Volume 56, Number 3, May-June 2022
|Page(s)||1089 - 1117|
|Published online||12 May 2022|
Performance analysis of discrete-time GeoX/G/1 retrial queue with various vacation policies and impatient customers
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: firstname.lastname@example.org
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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