Ergodicity and Related Bounds for One Particular Class of Markovian Time—Varying Queues with Heterogeneous Servers and Customer’s Impatience

Yacov Satin, Rostislav Razumchik, Ivan Kovalev and Alexander Zeifman ()
Additional contact information
Yacov Satin: Department of Applied Mathematics, Vologda State University, 15 Lenina Str., 160000 Vologda, Russia
Rostislav Razumchik: Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44-2 Vavilov Str., 119133 Moscow, Russia
Ivan Kovalev: Department of Applied Mathematics, Vologda State University, 15 Lenina Str., 160000 Vologda, Russia
Alexander Zeifman: Department of Applied Mathematics, Vologda State University, 15 Lenina Str., 160000 Vologda, Russia

Mathematics, 2023, vol. 11, issue 9, 1-15

Abstract: We consider a non-standard class of Markovian time: varying infinite capacity queues with possibly heterogeneous servers and impatience. We assume that during service time, a customer may switch to the faster server (with no delay), when such a server becomes available and no other customers are waiting. As a result, customers in the queue may become impatient and leave it. Under this setting and with certain restrictions on the intensity functions, the quantity of interest, the total number of customers in the system, is the level-dependent birth-and-death process (BPD). In this paper, for the first time in the literature, explicit upper bounds for the distance between two probability distributions of this BDP are obtained. Using the obtained ergodicity bounds in combination with the sensitivity bounds, we assess the stability of BDP under perturbations. Truncation bounds are also given, which allow for numerical solutions with guaranteed truncation errors. Finally, we provide numerical results to support the findings.

Keywords: nonstationary queuing system; impatience; birth-death process; ergodicity; bounds; limiting characteristics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/9/1979/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/9/1979/ (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:11:y:2023:i:9:p:1979-:d:1129969

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 ().