On Truncation of the Matrix-Geometric Stationary Distributions

Valeriy A. Naumov, Yuliya V. Gaidamaka and Konstantin E. Samouylov
Additional contact information
Valeriy A. Naumov: Service Innovation Research Institute, 00120 Helsinki, Finland
Yuliya V. Gaidamaka: Department of Applied Informatics and Probability, Peoples’ Friendship University of Russia (RUDN University), Miklukho-Maklaya St. 6, Moscow 117198, Russia
Konstantin E. Samouylov: Department of Applied Informatics and Probability, Peoples’ Friendship University of Russia (RUDN University), Miklukho-Maklaya St. 6, Moscow 117198, Russia

Mathematics, 2019, vol. 7, issue 9, 1-10

Abstract: In this paper, we study queueing systems with an infinite and finite number of waiting places that can be modeled by a Quasi-Birth-and-Death process. We derive the conditions under which the stationary distribution for a loss system is a truncation of the stationary distribution of the Quasi-Birth-and-Death process and obtain the stationary distributions of both processes. We apply the obtained results to the analysis of a semi-open network in which a customer from an external queue replaces a customer leaving the system at the node from which the latter departed.

Keywords: Quasi-Birth-and-Death process; matrix-geometric solution; truncated distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/9/798/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/9/798/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:9:p:798-:d:262871

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().