SOJOURN TIME DISTIBUTIONS FOR M/M/c G-QUEUE

  • Shin, Yang-Woo (Department of Statistics, Changwon National University)
  • Published : 1998.04.01

Abstract

We consider an M/M/c queue with two types of custormers, positive customers and negative customers. Positive customers are ordinary ones who upon arrival, join a queue with the intention of getting served and each arrival of negative customer removes a positive customer in the system, if any presents, and then is disappeared immediately. The Laplace-Stieltjes transforms (LST's) of the sojourn time distributions of a tagged customer, joinly with the probability that the tagged customer completes his service without being removed are derived under the combinations of various service displines; FCFS, LCFS and PS and removal strategies; RCF, RCH and RCR.

Keywords

References

  1. Queueing Systems, Theory and Applications v.23 Wiener-Hopf analysis of and M/G/1 queue with negative customers and of a related class of random walks N. Bayer;O. J. Boxma
  2. Prob. Engin. Info. Sci. v.10 The workload in the M/G/1 queue with work removal R. J. Boucherie;O. J. Boxma
  3. Stochastic Models v.10 Waiting time distributions for M/M/N processor sharing queus J. Braband
  4. Operations Research v.43 Networks of queues with customer, signals and arbitrary service time distributions X. Chao
  5. Prob. Engin. Info. Sci. v.7 Generalized networks of queues with positve and nagative arrivals X. Chao;M. Pinedo
  6. Prob. Engin. Info. Sic. v.9 On queueing networks with signals and history-dependent routing X. Chao;M. Pinedo
  7. J. Appl. Prob. v.28 Product form networks with negative and positive customers E. Gelenbe
  8. J. Appl. Prob. v.28 Queues with negative arrivals E. Gelenbe;P. G. Glynn;K. Sigman
  9. J. Appl. Prob. v.30 Queueing networks with negative customers and negative queue lengths W. Henderson
  10. J. Appl. Prob. v.30 Sojourn times in single server queues with negative customers P. G. Harrison;E. Pitel
  11. J. Appl. Prob. v.32 Response time distributions in tandem G-networks P. G. Harrison;E. Pitel
  12. Adv. Appl. Prob. v.28 The M/G/1 queue with negative customers P. G. Harrison;E. Pitel
  13. Introduction to Probability Models(5th ed.) S. M. Ross