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A Law of the Iterated Logarithm for the Sojourn Time Process in Queues in Series

Author

Listed:
  • Saulius Minkevičius

    (Institute of Mathematics and Informatics of VU)

  • Vladimiras Dolgopolovas

    (Institute of Mathematics and Informatics of VU)

  • Leonidas L. Sakalauskas

    (Institute of Mathematics and Informatics of VU)

Abstract

The object of this research in the sphere of queueing theory is the law of the iterated logarithm under the conditions of heavy traffic in queues in series. In this paper, the laws of the iterated logarithm are proved for the values of important probabilistic characteristics of the queueing system, like the sojourn time of a customer, and maximum of the sojourn time of a customer. Also, we prove that the sojourn time of a customer can be approximated by some recurrent functional. We also provide the results of statistical simulations for various system parameters and distributions.

Suggested Citation

  • Saulius Minkevičius & Vladimiras Dolgopolovas & Leonidas L. Sakalauskas, 2016. "A Law of the Iterated Logarithm for the Sojourn Time Process in Queues in Series," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 37-57, March.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:1:d:10.1007_s11009-014-9402-y
    DOI: 10.1007/s11009-014-9402-y
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    References listed on IDEAS

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