# Binomial-Poisson entropic inequalities and the M/M/∞ queue

ESAIM: Probability and Statistics (2006)

- Volume: 10, page 317-339
- ISSN: 1292-8100

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topChafaï, Djalil. "Binomial-Poisson entropic inequalities and the M/M/∞ queue." ESAIM: Probability and Statistics 10 (2006): 317-339. <http://eudml.org/doc/249753>.

@article{Chafaï2006,

abstract = {
This article provides entropic inequalities for binomial-Poisson
distributions, derived from the two point space. They appear as local
inequalities of the M/M/∞ queue. They describe in particular the
exponential dissipation of Φ-entropies along this process. This simple
queueing process appears as a model of “constant curvature”, and plays for
the simple Poisson process the role played by the Ornstein-Uhlenbeck process
for Brownian Motion. Some of the inequalities are recovered by semi-group
interpolation. Additionally, we explore the behaviour of these entropic
inequalities under a particular scaling, which sees the Ornstein-Uhlenbeck
process as a fluid limit of M/M/∞
queues.
Proofs are elementary and rely essentially on the development of a
“Φ-calculus”.
},

author = {Chafaï, Djalil},

journal = {ESAIM: Probability and Statistics},

keywords = {Functional inequalities; Markov processes; entropy; birth and death
processes; queues.; functional inequalities; birth and death processes; queues},

language = {eng},

month = {9},

pages = {317-339},

publisher = {EDP Sciences},

title = {Binomial-Poisson entropic inequalities and the M/M/∞ queue},

url = {http://eudml.org/doc/249753},

volume = {10},

year = {2006},

}

TY - JOUR

AU - Chafaï, Djalil

TI - Binomial-Poisson entropic inequalities and the M/M/∞ queue

JO - ESAIM: Probability and Statistics

DA - 2006/9//

PB - EDP Sciences

VL - 10

SP - 317

EP - 339

AB -
This article provides entropic inequalities for binomial-Poisson
distributions, derived from the two point space. They appear as local
inequalities of the M/M/∞ queue. They describe in particular the
exponential dissipation of Φ-entropies along this process. This simple
queueing process appears as a model of “constant curvature”, and plays for
the simple Poisson process the role played by the Ornstein-Uhlenbeck process
for Brownian Motion. Some of the inequalities are recovered by semi-group
interpolation. Additionally, we explore the behaviour of these entropic
inequalities under a particular scaling, which sees the Ornstein-Uhlenbeck
process as a fluid limit of M/M/∞
queues.
Proofs are elementary and rely essentially on the development of a
“Φ-calculus”.

LA - eng

KW - Functional inequalities; Markov processes; entropy; birth and death
processes; queues.; functional inequalities; birth and death processes; queues

UR - http://eudml.org/doc/249753

ER -

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