Strategy Analysis of Retrial Queue with Parallel Customer and Standby Server

Xinlei Liu (), Xiuli Xu () and Mingxin Liu
Additional contact information
Xinlei Liu: Yanshan University
Xiuli Xu: Yanshan University
Mingxin Liu: Guangdong Ocean University

Methodology and Computing in Applied Probability, 2024, vol. 26, issue 3, 1-22

Abstract: Abstract The objective of this study is devoted to studying the equilibrium strategy of an unreliable M/M/1+1 retrial queue model, which contains two types of parallel customers and batch service provided by a standby server. Two kinds of customers in this queuing system enter the system in parallel and follow the exponential distribution with different parameters. If the server stays idle, an arrival obtains service immediately; Otherwise, he enters the retrial space and waits for service. When a failure occurs, new customers will not be allowed to enter and the customer who is being served will be excluded from the system. Meanwhile, the system enables the standby server to serve customers in the retrial space with batch service mode. Based on the revenue-cost theory, we propose a benefit function and perform the equilibrium analysis for two types of parallel customers in both fully observable and almost observable cases. In addition, the average social benefits of this particular system are detailed analyzed by using symbolic calculation. Finally, the numerical illustrations that aid in visualizing the changes in customer behavior strategies and social benefits as the different system parameters.

Keywords: Retrial queue; Parallel customers; Batch service; Equilibrium strategy; Social benefits; 60K25; 91B50 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-024-10098-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:metcap:v:26:y:2024:i:3:d:10.1007_s11009-024-10098-7

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-024-10098-7

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().