Non-stationary flows in queuing networks without queue and with deterministic service time | Vestnik Tomskogo gosudarstvennogo universiteta. Upravlenie, vychislitelnaja tehnika i informatika – Tomsk State University Journal of Control and Computer Science. 2025. № 73. DOI: 10.17223/19988605/73/5

Non-stationary flows in queuing networks without queue and with deterministic service time

The paper builds a mathematical model of an acyclic queuing network with an unsteady Poisson input flow, no queue, and deterministic service time. The non-stationary intensities of the flows passing through the network are calculated. It is proving that if the input flow is Poisson, then all other flows passing through the network are also Poisson. Moreover, the number of customers located in each node of the network also has a Poisson distribution. The parameters of these Poisson distributions are calculated using special integral relations. The author declares no conflicts of interests.

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Keywords

Poisson flow, acyclic network, directed graph, coloring theorem, maximum path length in graph

Authors

Name	Organization	E-mail
Tsitsiashvili Gurami Sh.	Institute for Applied Mathematics, Far Eastern Branch of RAS	guram@iam.dvo.ru

Всего: 1

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