Non-Markovian Feedback Retrial Queue with Two Types of Customers and Delayed Repair Under Bernoulli Working Vacation

Authors

  • Sundarapandiyan S Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamilnadu, India
  • Nandhini S Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamilnadu, India https://orcid.org/0000-0002-2506-732X

DOI:

https://doi.org/10.37256/cm.5220243940

Keywords:

retrial queue, G-queue, working vacation, delayed repair, feedback, supplementary variable technique

Abstract

This paper deals with an M/G/1 feedback retrial G-queue and delayed repair incorporating Bernoulli working vacation. Arrivals of both favorable and unfavorable consumers are two independent Poisson processes. The server is subjected to breakdown during the regular busy period due to the arrival of unfavorable customers and then the server will be down for a short period of time. Further, the concept of delay time is also discussed. After the fulfillment of regular service, the dissatisfied consumer may re-join the orbit to receive another service as a feedback consumer. During the working vacation period, the server provides the service to consumers at a reduced rate. By applying the supplementary variable technique (SVT), we have analyzed the steady-state probability generating function (PGF) for the system size and orbit size. In addition, we have presented the system performance, reliability indicators, and stochastic decomposition property. Finally, we provided numerical examples to illustrate our model’s mathematical results.

Downloads

Published

2024-05-10

How to Cite

1.
S S, S N. Non-Markovian Feedback Retrial Queue with Two Types of Customers and Delayed Repair Under Bernoulli Working Vacation. Contemp. Math. [Internet]. 2024 May 10 [cited 2024 May 28];5(2):2093-122. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/3940