On fast simulation of the time to saturation of slotted ALOHA

On fast simulation of the time to saturation of slotted ALOHA

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Article ID: iaor1994355
Country: Israel
Volume: 29
Issue: 3
Start Page Number: 682
End Page Number: 690
Publication Date: Sep 1992
Journal: Journal of Applied Probability
Authors:
Keywords: statistics: sampling
Abstract:

Cottrell et al. 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.

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