Informatics and Applications
2019, Volume 13, Issue 3, pp 14-19
ON THE BOUNDS OF THE RATE OF CONVERGENCE FOR SOME QUEUEING MODELS WITH INCOMPLETELY DEFINED INTENSITIES
- A. I. Zeifman
- Y. A. Satin
- K. M. Kiseleva
Abstract
The authors consider some queuing systems with incompletely defined 1-periodical intensities under corresponding conditions. The authors deal with Mt/Mt/S queue for any number of servers S and Mt/Mt/S/S (the Erlang model). Estimates of the rate of convergence in weakly ergodic situation are obtained by applying the method of the logarithmic norm of the operator of a linear function. The examples with exact given values of intensities and different variations of amplitude and frequency are considered, ergodicity conditions and estimates of the rate of convergence are obtained for each model, and plots of the effect of intensities' amplitude and frequency of incoming requirements on the limiting characteristics of the process are constructed. The authors use the general algorithm to build graphs, it is associated with solving the Cauchy problem for the forward Kolmogorov system on the corresponding interval, which has already been used by the authors in previous papers.
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[+] About this article
Title
ON THE BOUNDS OF THE RATE OF CONVERGENCE FOR SOME QUEUEING MODELS WITH INCOMPLETELY DEFINED INTENSITIES
Journal
Informatics and Applications
2019, Volume 13, Issue 3, pp 14-19
Cover Date
2019-09-30
DOI
10.14357/19922264190303
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
queuing systems; incompletely defined intensities; rate of convergence; ergodicity; logarithmic norm; Mt/Mt/S queue; Mt/Mt/S/S queue
Authors
A. I. Zeifman  ,  ,  , Y. A. Satin , and K. M. Kiseleva
Author Affiliations
Vologda State University, 15 Lenin Str., Vologda 160000, Russian Federation
Institute of Applied Mathematical Research, Karelian Research Centre of the Russian Academy of Sciences,
11 Pushkinskaya Str., Petrozavodsk 185910, Karelia, Russian Federation
Vologda Research Center of the Russian Academy of Sciences, 56A Gorky Str., Vologda 160014, Russian Federation
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