From 7d92cf6906ab610164c0f6c7db582c423849c274 Mon Sep 17 00:00:00 2001 From: Florian Mathieu Date: Fri, 21 Mar 2025 00:07:22 +0100 Subject: [PATCH] ajout dossier, cours, images sur le routage et algorithme de routage --- Routage/README.md | 207 ++++++++++++++++++++++++++ Routage/animation_djikstra.py | 55 +++++++ Routage/assets/Bellman-Ford.PNG | Bin 0 -> 168300 bytes Routage/assets/Dijkstra.PNG | Bin 0 -> 26978 bytes Routage/assets/Dijkstra_Animation.gif | Bin 0 -> 9051 bytes Routage/assets/Vector_Distance.png | Bin 0 -> 104866 bytes Routage/assets/allo.jpg | Bin 0 -> 21782 bytes Routage/assets/base.png | Bin 0 -> 317781 bytes Routage/assets/bo.png | Bin 0 -> 93852 bytes Routage/assets/bo_2.png | Bin 0 -> 97575 bytes Routage/assets/filius.png | Bin 0 -> 108788 bytes Routage/assets/jamy.png | Bin 0 -> 110342 bytes Routage/assets/reseau_exemple.jpg | Bin 0 -> 11443 bytes Routage/assets/routage.png | Bin 0 -> 148745 bytes Routage/assets/tables.jpg | Bin 0 -> 209990 bytes Routage/assets/yo.jpg | Bin 0 -> 59194 bytes Routage/dijkstra.py | 44 ++++++ 17 files changed, 306 insertions(+) create mode 100644 Routage/README.md create mode 100644 Routage/animation_djikstra.py create mode 100644 Routage/assets/Bellman-Ford.PNG create mode 100644 Routage/assets/Dijkstra.PNG create mode 100644 Routage/assets/Dijkstra_Animation.gif create mode 100644 Routage/assets/Vector_Distance.png create mode 100644 Routage/assets/allo.jpg create mode 100644 Routage/assets/base.png create mode 100644 Routage/assets/bo.png create mode 100644 Routage/assets/bo_2.png create mode 100644 Routage/assets/filius.png create mode 100644 Routage/assets/jamy.png create mode 100644 Routage/assets/reseau_exemple.jpg create mode 100644 Routage/assets/routage.png create mode 100644 Routage/assets/tables.jpg create mode 100644 Routage/assets/yo.jpg create mode 100644 Routage/dijkstra.py diff --git a/Routage/README.md b/Routage/README.md new file mode 100644 index 0000000..1c6c585 --- /dev/null +++ b/Routage/README.md @@ -0,0 +1,207 @@ +## Réseaux et algorithmes de routage + +> Processus fondamental des réseaux informatiques, le routage permet d’acheminer les paquets de données d’une source à une destination à travers un réseau. + +### Le Programme + +bo_routage + + + +bo_graphe + + + +Et oui, encore des graphes ! + +-------------- + +### Le routage, pourquoi faire ? + +Lorsqu’un ordinateur envoie des données à un autre ordinateur situé sur un réseau différent, ces données doivent transiter par plusieurs équipements intermédiaires, appelés routeurs, qui déterminent le meilleur chemin à suivre. + +L’acheminement efficace des données est crucial pour garantir la rapidité, la fiabilité et l’optimisation des ressources réseau. Sans un bon algorithme de routage, les réseaux seraient sujets à des retards importants, des congestions et des interruptions de communication. + + + +routage_filius + + + +### Mais dis moi Jamy, qu'est ce qu'un routeur ? + + + +allo + + + +Un routeur est en quelque chose un hôte, un ordinateur, qui possède deux périphériques réseau, qui disposent d'une adresse IP chacun. + +Lorsque des données transitent sur le réseau, chaque routeur va en recevoir, et pourra décider de les transmettre à telle ou telle machine. +Pour ne pas se tromper et faire le bon choix, le routeur se servira de **tables de routage.** + +Celles-ci peuvent être définies de manière **statique**, de manière **dynamique** ou tout simplement mises en place par défaut. + +- **Routage statique** : Les routes sont définies manuellement par l’administrateur réseau et restent inchangées, sauf en cas d’intervention humaine. +- **Routage dynamique** : Les routes sont déterminées automatiquement grâce à des protocoles de routage qui s’adaptent aux changements du réseau. +- **Routage par défaut** : Utilisation d’une route unique lorsqu’aucune autre route spécifique n’est définie. + + + +yo + + + +### Mais alors, ces tables de routage ? + +Supposons un réseau représenté par ce graphe : + +![reseau_exemple](assets/reseau_exemple.jpg) + + + + + +Certaines tables de