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On fast simulation of the time to saturation of slotted ALOHA

Part of: Limit theorems

Published online by Cambridge University Press:  14 July 2016

V. Anantharam
V. Anantharam*
Affiliation:
Cornell University
*
∗Postal address: School of Electrical Engineering, Cornell University, Ithaca, NY 14853, USA.
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Abstract

Cottrell et al. (1983) have indicated how ideas from the large deviations theory lead to fast simulation schemes that estimate the mean time taken by the slotted ALOHA protocol to saturate starting empty. Such fast simulation schemes are particularly useful when the attempt probability is small. The remaining time to saturation when the protocol has been operating for a time is more accurately described by the quasi-stationary exit time from the stable regime. The purpose of this article is to prove that the ratio of the quasi-stationary exit time to the exit time starting empty approaches 1 as the attempt probability becomes small.

Keywords

IMPORTANCE SAMPLINGLARGE DEVIATIONSMULTIPLE-ACCESSQUASI-STATIONARY DISTRIBUTION

MSC classification

Secondary: 60F10: Large deviations
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 3 , September 1992 , pp. 682 - 690
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

Research supported by NSF under NCR 8710840 and a PYI award, by IBM under a Faculty Development Award, and by BellCore Inc.

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