About some extended Erlang-Sevast'yanov queueing system and its convergence rate (English and Russian versions)

TL;DR

This paper derives an upper bound for the convergence rate of the distribution in a multi-server queueing system with state-dependent arrival and service intensities, enhancing understanding of its long-term behavior.

Contribution

It provides a new upper bound for the convergence rate in an extended Erlang-Sevast'yanov queueing model with state-dependent parameters.

Findings

Upper bound for convergence rate obtained

Applicable to systems with infinite servers and state-dependent intensities

Improves understanding of system stability and long-term distribution

Abstract

The upper bound for the convergence rate of the distribution of the state of a queuing system with infinitely many servers is obtained, in the case when the intensity of the incoming flow and the intensity of the service depend on the state of the system. Typos and spelling errors have been corrected in the new version of the text; the content of the text has remained unchanged. ----- Poluchena ocenka sverhu dlia skorosti shodimosti raspredeleniia sostoianiia beskonechnolinejnoj sistemy massovogo obsluzhivaniia v sluchae, kogda intensivnost` vhodiashchego potoka i intensivnost` obsluzhivaniia zavisiat ot sostoianiia sistemy. Opechatki i orfograficheskie oshibki ispravleny v novoj versii teksta; soderzhanie teksta ostalos' neizmennym.