routage pourraient être celles-ci : + +### Table de routage du routeur A +| Destination | Routeur suivant | Distance | +| ----------- | --------------- | -------- | +| B | B | 1 | +| C | C | 1 | +| D | D | 1 | +| E | C | 2 | +| F | C | 2 | +| G | C | 3 | + +### Table de routage du routeur B +| Destination | Routeur suivant | Distance | +| ----------- | --------------- | -------- | +| A | A | 1 | +| C | A | 2 | +| D | D | 1 | +| E | D | 2 | +| F | A | 3 | +| G | D | 3 | + + + +Comme on peut le voir, on dispose de plusieurs informations : + +Depuis le routeur X, pour atteindre une destination, on va indiquer par quel routeur on passera, et la distance / le coût pour atteindre notre destination. + +On parle alors de **passerelle** quand un routeur permet d'accéder à un sous-réseau différent du notre. + + + +### Les algorithmes de routage + +Il paraît évident qu'un réseau aussi grand qu'internet ne peut pas reposer sur des tables de routages manuelles. On a donc décidé d'automatiser cette tâche à l'aide d'algorithmes. +Ainsi, ceux-ci permettent aux routeurs de choisir le chemin optimal pour transmettre les données. On distingue deux grandes catégories : + +- **Les algorithmes à état de liens (Link-State)** : Chaque routeur construit une carte du réseau et calcule les meilleurs chemins avec des algorithmes comme **Dijkstra**. +- **Les algorithmes à vecteur de distance (Distance-Vector)** : Chaque routeur échange des informations avec ses voisins et met à jour ses routes selon l’algorithme de **Bellman-Ford.** + +#### RIP (Routing Information Protocol) + +Ici, chaque routeur va attribuer une distance la plus courte possible à chaque destination accessible. +Cette distance sera indiquée en unité de sauts (hop), avec un saut = un routeur traversé. + +Pour commencer, chaque routeur va écrire dans sa table les plus proches voisins, c'est à dire les routeurs accessibles à 0 de distance. + +Puis, toutes les 30 secondes, chaque routeur va propager les informations de sa table vers ses voisins immédiats, qui mettront leur propre table à jour avec ces informations, notamment si un chemin plus court vers une destination existe ! + +Puis que l'on dispose d'un routeur comme **direction**, et d'une **distance**, on a donc un **vecteur**. + +**Attention** ! + +Si un routeur (et donc un réseau) n'est plus accessible passé 3 minutes, il sera supprimé des tables de routages. + + + +À retenir : + +- Distance en terme de sauts (ou hop en anglais) +- Chaque routeur ne possède les informations que sur son voisinnage direct. On parle de ***routing by rumor*** : aucune vision globale du réseau, on fait confiance aux voisins pour savoir ce qu'il en est. +- Au delà de 15 sauts, on considère un routeur inaccessible. +- Utilise l’algorithme à vecteur de distance de Bellman-Ford et est simple à configurer, mais limité en performance. +- Convient aux petits réseaux +- Premiere algorithme de routage de l'histoire + + + + + +resume_rip + + + + + +#### OSPF (Open Shortest Path First) + +Basé sur l’algorithme de Dijkstra, il est plus rapide et plus efficace que RIP. + +Mis au point pour combler les lacunes du RIP, il est plus complet mais également plus complexe. + +- Tous les routeurs ont une vision globale du réseau. +- Les distances sont mesurées en termes de coûts d'une liaison ou de débit d'une liaison. +- Le coût d'une liaison en OSPF est donné par la formule : + + +$$ +\text{coût} = \frac{10^8}{d} +$$ + + +où d est le débit nominal. + +- Chaque réseau pourra être représenté sous forme de graphe. +- On recherchera les routes les moins couteuses, et sans cycle. +- Chaque routeur devient alors la racine d'un arbre contenant les meilleurs routes. + + + +dijikstra + + + + + + + +Enfin, il reste un algorithme : + +**BGP (Border Gateway Protocol)** : Utilisé pour l’échange de routes entre différents fournisseurs d’accès à Internet (FAI). + +Que nous ne verrons pas cette année. + +Merci jamy ! + +![merci jamy](assets/jamy.png) + + + + + +----------- + +### Sources + +- Hatier prépabac +- [Site d'Olivier Duranton](https://www.duranton.net/?darkmode=non&niveau=terminaleNSI&chapitre=11) +- Leçon réseau et algorithme de routage préparée lors du Capes (et j'ai eu une bonne note, eh oui) + +-------------- + + + +Auteur : Florian Mathieu + +Licence CC BY NC + +Licence Creative Commons
