31. On extreme values in queues in series

Saulius Minkevičius1, Edvinas Greičius2

Vilnius University, Faculty of Mathematics and Informatics, Naugarduko 24, 03225 Vilnius, Lithuania

1Corresponding author

E-mail: 1minkevicius.saulius@gmail.com, 2edvinas.greicius@gmail.com

Received 4 October 2016; received in revised form 24 January 2017; accepted 25 January 2017

DOI https://doi.org/10.21595/mme.2017.17808

 

Abstract. A model of queues in series under conditions of heavy traffic is developed in this paper. This is a mathematical model to measure performance of complex computer networks operating under conditions of heavy traffic. Two limit theorems are derived by investigating extreme values of a virtual waiting time of customers in queues in series. Due to serious technical difficulties, research does not often consider intermediate models of queues in series. Note that the research of extreme values in more specific systems than the classical example GI/G/N (multiserver queue, queues in series, etc.) was introduced only 20 years ago [1]. There are many real‑world applications at various hierarchical levels for both queues in series and tandem queues, for example, in high-speed communication networks (from architecture of the router to protocol stacks [2]).

Keywords: queues in series, performance evaluation, heavy traffic, queueing systems.

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Cite this article

Minkevičius Saulius, Greičius Edvinas On extreme values in queues in series. Mathematical Models in Engineering, Vol. 3, Issue 1, 2017, p. 17‑26.

 

Mathematical Models in Engineering. June 2017, Volume 3, Issue 1

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