Open Access
Research Article
Stochastic modeling of a retrial queue with server vacations and customer impatience in a multi-level environment
*C. T. Dora PravinaCorresponding authortdorapravinac@veltech.edu.inDepartment of Mathematics Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology AvadiDepartment of Mathematics Vel Tech Rangarajan Dr Sagunthala R &D Institute of Science and Technology Avadi Chennai, Tamil Nadu, 600055, IndiaView full profile → , G. Hemavathihemagovidh@gmail.comDepartment of Mathematics Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology AvadiChennai, Tamil Nadu, 600062, IndiaView full profile → , Sukumaran DamodaranSukumaran.d@velhightech.comDepartment of Mathematics Vel Tech High Tech Dr. Rangarajan Dr. Sakunthala Engineering College Avadi Chennai, Tamil Nadu, 600062, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Nov 2025
- Published Online:
- 01 Jun 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIOS-2175
- Pages:
- 2391–2400
Abstract
This paper analyzes a single-server retrial queue with vacations and customer impatience in a multi-level stochastic environment. Customer arrivals follow a Poisson process whose rate depends on the environment level and receive immediate exponential service if the server is idle. Otherwise, the customer joins an orbit and is queued as per the FCFS discipline, and retries for service follows an exponential distribution. Whenever the system becomes empty, the server takes a vacation during which arrivals enter the orbit but are not served, and orbiting customers may abandon due to impatience. After vacation, the server stays idle until service is triggered by a new arrival or a retrial.
Keywords
Subject Classifications
60K2560J2790B2290B25
References
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