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.

Keywords: 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/articles/10.1051/ps:2002006/} }

TY - JOUR AU - Madan, Kailash C. AU - Abu-Dayyeh, Walid TI - Restricted admissibility of batches into an $M$/$G$/1 type bulk queue with modified Bernoulli schedule server vacations JO - ESAIM: Probability and Statistics PY - 2002 SP - 113 EP - 125 VL - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2002006/ DO - 10.1051/ps:2002006 LA - en ID - PS_2002__6__113_0 ER -

%0 Journal Article %A Madan, Kailash C. %A Abu-Dayyeh, Walid %T Restricted admissibility of batches into an $M$/$G$/1 type bulk queue with modified Bernoulli schedule server vacations %J ESAIM: Probability and Statistics %D 2002 %P 113-125 %V 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps:2002006/ %R 10.1051/ps:2002006 %G en %F 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, Volume 6 (2002), pp. 113-125. doi : 10.1051/ps:2002006. http://www.numdam.org/articles/10.1051/ps:2002006/

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