30 A model for a system subject to randmo shocks LEE,E.Y.;LEE,J. https://doi.org/10.2307/3214528
  7. Queueing Theory LEE,H.W.
  8. Journal of Applied Probability v.31 Analysis of the $M^X$/G/1 queue with N-policy and multiple vacations LEE,H.W.;LEE,S.S.;PARK.J.O.;CHAE,K.C. https://doi.org/10.2307/3215040
  9. Ph.D. Thesis, Department of Industrial Engineering, Korea Advanced Institute of Science and Technology Analysis of Queueing Models under the D-policy PARK,Y.I.
  10. Journal of the Korean Statistical Society v.28 Analysis of unfinished work and queue waiting time for the M/G/1 queue with D-policy PARK,Y.I.;CHAE,K.C.
  11. Journal of the Korean Statistical Society v.32 Correction and addendum : Analysis of unfinished work and queue waiting time for the M/G/1 queue with D-policy PARK,Y.I.;CHAE,K.C.
  12. Stochastic Analysis and Applications v.18 A random review replacement model for a system subject to compound Poisson shocks PARK,Y.I.;CHAE,K.C.;LEE,H.S. https://doi.org/10.1080/07362990008809660
  13. Queueing Analysis v.1 TAKAGI,H.