Journal of Integer Sequences, Vol. 13 (2010), Article 10.5.5

Integer Sequences from Queueing Theory

Joseph Abate
900 Hammond Road
Ridgewood, NJ 07450-2908

Ward Whitt
Department of Industrial Engineering and Operations Research
Columbia University
New York, NY 10027-6699


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.

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(Concerned with sequences A000108 A001003 A006318 A093252 A093526 A103210 A103211 A107841 A122525 A131763 A137216 A155069.)

Received February 19 2010; revised version received May 2 2010. Published in Journal of Integer Sequences, May 3 2010.

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