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

Saulius Minkevičius (), Vladimiras Dolgopolovas () and Leonidas L. Sakalauskas
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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

Methodology and Computing in Applied Probability, 2016, vol. 18, issue 1, 37-57

Abstract: 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.

Keywords: Queueing systems; Queues in series; Heavy traffic; A law of the iterated logarithm; Sojourn time of a customer; Maximum of the sojourn time of a customer; Statistical modeling; Monte Carlo simulation; 60K25; 60G70; 60F17 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s11009-014-9402-y

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