In dynamic-frame Aloha, subsequent frame lengths must be optimally chosen to maximize throughput. When the initial population size N is known, numerical evaluations show that the maximum efficiency is achieved by setting the frame length equal to the backlog size at each subsequent frame; however, to the best of our knowledge, a formal proof of this result is still missing, and is provided here. As byproduct, we also prove that the asymptotic efficiency in the optimal case is e(-1), provide tight upper and lower bounds for the length of the entire transmission period, and show that its asymptotic behavior is similar to ne - zeta ln(n) with zeta = -0.5/ ln(1 - e(-1)).

A Formal Proof of the Optimal Frame Setting for Dynamic-Frame Aloha With Known Population Size

BARLETTA, LUCA;BORGONOVO, FLAMINIO;CESANA, MATTEO
2014-01-01

Abstract

In dynamic-frame Aloha, subsequent frame lengths must be optimally chosen to maximize throughput. When the initial population size N is known, numerical evaluations show that the maximum efficiency is achieved by setting the frame length equal to the backlog size at each subsequent frame; however, to the best of our knowledge, a formal proof of this result is still missing, and is provided here. As byproduct, we also prove that the asymptotic efficiency in the optimal case is e(-1), provide tight upper and lower bounds for the length of the entire transmission period, and show that its asymptotic behavior is similar to ne - zeta ln(n) with zeta = -0.5/ ln(1 - e(-1)).
Radiofrequency identification; Random variables; Statistics
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/845959
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