Price Decisions in a Two-Server Queue Considering Customer Retrial Behavior: Profit-Driven Versus Social-Driven

Xiaoli Cai, Miaomiao Yu () and Yunling Yang
Additional contact information
Xiaoli Cai: College of Management Science, Chengdu University of Technology, Chengdu 610059, China
Miaomiao Yu: School of Mathematics Sciences, Sichuan Normal University, Chengdu 610066, China
Yunling Yang: Department of Mathematics, Faculty 3-Mathematics and Computer Science, University of Bremen, 28359 Bremen, Germany

Mathematics, 2025, vol. 13, issue 8, 1-21

Abstract: This study investigates price decisions in a queue with two servers, where customers exhibit retrial behavior. There is no waiting space. Arrival customers have the option to either join the system or balk; when the two servers are occupied, those who decide to enter become repeat customers. Two scenarios where the waiting lines in orbit are unobservable and observable are considered. We analyze customers’ behavior and derive their Nash equilibrium strategies under both cases. Additionally, we examine optimal pricing decisions aimed at maximizing profit and social welfare, respectively. Moreover, we demonstrate that these objectives often lead to divergent outcomes. Compared to a single-server queue, the reduction in customers’ sojourn time is more obvious when the waiting line is unobservable. Under certain conditions—such as a large potential market size, high customer impatience, or a low retrial rate—increasing the number of service personnel can enhance both profit and social welfare. Notably, a profit-maximizing manager is more incentivized to increase servers than the social planner. These findings provide valuable insights for balancing operational efficiency, profitability, and customer satisfaction in queue management systems.

Keywords: two-server queue; retrial behavior; price decision; equilibrium analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/8/1310/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/8/1310/ (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:13:y:2025:i:8:p:1310-:d:1636196

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 ().