Informatics and Applications
2026, Volume 20, Issue 2, pp 89-95
ANALYSIS OF AN M/G/1 QUEUE WITH EVENT-DEPENDENT ARRIVAL RATES UNDER HEAVY TRAFFIC CONDITION
- A. K. Bergovin
- V. G. Ushakov
Abstract
A single-server queueing system with an unlimited waiting capacity and arbitrary service time distribution is studied, in which the arrival rate of the Poisson input process depends on the last event in the system: an arrival or a service completion. Input flows of this structure make it possible to model situations where the behavior of the incoming flow depends on the system's operation. The method of supplementary components serves as the mathematical apparatus of the study, with the help of which the distribution of the number of customers in the system was found in the nonstationary regime and, as a consequence, in the stationary regime as well. Given that most real-world systems are heavily loaded, there arises a need to investigate the system's characteristics under critical load conditions; therefore, the second part of the paper is devoted to this task. Based on the analysis of the queue-length behavior under critical load, the limiting distribution of the number of customers in the system is obtained in explicit form.
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[+] About this article
Title
ANALYSIS OF AN M/G/1 QUEUE WITH EVENT-DEPENDENT ARRIVAL RATES UNDER HEAVY TRAFFIC CONDITION
Journal
Informatics and Applications
2026, Volume 20, Issue 2, pp 89-95
Cover Date
2026-10-07
DOI
10.14357/19922264260208
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
Poisson flow; event-dependent rate; queue length; supplementary variable method; heavy traffic
Authors
A. K. Bergovin  ,  and V. G. Ushakov , 
Author Affiliations
Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M. V Lomonosov Moscow State University, 1-52 Leninskie Gory, GSP-1, Moscow 119991, Russian Federation
Moscow Center for Fundamental and Applied Mathematics, M.V. Lomonosov Moscow State University, 1 Leninskie Gory, GSP-1, Moscow 119991, Russian Federation
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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