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On The Transient Departure Process of M x/G/1 Queueing System with Single Server Vacation

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Abstract

This paper studies the transient departure process of M x/G/1 queueing system with single server vacation. We present a simple probability decomposition method to derive the expected number of departures occurring in finite time interval from any initial state and the asymptotic expansion of the expected number. Especially, we derive some more practical results for some special cases.

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References

  1. Y. H. Tang and X. W. Tang, The queue length distribution for M x/G/1 queue with single server vacation, Acta Math. Scientia, 2000, 20(3): 397–408.

    Google Scholar 

  2. H. Ali, Expected number of departures in M/M/1 and GI/G/1 queues, Adv. Appl. Proba., 1990, 22(3): 770–772.

    Article  Google Scholar 

  3. X. Chao, On the departure processes of M/M/1/N and GI/G/1/N queues, Adv. Appl. Proba., 1992, 24(3): 751–753.

    Article  Google Scholar 

  4. J. R. Hubbard, C. D. Pegden, and M. Rosenshine, The departure process for the M/M/1 queue, J. Appl. Proba., 1986, 23(1): 249–255.

    Article  Google Scholar 

  5. J. W. Cohen, The Single Server Queue, North-Holland, Amsterdam, 1982.

    Google Scholar 

  6. V. Ramaswami, The M/G/1 queue and its detailed analysis, Adv. Appl. Proba., 1980, 12(1): 222–261.

    Article  Google Scholar 

  7. M. S. Ross, Stochastic Processes, Wiley, New York, 1983.

    Google Scholar 

  8. D. V. Widder, The Laplace Transform, Princeton University Press, Princeton, 1941.

    Google Scholar 

  9. Y. H. Tang, The departure process of M/G/1 queueing model with server vacation and exhaustive service discipline, J. Appl. Proba., 1994, 31(4): 1070–1082.

    Article  Google Scholar 

  10. Y. H. Tang, The transient solution for M/G/1 queue with server vacations. Acta Math. Scientia, 1997, 17(3): 276–282.

    Google Scholar 

  11. Y. H. Tang and X. W. Tang, The queue length distribution for M/G//1 queue with delay single server vacation, J. of Sys. Sci. & Sys. Engi., 2000, 9(2): 171–178.

    Google Scholar 

  12. B. T. Doshi, Queueing systems with vacations-A survey, Queueing Systems, 1986, 1(1): 29–66.

    Article  Google Scholar 

  13. M. L. Chaudhry and J. G. C. Templeton, A First Course in Bulk Queues, Wiley, New York, 1983.

    Google Scholar 

  14. Y. Levy and Y. Yechiali, Utilization of idle time in an M/G/1 queueing system, Mgmt. Sci., 1975, 22(2): 202–211.

    Google Scholar 

  15. H. S. Lee and M. M. Srinivasan, Control policies for the M x/G/1 queueing system, Mgmt. Sci., 1989, 35(6): 708–721.

    Article  Google Scholar 

  16. Y. Baba, On the M x/G/1 queue with vacation time, O. R. Letters, 1986, 5(2): 93–98.

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics & software Science, Sichuan Normal University, Chengdu, 610066, China

    Yinghui Tang

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  1. Yinghui Tang
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Correspondence to Yinghui Tang.

Additional information

This research is supported by Natural Science Foundation of the Education Department of Sichuan Province ([2006]A067) and the Talent Introduction Foundation of Sichuan Normal University.

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Tang, Y. On The Transient Departure Process of M x/G/1 Queueing System with Single Server Vacation. Jrl Syst Sci & Complex 20, 562–571 (2007). https://doi.org/10.1007/s11424-007-9054-x

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  • DOI: https://doi.org/10.1007/s11424-007-9054-x

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