Informatics and Applications
2022, Volume 16, Issue 1, pp 61-67
THE COMPARISON OF WAITING TIME EXTREMAL INDEXES IN M/G/1 QUEUEING SYSTEMS
Abstract
The theorem which states that if the initial stationary sequences are stochastically ordered, there are limiting distributions for maxima and the normalizing sequences are ordered, then their extreme indexes are also ordered is proved. This result is applied to compare the extreme indexes of stationary waiting times in two M/G/1 systems with the same input flows and stochastically ordered service times. Three examples of queueing systems with exponential distribution, Pareto distribution, and Weibull distribution of service times are considered. For these distributions, the relations between the parameters guaranteeing the stochastic ordering of the distributions and the normalizing sequences are obtained.
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[+] About this article
Title
THE COMPARISON OF WAITING TIME EXTREMAL INDEXES IN M/G/1 QUEUEING SYSTEMS
Journal
Informatics and Applications
2022, Volume 16, Issue 1, pp 61-67
Cover Date
2022-03-30
DOI
10.14357/19922264220109
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
extreme value distributions; extremal index; queueing system; stochastic ordering
Authors
I. V. Peshkova 
Author Affiliations
Petrozavodsk State University, 33 Lenina Pr., Petrozavodsk 185910, Russian Federation
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