Applications of Stochastic Semigroups to Queueing Models

Piotr Gwiżdż

doi:10.2478/amsil-2018-0007

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Applications of Stochastic Semigroups to Queueing Models

Annales Mathematicae Silesianae

Volume 33 (2019): Issue 1 (September 2019)

By: Piotr Gwiżdż

Open Access

|Jul 2019

Abstract

Non-markovian queueing systems can be extended to piecewise-deterministic Markov processes by appending supplementary variables to the system. Then their analysis leads to an infinite system of partial differential equations with an infinite number of variables and non-local boundary conditions. We show how one can study such systems by using the theory of stochastic semigroups.

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Articles in this issue

DOI: https://doi.org/10.2478/amsil-2018-0007 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 121 - 142

Submitted on: Apr 18, 2018

Accepted on: May 22, 2018

Published on: Jul 18, 2019

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

stochastic semigroup,

invariant density,

piecewise deterministic Markov process,

queueing systems

Related subjects:

Mathematics,

General mathematics

© 2019 Piotr Gwiżdż, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 33 (2019): Issue 1 (September 2019)