<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

Applications of Stochastic Semigroups to Queueing Models

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Applications of Stochastic Semigroups to Queueing Models"}

Non-markovian queueing systems can be extended to piecewise-deterministic Markov processes by appending supplementary variables to the system. Then their...

Applications of Stochastic Semigroups to Queueing Models

Published Online: Jul 18, 2019

Page range: 121 - 142

Received: Apr 18, 2018

Accepted: May 22, 2018

DOI: https://doi.org/10.2478/amsil-2018-0007

Keywords
stochastic semigroup, invariant density, piecewise deterministic Markov process, queueing systems

© 2019 Piotr Gwiżdż, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Applications of Stochastic Semigroups to Queueing Models

Published Online: Jul 18, 2019

Page range: 121 - 142

Received: Apr 18, 2018

Accepted: May 22, 2018

DOI: https://doi.org/10.2478/amsil-2018-0007

Keywordsstochastic semigroup, invariant density, piecewise deterministic Markov process, queueing systems

© 2019 Piotr Gwiżdż, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
stochastic semigroup, invariant density, piecewise deterministic Markov process, queueing systems