Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In dynamic-frame Aloha, subsequent frame lengths must be optimally chosen to maximize throughput. When the initial population size    \({\cal N}\)    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; hover, to the best of our knowledge, a formal proof of this result is still missing, and is provided here. As byproduct,  also prove that the asymptotic efficiency in the optimal case is    \(e^{-1}\)   , provide tight upper and lor bounds for the length of the entire transmission period, and show that its asymptotic behavior is    \(\sim ne-\zeta \ln (n)\)    with    \(\zeta =-0.5/\ln (1-e^{-1})\)   .
['Luca Barletta', 'Flaminio Borgonovo', 'Matteo Cesana']
I am writing a research paper on a idea A Formal Proof of the Optimal Frame Setting for Dynamic-Frame Aloha With Known Population Size
[{"from": "human", "value": "I am writing a research paper on a idea A Formal Proof of the Optimal Frame Setting for Dynamic-Frame Aloha With Known Population Size"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In dynamic-frame Aloha, subsequent frame lengths must be optimally chosen to maximize throughput. When the initial population size    \\({\\cal 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; hover, to the best of our knowledge, a formal proof of this result is still missing, and is provided here. As byproduct,  also prove that the asymptotic efficiency in the optimal case is    \\(e^{-1}\\)   , provide tight upper and lor bounds for the length of the entire transmission period, and show that its asymptotic behavior is    \\(\\sim ne-\\zeta \\ln (n)\\)    with    \\(\\zeta =-0.5/\\ln (1-e^{-1})\\)   ."}]