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

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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.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics of VU, Akademijos 4, 08663, Vilnius, Lithuania

    Saulius Minkevičius, Vladimiras Dolgopolovas & Leonidas L. Sakalauskas

Authors
  1. Saulius Minkevičius
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  2. Vladimiras Dolgopolovas
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  3. Leonidas L. Sakalauskas
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Correspondence to Vladimiras Dolgopolovas.

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Research supported in part by the National Complex Programme “Theoretical and Engineering aspects of e-service technology creation and application in high-performing calculation platforms”

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Minkevičius, S., Dolgopolovas, V. & Sakalauskas, L.L. A Law of the Iterated Logarithm for the Sojourn Time Process in Queues in Series. Methodol Comput Appl Probab 18, 37–57 (2016). https://doi.org/10.1007/s11009-014-9402-y

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  • DOI: https://doi.org/10.1007/s11009-014-9402-y

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