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Heavy Traffic Limits for the Extreme Waiting Time in Multi-phase Queueing Systems

Author

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  • Saulius Minkevičius

    (Vilnius University)

  • Edvinas Greičius

    (Vilnius University)

Abstract

The main object of this research is a functional limit theorem under conditions of heavy traffic in multi-phase queueing systems. In this paper, limit theorems are proved for extreme values of important probabilistic characteristics of a queueing system, as well as maxima and minima of a waiting time and cumulative waiting time of a customer are investigated and illustrative numerical examples of simulation of multi-phase queueing systems are presented.

Suggested Citation

  • Saulius Minkevičius & Edvinas Greičius, 2019. "Heavy Traffic Limits for the Extreme Waiting Time in Multi-phase Queueing Systems," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 109-124, March.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:1:d:10.1007_s11009-018-9641-4
    DOI: 10.1007/s11009-018-9641-4
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    References listed on IDEAS

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    1. Martin I. Reiman, 1984. "Open Queueing Networks in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 9(3), pages 441-458, August.
    2. Sakalauskas, L. L. & Minkevicius, S., 2000. "On the law of the iterated logarithm in open queueing networks," European Journal of Operational Research, Elsevier, vol. 120(3), pages 632-640, February.
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