Performance Study of an M/M/1 Retrial Queueing System with Balking, Dissatisfied Customers, and Server Vacations

Authors

  • Ismailkhan Enayathulla Khan Department of Mathematics, School of advanced sciences, Vellore Institute of Technology, Vellore-632014, India
  • Rajendran Paramasivam Department of Mathematics, School of advanced sciences, Vellore Institute of Technology, Vellore-632014, India https://orcid.org/0000-0003-3694-2190

DOI:

https://doi.org/10.37256/cm.4320233117

Keywords:

retrial queue, balking, server break, dissatisfied customer

Abstract

This study considers a single server retrial queueing system with dissatisfied customers, server vacations, and balking customers. When new arrivals clients see an idle server available, they immediately enter service. If a new arrival sees the server busy, that arrival may balk and leave the system. Otherwise, the new arrival will enter a retrial orbit and try again later. Customers who are dissatisfied with the service will be served again until the service is completed successfully. The server begins a vacation when the current customer completes service. Birth and death state transitions are given. Steady-state distributions for queue length are found. Furthermore, a recursive technique is used to evaluate probabilities. Several performance measures of the system are identified and effects of changes to parameters are observed.

Downloads

Published

2023-08-15

How to Cite

1.
Khan IE, Paramasivam R. Performance Study of an M/M/1 Retrial Queueing System with Balking, Dissatisfied Customers, and Server Vacations. Contemp. Math. [Internet]. 2023 Aug. 15 [cited 2024 Mar. 4];4(3):467-83. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/3117