Restricted admissibility of batches into an M / G /1 type bulk queue with modified Bernoulli schedule server vacations

Kailash C. Madan; Walid Abu-Dayyeh

ESAIM: Probability and Statistics (2002)

  • Volume: 6, page 113-125
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Madan, Kailash C., and 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 6 (2002): 113-125. <http://eudml.org/doc/244792>.

@article{Madan2002,
abstract = {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.},
author = {Madan, Kailash C., Abu-Dayyeh, Walid},
journal = {ESAIM: Probability and Statistics},
keywords = {steady state; compound Poisson process; Bernoulli schedule server vacations; exponential vacation periods; restricted admissibility of batches},
language = {eng},
pages = {113-125},
publisher = {EDP-Sciences},
title = {Restricted admissibility of batches into an $M$/$G$/1 type bulk queue with modified Bernoulli schedule server vacations},
url = {http://eudml.org/doc/244792},
volume = {6},
year = {2002},
}

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
PB - EDP-Sciences
VL - 6
SP - 113
EP - 125
AB - 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.
LA - eng
KW - steady state; compound Poisson process; Bernoulli schedule server vacations; exponential vacation periods; restricted admissibility of batches
UR - http://eudml.org/doc/244792
ER -

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