Restricted admissibility of batches into an M/G/1 type bulk queue with modified Bernoulli schedule server vacations
ESAIM: Probability and Statistics, Tome 6 (2002) , pp. 113-125.

We investigate the steady state behavior of an M/G/1 queue with modified Bernoulli schedule server vacations. Batches of variable size arrive at the system according to a compound Poisson process. However, all arriving batches are not allowed into the system. The restriction policy differs when the server is available in the system and when he is on vacation. We obtain in closed form, the steady state probability generating functions for the number of customers in the queue for various states of the server, the average number of customers as well as their average waiting time in the queue and the system. Many special cases of interest including complete admissibility, partial admissibility and no server vacations have been discusssed. Some known results are derived as particular cases of our model.

DOI : https://doi.org/10.1051/ps:2002006
Classification : 60k25
Mots clés : steady state, compound Poisson process, Bernoulli schedule server vacations, exponential vacation periods, restricted admissibility of batches
@article{PS_2002__6__113_0,
     author = {Madan, Kailash C. and Abu-Dayyeh, Walid},
     title = {Restricted admissibility of batches into an $M$/$G$/1 type bulk queue with modified Bernoulli schedule server vacations},
     journal = {ESAIM: Probability and Statistics},
     pages = {113--125},
     publisher = {EDP-Sciences},
     volume = {6},
     year = {2002},
     doi = {10.1051/ps:2002006},
     zbl = {1003.60083},
     language = {en},
     url = {http://www.numdam.org/item/PS_2002__6__113_0/}
}
Madan, Kailash C.; Abu-Dayyeh, Walid. Restricted admissibility of batches into an $M$/$G$/1 type bulk queue with modified Bernoulli schedule server vacations. ESAIM: Probability and Statistics, Tome 6 (2002) , pp. 113-125. doi : 10.1051/ps:2002006. http://www.numdam.org/item/PS_2002__6__113_0/

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