Ce cours est mis à disposition selon les termes de la Licence Creative Commons Attribution - Pas d’Utilisation Commerciale - Partage dans les Mêmes Conditions 4.0 International. + + + diff --git a/Routage/animation_djikstra.py b/Routage/animation_djikstra.py new file mode 100644 index 0000000..83df4e9 --- /dev/null +++ b/Routage/animation_djikstra.py @@ -0,0 +1,55 @@ +import networkx as nx +import matplotlib.pyplot as plt +import matplotlib.animation as animation + +# Création du graphe +G = nx.DiGraph() +edges = [ + (0, 1, 4), (0, 2, 1), + (2, 1, 2), (1, 3, 1), + (2, 3, 5), (3, 4, 3) +] +G.add_weighted_edges_from(edges) + +# Position des nœuds pour affichage +pos = nx.spring_layout(G, seed=42) +labels = {n: str(n) for n in G.nodes()} + +# Initialisation de la figure +fig, ax = plt.subplots(figsize=(6, 6)) + +# Algorithme de Dijkstra avec animation +def dijkstra_animation(start_node=0): + distances = {node: float('inf') for node in G.nodes()} + distances[start_node] = 0 + visited = set() + steps = [] + + while len(visited) < len(G.nodes()): + min_node = min((node for node in distances if node not in visited), key=lambda x: distances[x]) + visited.add(min_node) + + for neighbor in G.neighbors(min_node): + new_distance = distances[min_node] + G[min_node][neighbor]["weight"] + if new_distance < distances[neighbor]: + distances[neighbor] = new_distance + + steps.append((visited.copy(), [(min_node, v) for v in G.neighbors(min_node)])) + + return steps + +steps = dijkstra_animation() + +def update(frame): + ax.clear() + visited, edges = steps[frame] + node_colors = ["green" if n in visited else "lightblue" for n in G.nodes()] + edge_colors = ["red" if (u, v) in edges else "black" for u, v in G.edges()] + + nx.draw(G, pos, with_labels=True, labels=labels, node_size=800, + node_color=node_colors, edge_color=edge_colors, font_size=14, font_weight="bold", ax=ax) + edge_labels = {(u, v): G[u][v]["weight"] for u, v in G.edges()} + nx.draw_networkx_edge_labels(G, pos, edge_labels=edge_labels, font_size=12, ax=ax) + +ani = animation.FuncAnimation(fig, update, frames=len(steps), repeat=False, interval=1000) +plt.show() diff --git a/Routage/assets/Bellman-Ford.PNG b/Routage/assets/Bellman-Ford.PNG new file mode 100644 index 0000000000000000000000000000000000000000..3b3e13b15a772e40cc2cc602cdce31554fc3f70d GIT binary patch literal 168300 zcmdqI^-~?evp$SF1a}PtcXv&2hv04pcXtWy?s|f|yZbpf!5xCTJG{A{dvAT~{tNF9 z(_6i>-CbKVwfl7UGm*-QQm9CTNDvSZs4~*uRUsgt3?LvN0}$Z;-O1n^jrezgbWxQO zhp3q%KK`e`0K^o;ARy}Fk>8AA|LKU1(%LQ%5SXt2H6S-F$UGq+K8t0(i>Z4WoV_3V z7y{D1g}sEl3qJO?O~0GPkCMLD*ZPfeD%-kLXZ#B%Y0M$Ap`iVbDHvUS@-GQ={oH7dfxxx`F>yA z8!qyUcAIpG9`IKD+`L4}ZSa!`JekD>2~X_U_uoPU;^VaU zb(ZmJwZo0!;d~A6e<$FHub{VkU#|mlVGTy($VNkv@u1Lnw*#U7Bm5!W_5$9<8LvQ7 zQ<5?=GXLZ4zx;j){JhQ&;70DEXJDA!+$8-!4)Z_2EEYkUnjSpjh06cODBuHZI1N=> zf9=Kt8iV$ZaGhrIfKfnL&RAq@W8 z=YKig!i4=lL5u!>7Su4>UZBS%+%_QY+4pb?+s@u})n_Dk?Lc1G^7PG*g3dN<8;%%+7%WrBMoFGV>Z^%{K)60kPa-Do$ z#PC^OQ)Tc}%3hZt2;b11ZMIViNSkaQeFPE+bk6p^h8mZ*u}mlB{rz~HJ@i{ozi>VX z=cCahoaCPk;kaVH$QN3kzoc>DIsNm<;{I;(^5x(lnhbN{K60jE84YsWuD``)Cv zS$*jP$&hC?T$1YaJo*vlY>zgCk+7C#BpwMZPRjri{)ndHY zcFv>mpHTz5-8W!>3xiE4o0`Fth0ZiC;-ER9{szOjEX&&Nc@uK--`zQ-NA_E=yuWV% zJ%_g`f3>`o{kiVr0Y?GLzpd@ZH!wT_(4OWHTmto8GrN$I{AVMm9^7hD{4i^8prI7;Z_sz$ z7x@GPh{F)9*`DGL){6+OF#*=M-iO0+tczOm_jv>v5EwmTKbTQKXr z)Nvvd@Fon>(3!WZbR10wmb3!|n{FZF*p2pq&JFoBpb|~AG{b!TWjKwL0&V1mN`}AQizMHp3 zGlJgLk-MhAl9R!O*a3I9{WpB&x$gE-zCE=}TH$9Gx512~>1M2FO5NBp-wgjv@eG`m z*S)^%WxAnkjaJhoD3{t42&FWac7cRZT0sz%m#J4BmsL^7OmcspZP#=J{YuG0ma{1N z3nPlq!8up}_~3g~pUcX1y6OKmnVL*N>fvyquhqd{OmBWHJ5MK>IUYOL?-OQoT

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[("A","B",4),("A","C",3),("A","D",2), + ("B","E",1),("C","D",1),("C","E",1),("D","E",1)]) + + + + \ No newline at end of file

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