An N-policy discrete-time Geo/G/1 queue with modified multiple server vacations and Bernoulli feedback
RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 2, pp. 367-387.

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.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2017027
Classification : 60K25, 68M20, 90B22
Mots-clés : Discrete-time queue, N-policy, Bernoulli feedback, Modified multiple vacations, Cost optimization
Lan, Shaojun 1 ; Tang, Yinghui 1

1
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     author = {Lan, Shaojun and Tang, Yinghui},
     title = {An {N-policy} discrete-time {Geo/G/1} queue with modified multiple server vacations and {Bernoulli} feedback},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {367--387},
     publisher = {EDP-Sciences},
     volume = {53},
     number = {2},
     year = {2019},
     doi = {10.1051/ro/2017027},
     zbl = {1423.60141},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro/2017027/}
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Lan, Shaojun; Tang, Yinghui. An N-policy discrete-time Geo/G/1 queue with modified multiple server vacations and Bernoulli feedback. RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 2, pp. 367-387. doi : 10.1051/ro/2017027. http://www.numdam.org/articles/10.1051/ro/2017027/

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