Issue |
RAIRO-Oper. Res.
Volume 56, Number 3, May-June 2022
|
|
---|---|---|
Page(s) | 1089 - 1117 | |
DOI | https://doi.org/10.1051/ro/2022042 | |
Published online | 12 May 2022 |
Performance analysis of discrete-time GeoX/G/1 retrial queue with various vacation policies and impatient customers
1
Department of Mathematics, PSG College of Technology, Coimbatore 641004, Tamil Nadu, India
2
Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas 110016, New Delhi, India
* Corresponding author: rajasudharajesh@gmail.com
Received:
25
January
2021
Accepted:
4
March
2022
This paper studies the behavior of a batch arrival single server retrial queueing model under three different vacation policies. Three types of vacation policies, single vacation, multiple vacations, and atmost J-vacations with impatient customers in general retrial times are considered. The probability generating function and marginal generating function of orbit size are obtained in a steady state. The stability condition for each vacation model is derived. Performance measures such as mean orbit size, mean system size, mean waiting time of a customer, and the probabilities of the server being in different states have also been determined. Based on performance characteristics, a comparative analysis is performed among the three vacations. Numerical illustrations are displayed to establish the consistency of the theory developed.
Mathematics Subject Classification: 60K25 / 68M20 / 90B22
Key words: Discrete-time / retrial / batch arrival / single server / impatient customers / single vacation / multiple vacations / J vacations
© The authors. Published by EDP Sciences, ROADEF, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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