Diffusion Limit for Single-Server Retrial Queues with Renewal Input and Outgoing Calls

Anatoly Nazarov, Tuan Phung-Duc, Svetlana Paul and Olga Lizyura
Additional contact information
Anatoly Nazarov: Institute of Applied Mathematics and Computer Science, National Research Tomsk State University, 36 Lenina Ave., 634050 Tomsk, Russia
Tuan Phung-Duc: Department of Policy and Planning Sciences, Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1 Tennodai, Tsukuba 305-8573, Ibaraki, Japan
Svetlana Paul: Institute of Applied Mathematics and Computer Science, National Research Tomsk State University, 36 Lenina Ave., 634050 Tomsk, Russia
Olga Lizyura: Institute of Applied Mathematics and Computer Science, National Research Tomsk State University, 36 Lenina Ave., 634050 Tomsk, Russia

Mathematics, 2022, vol. 10, issue 6, 1-14

Abstract: This paper studies a single-server retrial queue with two types of calls (incoming and outgoing calls). Incoming calls arrive at the server according to a renewal process, and outgoing calls of N − 1 ( N ≥ 2 ) categories occur according to N − 1 independent Poisson processes. Upon arrival, if the server is occupied, an incoming call joins a virtual infinite queue called the orbit, and after an exponentially distributed time in orbit enters the server again, while outgoing calls are lost if the server is busy at the time of their arrivals. Although M/G/1 retrial queues and their variants are extensively studied in the literature, the GI/M/1 retrial queues are less studied due to their complexity. This paper aims to obtain a diffusion limit for the number of calls in orbit when the retrial rate is extremely low. Based on the diffusion limit, we built an approximation to the distribution of the number of calls in orbit.

Keywords: retrial queue; two-way communication; renewal process; diffusion approximation; incoming call; outgoing call (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/6/948/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/6/948/ (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:10:y:2022:i:6:p:948-:d:772342

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 ().