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On pathwise behavior of multiserver queues

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Abstract

In this paper, by exploiting recent results on the pathwise behavior of the workload process in single server, work conserving queues of theG/G/1/∞ type, we show that the workload of multiserver, work conserving queues ofG/G/m/∞ (m<∞) (andG/G/∞) queues satisfies an o(t) growth condition, provided that the time average of the work brought into the system is less thanm form < ∞ (and finite form=∞).

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References

  1. F. Baccelli and P. Brémaud,Elements of Queueing Theory (Springer, Berlin, 1994) to appear.

    Google Scholar 

  2. N. Bambos and J. Walrand, On stability and performance of parallel processing, J. ACM 38 (1991) 425–452.

    Google Scholar 

  3. A.A. Borovkov,Asymptotic Methods in Queueing Theory (Wiley, New York, 1984).

    Google Scholar 

  4. A.A. Borovkov,Stochastic Processes in Queueing Theory, Applications of Mathematics 4 (Springer, Berlin, 1976).

    Google Scholar 

  5. A.A. Borovkov, Ergodicity and stability theorems for a class of stochastic equations and their applications, Theor. Prob. Appl. 23 (1978) 227–247.

    Google Scholar 

  6. A. Brandt, On stationary waiting times and limiting behavior of queues with many servers I: theG/G/m/∞ case, Elektron. Inform. Kybern. 21 (1985) 47–64.

    Google Scholar 

  7. A. Brandt, On stationary waiting times and limiting behavior of queues with many servers II:, theG/GI/m/∞ case, Elektron. Inform Kybern. 21 (1985) 151–162.

    Google Scholar 

  8. A. Brandt, P. Franken and B. Lisek,Stationary Stochastic Models (Akademie, Berlin, 1990).

    Google Scholar 

  9. M. El Taha and S. Stidham, Sample-path stability conditions for input-output processes, preprint (1992).

  10. S.G. Foss, Ergodicity conditions in multiserver queueing systems with waiting time, Sibirsk. Math. Zh. 24 (1983) 168–175.

    Google Scholar 

  11. J. Kiefer and J. Wolfowitz, On the theory of queues with many servers, Trans. Am. Math. Soc. 78 (1955) 1–18.

    Google Scholar 

  12. R. Loynes, The stability of queues with non- independent inter-arrival and service times, Proc. Cambridge Phil. Soc. 58 (1962) 492–520.

    Google Scholar 

  13. R. Mazumdar, F. Guillemin, V. Badrinath and R. Kannurpatti, On pathwise behavior of queues., Oper. Res. Lett. 12 (1992) 263–270.

    Google Scholar 

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Authors and Affiliations

  1. Route de Trégastel, Centre National d'Etudes des Télécommunications Lannion-A, 22300, Lannion, France

    Fabrice Guillemin

  2. INRS-Télécommunications, Université du Québec, Ile-des-Soeurs, P.Q. H3E1H6, Canada

    Ravi R. Mazumdar

Authors
  1. Fabrice Guillemin
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  2. Ravi R. Mazumdar
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Guillemin, F., Mazumdar, R.R. On pathwise behavior of multiserver queues. Queueing Syst 15, 279–288 (1994). https://doi.org/10.1007/BF01189241

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