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Bull. Korean Math. Soc. 2016; 53(4): 985-1004

Printed July 31, 2016

https://doi.org/10.4134/BKMS.b150337

Copyright © The Korean Mathematical Society.

Stability of $MAP/PH/c/K$ queue with customer retrials and server vacations

Yang Woo Shin

Changwon National University

Abstract

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We consider the $MAP/PH/c/K$ queue in which blocked customers retry to get service and servers may take vacations. The time interval between retrials and vacation times are of phase type (PH) distributions. Using the method of mean drift, a sufficient condition of ergodicity is provided. A condition for the system to be unstable is also given by the stochastic comparison method.

Keywords: retrial queue, vacation queue, Markovian arrival process (MAP), PH-distribution, positive recurrent

MSC numbers: Primary 60K25, 60J27, 90B22

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