Performance analysis of discrete-time $Geo^{X} / G / 1$ retrial queue with various vacation policies and impatient customers

R, Rajasudha; R, Arumuganathan; S, Dharmaraja

doi:10.1051/ro/2022042

Performance analysis of discrete-time

G e o^{X} / G / 1

retrial queue with various vacation policies and impatient customers

R, Rajasudha ; R, Arumuganathan ; S, Dharmaraja

RAIRO. Operations Research, Tome 56 (2022) no. 3, pp. 1089-1117

Résumé

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.

MR Zbl

DOI : 10.1051/ro/2022042

Classification : 60K25, 68M20, 90B22
Keywords: Discrete-time, retrial, batch arrival, single server, impatient customers, single vacation, multiple vacations, $$ vacations

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     author = {R, Rajasudha and R, Arumuganathan and S, Dharmaraja},
     title = {Performance analysis of discrete-time $Geo^{X} / G / 1$ retrial queue with various vacation policies and impatient customers},
     journal = {RAIRO. Operations Research},
     pages = {1089--1117},
     year = {2022},
     publisher = {EDP-Sciences},
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     number = {3},
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     mrnumber = {4420291},
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R, Rajasudha; R, Arumuganathan; S, Dharmaraja. Performance analysis of discrete-time $Geo^{X} / G / 1$ retrial queue with various vacation policies and impatient customers. RAIRO. Operations Research, Tome 56 (2022) no. 3, pp. 1089-1117. doi: 10.1051/ro/2022042

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