Systems and Means of Informatics
2026, Volume 36, Issue 3, pp 35-46
STABILITY CRITERION OF A MULTICLASS QUEUEING SYSTEM WITH NONIDENTIAL SERVERS
Abstract
The paper provides a new, short proof of the stability criterion for a multiclass stochastic M/G/m-type queueing system with an unlimited buffer for the waiting customers and different classes of customers such that the service time of a customer depends both on their class and the assigned server. The proof is based on the theory of regenerative processes and a balance relation for the number of customers in the system, unlike the proof found earlier which used a balance relation for the workload process. The criterion is constructively formulated and has the following evident intuitive interpretation: the input rate must be less than the (properly defined) maximal capacity of the system. Moreover, the proof shows all the main steps of the regenerative stability analysis method of stochastic queueing systems.
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[+] About this article
Title
STABILITY CRITERION OF A MULTICLASS QUEUEING SYSTEM WITH NONIDENTIAL SERVERS
Journal
Systems and Means of Informatics
Volume 36, Issue 3, pp 35-46
Cover Date
2026-11-15
DOI
10.14357/08696527260302
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
multiserver queueing system; regeneration; nonidentical servers; customers of different classes; stability criterion
Authors
E. V. Morozov  , 
Author Affiliations
Institute of Applied Mathematical Research of Karelian Research Centre of the Russian Academy of Science, 11 Pushkinskaya Str., Petrozavodsk 185910, Republic of Karelia, Russian Federation
Petrozavodsk State University, 33 Lenina Pr., Petrozavodsk 185910, Republic of Karelia, Russian Federation
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