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A mathematical model for file fragment diffusion and a neural predictor to manage priority queues over BitTorrent

100%
Napoli C., Pappalardo G., Tramontana E.
International Journal of Applied Mathematics and Computer Science
|
2016
|
tom 26
|
nr 1
147-160
EN
BitTorrent splits the files that are shared on a P2P network into fragments and then spreads these by giving the highest priority to the rarest fragment. We propose a mathematical model that takes into account several factors such as the peer distance, communication delays, and file fragment availability in a future period also by using a neural network module designed to model the behaviour of the peers. The ensemble comprising the proposed mathematical model and a neural network provides a solution for choosing the file fragments that have to be spread first, in order to ensure their continuous availability, taking into account that some peers will disconnect.
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A nonlocal coagulation-fragmentation model

86%
Lachowicz M., Wrzosek D.
Applicationes Mathematicae
|
2000
|
tom 27
|
nr 1
45-66
EN
A new nonlocal discrete model of cluster coagulation and fragmentation is proposed. In the model the spatial structure of the processes is taken into account: the clusters may coalesce at a distance between their centers and may diffuse in the physical space Ω. The model is expressed in terms of an infinite system of integro-differential bilinear equations. We prove that some results known in the spatially homogeneous case can be extended to the nonlocal model. In contrast to the corresponding local models the analysis can be carried out in the $L_1(Ω)$ setting. Our purpose is to study global (in time) existence, mass conservation and well-posedness of the model.
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