English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

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<sup>-1</sup>, provide tight upper and lower bounds for the length of the entire transmission period, and show that its asymptotic behavior is ~ne-&#x03B6; ln(n) with &#x03B6; =-0.5/\ln (1-e<sup>-1</sup>).

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