Informatics and Applications
2022, Volume 16, Issue 4, pp 26-33
ON BOUNDS OF THE STATIONARY WAITING TIME EXTREMAL INDEX IN M/G/1 SYSTEM WITH MIXTURE SERVICE TIMES
Abstract
It is proved that if the original stationary sequence has m-component mixture distribution with stochastically ordered components, there are limit distributions for the maxima of all components, and the normalizing sequences are ordered, then the extremal index of the original sequence is within the boundaries of the extremal indexes of the smallest and largest components. This result is used to estimate the extremal index of the stationary waiting time in a queuing system of type M/G/1 in which the queuing time is given by an m-component distribution mixture. An example of a system M/Hm/1 with hyperexponential service time is considered. Using the exact simulation approach, the results of estimating the extremal index of stationary waiting time in the system M/H2/1 are obtained.
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[+] About this article
Title
ON BOUNDS OF THE STATIONARY WAITING TIME EXTREMAL INDEX IN M/G/1 SYSTEM WITH MIXTURE SERVICE TIMES
Journal
Informatics and Applications
2022, Volume 16, Issue 4, pp 26-33
Cover Date
2022-12-30
DOI
10.14357/19922264220405
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 Prosp., Petrozavodsk 185910, Russian Federation
Karelian Research Centre of the Russian Academy of Sciences, 11 Pushkinskaya Str., Petrozavodsk 185910, Russian Federation
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