Analysis of a Queuing System with Possibility of Waiting Customers Jockeying between Two Groups of Servers

Sergei A. Dudin (), Olga S. Dudina and Olga I. Kostyukova
Additional contact information
Sergei A. Dudin: Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus
Olga S. Dudina: Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus
Olga I. Kostyukova: Institute of Mathematics, National Academy of Sciences of Belarus, 220072 Minsk, Belarus

Mathematics, 2023, vol. 11, issue 6, 1-21

Abstract: In this paper, we consider a queueing system consisting of two multi-server subsystems that is designed for the service of clients arriving at a system according to a Markovian arrival process ( MAP ). Arriving clients receive information about the number of clients present in both subsystems and use this information to make a randomized decision to balk (depart without receiving service) or join the system. In the latter case, they also decide which subsystem they would like to join. One subsystem has an infinite buffer, while the buffer of the second subsystem is finite. The service time distribution is exponential in the first subsystem and phase-type in the second subsystem. During the waiting in the chosen buffers, after the random time intervals, each waiting client checks the status of the alternative subsystem. If some server in that subsystem is idle during this epoch, the client immediately leaves the buffer where it has been staying and starts a service in the alternative subsystem. The problem of computing the steady-state distribution of this system is solved. The feasibility of the proposed solution and certain features of the system’s behavior are numerically illustrated.

Keywords: MAP; level-dependent QBD -process; balking; jockeying; performance evaluation (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 (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/6/1475/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/6/1475/ (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:6:p:1475-:d:1100398

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 ().