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The M/G-G/1 Oscillating Queueing System

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Abstract

In this paper oscillating queueing system is studied. Oscillating queueing systems are interesting practical objects and researches in this subject are a natural continuation of previous studies on oscillating stochastic processes. It is shown a powerful method for finding characteristic quantities of queuing systems (potential method). Using this method the steady-state distribution of the length of the queue in the M/G-G/1 oscillating system is found and presented in explicit formula. In addition, a numerical example is given.

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References

  1. A.A. Borovkov, The limit distribution for an oscillating random walk, Teor. Veroyatnost. Primenen. 25(3) (1980).

  2. M.S. Bratiychuk and D.V. Gusak, Ergodic distribution of an oscillating process with independent increments, Ukrainian. Math. J. 38(5) (1986).

  3. J.W. Cohen, The Single Server Queue (North-Holland, Amsterdam, 1982).

    Google Scholar 

  4. W. Feller, Probability Theory and its Applications, Vol. II (Wiley, New York, 1966).

    Google Scholar 

  5. D.V. Gusak, On oscillating schemes of a random walk, Teor. Veroyatnost. Mat. Statist. 39 (1988).

  6. D.V. Gusak, Oscillating processes with independent increments and non-degenerate Wiener component, Ukrainian Math. J. 42(10) (1991).

  7. J. Keilson and R.D. Servi, Oscillating random walk models for GI/G/1 vacation systems with Bernoulli schedules, J. Appl. Probab. 23 (1986).

  8. J.H. Kemperman, The oscillating random walk, Stochastic Process. Appl. 2(1) (1974).

  9. W.S. Korolyuk, Boundary Problems for Compound Poisson Processes (Naukowa Dumka, Kiev, 1975).

    Google Scholar 

  10. V.I. Lotov, On oscillating random walks, Siberian Math. J. 37(4) (1996).

  11. B.A. Rogozin and S.G. Foss, Recurrence of an oscillating random walk, Teor. Veroyatnost. Primenen. 23(1) (1978).

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Authors and Affiliations

  1. Institute of Computer Sciences, Silesian University of Technology, Akademicka 16, 44-100, Gliwice, Poland

    Andrzej Chydzinski

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  1. Andrzej Chydzinski
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Chydzinski, A. The M/G-G/1 Oscillating Queueing System. Queueing Systems 42, 255–268 (2002). https://doi.org/10.1023/A:1020523931025

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  • DOI: https://doi.org/10.1023/A:1020523931025

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