Steady State Probabilities for the Server Vacation Model with Group Arrivals and under Control operating Policy

제어운영 정책하에 있는 집단으로 도착하는 서어버 휴가 모형의 안정상태 확률

  • Published : 1991.12.01

Abstract

In this study, an efficient algorithm is developed to compute steady state probabilities for the following M$_{x}$G/1 server vacation system under control-operating poligy: At the end of a busy period, the server takes a sequence of vacations, each for a random amount of time. At the end of each vacation, he inspects the length of the queue. If the queue length at this time is equal to or greater than a prespecified threshold value r, he begins to serve the queue until it is empty.y.

Keywords

References

  1. Opns. Res v.37 no.2 (R,r)Production/Inventory Systems Altiok,T.
  2. Oper. Res. Lett v.5 On the $M^X$/G/1 Queue with Vacation Time Baba,Y.
  3. Journal of the Operations Research Society of Japan v.27 On the $M^X$/G/1 Queue with Finite Waiting Room Baba,Y.
  4. IEEE Trans. Commun v.18 Buffer Behaviour for Batch Poisson Arrival and Single Constant Output Chu,W.W.
  5. IEEE Trans. Commun v.20 On the Analysis and Modeling of a Class of Computer Communication Systems Chu,W.W.;A.G.Konheim
  6. Queueing System v.1 Queueing System with Vacations-A Survey Doshi,B.T.
  7. Opns. Res. v.33 Stochastic Decompositions in the M/G/1 Queue with Generalized Vacations Fuhrmann,S.W.;R.B.Cooper
  8. Camp.& Opns. Res. v.8 no.3 Production/Inventory Systems with a Stochastic Production Rate under a Continuous Review Policy Gavish,B.;S.C.Graves
  9. Opns. Res. v.25 A Classified Biliography of Research on Optimal Design and Contral of Queues Grabill,T.;Gross;N.Magazine
  10. Naval Research Logistics v.36 The Threshold Policy in the M/G/1 Queue with Server Vacations Kella,O.
  11. Mgmt. Sci. v.35 no.6 Control Policies for the $M^X$/G/1 Queueing System Lee,H.S.;M.M.Srinivasan
  12. Matrix-Geometric Stochastic Models Neuts,M.F.
  13. Applied Probability Models with Optimization Applications Ross,S.M.
  14. Mgmt. Sci. v.37 no.7 Random Review Production/Inventory Systems with Compound Poisson Demands and Arbitrary Processing Times Srinivasan,M.M.;H.S.Lee
  15. Tech. Report TR 87-0032 Queueing Analysis of Vacation Models, PartⅠ: M/G/1, Part Ⅱ: M/G/1 with Vacations Takagi,H.
  16. European J. Oper. Res. v.23 Control of the Service Process in a Queueing System Teghem,J.
  17. Stochastic Modeling and Analysis : a Computational Approach Tijms,H.C.
  18. Mgmt. Sci. v.27 Algorithms for the State Probabilities in a General Class of Single Server Queueing Systems with Group Arrivals Van Hoorn,M.H.