Geodesic
Integer sequences from queueing theory
Journal of integer sequences, Tome 13 (2010) no. 5.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Operators on probability distributions can be expressed as operators on the associated moment sequences, and so correspond to operators on integer sequences. Thus, there is an opportunity to apply each theory to the other. Moreover, probability models can be sources of integer sequences, both classical and new, as we show by considering the classical $M/G/1$ single-server queueing model. We identify moment sequences that are integer sequences. We establish connections between the $M/M/1$ busy period distribution and the Catalan and Schroeder numbers.
Classification : 11B25, 60K25
Keywords: integer sequence, moment sequence, probability, probability density function, probability moment sequence, the moment problem, queue, queueing, Laplace transforms, moment generating functions, generating functions, continued fractions, Hankel transform, renewal theory, birth-and-death process, stationary excess distribution, stationary lifetime distribution, exponential mixture, single-server queue, M/M/ 
@article{JIS_2010__13_5_a1,
     author = {Abate, Joseph and Whitt, Ward},
     title = {Integer sequences from queueing theory},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {13},
     number = {5},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2010__13_5_a1/}
}
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Abate, Joseph; Whitt, Ward. Integer sequences from queueing theory. Journal of integer sequences, Tome 13 (2010) no. 5. http://geodesic.mathdoc.fr/item/JIS_2010__13_5_a1/