Approximation of the birth process

TL;DR

This paper investigates queuing systems with infinite devices and nonstationary Poisson arrivals, demonstrating that approximating the birth process with Poisson flows is ineffective for long-term predictions.

Contribution

It reveals the limitations of using Poisson flow approximations for birth processes in complex queuing systems with Markov-controlled flows.

Findings

Poisson approximation is ineffective for long-term forecasting.

Queuing systems with Markov-controlled flows are complex.

Poisson flows do not accurately model birth processes over time.

Abstract

Queuing systems with an unlimited number of devices with an incoming nonstationary Poisson flow and a random flow controlled by a Markov chain are investigated. The inexpediency of ap-proximation of the birth process by Poisson flows in long-term forecasting is shown.