Volume 53, Number 2, April-June 2019
|Page(s)||367 - 387|
|Published online||06 March 2019|
An N-policy discrete-time Geo/G/1 queue with modified multiple server vacations and Bernoulli feedback*
1 School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, Sichuan, P.R. China
2 School of Fundamental Education, Sichuan Normal University, Chengdu 610068, Sichuan, P.R. China
** Corresponding author: email@example.com
Accepted: 31 March 2017
This paper deals with a single-server discrete-time Geo/G/1 queueing model with Bernoulli feedback and N-policy where the server leaves for modified multiple vacations once the system becomes empty. Applying the law of probability decomposition, the renewal theory and the probability generating function technique, we explicitly derive the transient queue length distribution as well as the recursive expressions of the steady-state queue length distribution. Especially, some corresponding results under special cases are directly obtained. Furthermore, some numerical results are provided for illustrative purposes. Finally, a cost optimization problem is numerically analyzed under a given cost structure.
Mathematics Subject Classification: 60K25 / 68M20 / 90B22
Key words: Discrete-time queue / N-policy / Bernoulli feedback / Modified multiple vacations / Cost optimization
© EDP Sciences, ROADEF, SMAI 2019
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