diff --git a/latex/content.tex b/latex/content.tex index 4204cce..c548831 100644 --- a/latex/content.tex +++ b/latex/content.tex @@ -80,15 +80,37 @@ by various algorithms minimizing the waste of material. \subsection{1D : Networking} -on which humans -have decreasing control. +When managing network traffic at scale, efficiently routing packets is +necessary to avoid congestion, which leads to lower bandwidth and higher +latency. Say you're a internet service provider and your users are watching +videos on popular streaming platforms. You want to ensure that the traffic is +balanced between the different routes to minimize throttling and energy +consumption. -In this paper, we will focus on one-dimensional bin packing, where we try to -store items of different heights in a linear container. +\paragraph{} We can consider the different routes as bins and the users' +bandwidth as the items. If a bin overflows, we can redirect the traffic to +another route. Using less bins means less energy consumption and decreased +operating costs. This is a good example of bin packing in a dynamic +environment, where the items are constantly changing. Humans are not involved +in the process, as it is fast-paced and requires a high level of automation. +\vspace{0.4cm} + +\paragraph{} We have seen multiple examples of how bin packing algorithms can +be used in various technical fields. In these examples, a choice was made, +evaluating the process effectiveness and reliability, based on a probabilistic +analysis allowing the adaptation of the algorithm to the use case. We will now +conduct our own analysis and study various algorithms and their probabilistic +advantages, focusing on one-dimensional bin packing, where we try to store +items of different heights in a linear bin. \section{Next Fit Bin Packing algorithm} +\paragraph{} Each bin will have a fixed capacity of $ 1 $ and items and items +will be of random sizes between $ 0 $ and $ 1 $. We will run X simulations % TODO +with 10 packets. + + \cite{hofri:1987} % TODO mettre de l'Histoire