Systems and Means of Informatics
2026, Volume 36, Issue 1, pp 104-121
BUSY PERIOD ANALYSIS IN M/G/l RETRIAL QUEUE WITH CONSTANT RETRIAL RATE
- K. A. Zhukova
- E. V. Morozov
Abstract
The busy period of a stationary single-server retrial system with a constant retrial rate is studied. The analysis is based on a comparison of the original retrial system with a buffered M/G/l-type model featuring exceptional first service. It is shown that the busy period distribution satisfies a functional equation similar to the well-known equation for the conventional M/G/l system.
The main result is expressed in terms of Laplace-Stieltjes transforms for the continuous busy period duration and in terms of generating functions for the integer-valued busy period length. Several analytical examples are provided.
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[+] About this article
Title
BUSY PERIOD ANALYSIS IN M/G/l RETRIAL QUEUE WITH CONSTANT RETRIAL RATE
Journal
Systems and Means of Informatics
Volume 36, Issue 1, pp 104-121
Cover Date
2026-05-05
DOI
10.14357/08696527260107
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
retrial queue; busy period; regeneration; stationarity; Laplace- Stieltjes transform; constant retrial rate; first exceptional service
Authors
K. A. Zhukova  ,  and E. V. Morozov ,
Author Affiliations
Institute of Applied Mathematical Research of the Karelian Research Centre of the Russian Academy of Sciences, 11 Pushkinskaya Str., Petrozavodsk 185910, Russian Federation
Petrozavodsk State University, 33 Lenin Str., Petrozavodsk 185910, Republic of Karelia, Russian Federation
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