On convergence rate for an infinite-channel queuing system with Poisson input flow

TL;DR

This paper investigates the convergence rate of a regenerative process in an infinite-channel queueing system with Poisson input, focusing on how quickly the system approaches its stationary regime.

Contribution

It provides new estimates for the convergence rate of the queueing process with infinite servers and Poisson arrivals, enhancing understanding of its long-term behavior.

Findings

Derived bounds for convergence speed to stationarity

Analyzed the impact of Poisson input on system stability

Provided mathematical estimates for regenerative process convergence

Abstract

Obtaining estimates of the convergence rate of the regenerating process $Q(t)$ whose value at time $t$ is equal to the number of claims in the system $ M \backslash G \backslash \infty $ at this moment, to the limit (stationary) regime.