On Two Interacting Markovian Queueing Systems

On Two Interacting Markovian Queueing Systems

In this paper, we study a Markovian queuing system consisting of two subsystems of an arbitrary structure. Each subsystem generates a multi-class Markovian arrival process of customers arriving to the other subsystem. We derive the necessary and sufficient conditions for the stationary distribution...

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Main Authors: Valeriy A. Naumov, Yuliya V. Gaidamaka, Konstantin E. Samouylov
Format: Article
Language:English
Published: MDPI AG 2019-09-01
Series:Mathematics
Subjects:
Markovian arrival process
multi-class arrival processes
product form
Online Access:https://www.mdpi.com/2227-7390/7/9/799
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spelling doaj-f1132edda4784972a2f1e81e5809fb572020-11-25T02:41:25ZengMDPI AGMathematics2227-73902019-09-017979910.3390/math7090799math7090799On Two Interacting Markovian Queueing SystemsValeriy A. Naumov0Yuliya V. Gaidamaka1Konstantin E. Samouylov2Service Innovation Research Institute, 8 A Annankatu, Helsinki 00120, FinlandDepartment of Applied Informatics and Probability, Peoples’ Friendship University of Russia (RUDN University), Miklukho-Maklaya St. 6, Moscow 117198, RussianDepartment of Applied Informatics and Probability, Peoples’ Friendship University of Russia (RUDN University), Miklukho-Maklaya St. 6, Moscow 117198, RussianIn this paper, we study a Markovian queuing system consisting of two subsystems of an arbitrary structure. Each subsystem generates a multi-class Markovian arrival process of customers arriving to the other subsystem. We derive the necessary and sufficient conditions for the stationary distribution to be of product form and consider some particular cases of the subsystem interaction for which these conditions can be easily verified.https://www.mdpi.com/2227-7390/7/9/799Markovian arrival processmulti-class arrival processesproduct form
collection DOAJ
language English
format Article
sources DOAJ
author Valeriy A. Naumov
Yuliya V. Gaidamaka
Konstantin E. Samouylov
spellingShingle Valeriy A. Naumov
Yuliya V. Gaidamaka
Konstantin E. Samouylov
On Two Interacting Markovian Queueing Systems
Mathematics
Markovian arrival process
multi-class arrival processes
product form
author_facet Valeriy A. Naumov
Yuliya V. Gaidamaka
Konstantin E. Samouylov
author_sort Valeriy A. Naumov
title On Two Interacting Markovian Queueing Systems
title_short On Two Interacting Markovian Queueing Systems
title_full On Two Interacting Markovian Queueing Systems
title_fullStr On Two Interacting Markovian Queueing Systems
title_full_unstemmed On Two Interacting Markovian Queueing Systems
title_sort on two interacting markovian queueing systems
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2019-09-01
description In this paper, we study a Markovian queuing system consisting of two subsystems of an arbitrary structure. Each subsystem generates a multi-class Markovian arrival process of customers arriving to the other subsystem. We derive the necessary and sufficient conditions for the stationary distribution to be of product form and consider some particular cases of the subsystem interaction for which these conditions can be easily verified.
topic Markovian arrival process
multi-class arrival processes
product form
url https://www.mdpi.com/2227-7390/7/9/799
work_keys_str_mv AT valeriyanaumov ontwointeractingmarkovianqueueingsystems
AT yuliyavgaidamaka ontwointeractingmarkovianqueueingsystems
AT konstantinesamouylov ontwointeractingmarkovianqueueingsystems
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