{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# File d'attente, un exemple simple\n",
"\n",
"Cet exemple vient illustrer le paragraphe sur les files d'attente et l'espérance de vie des ampoules."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.0749720223112896"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import random\n",
"\n",
"\n",
"def generate_expo(mu):\n",
" return random.expovariate(mu)\n",
"\n",
"\n",
"generate_expo(2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Les paramètres de la simulation."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"S = 10000\n",
"iteration = 500\n",
"mu = 1.0 / 100"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On crée un tableau de ``S`` ampoules qui contient la durée de vie restante de chaque ampoule."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"itération : 0 moyenne durée : 0.0 grillées : 10000\n",
"itération : 100 moyenne durée : 99.7184 grillées : 95\n",
"itération : 200 moyenne durée : 98.7154 grillées : 93\n",
"itération : 300 moyenne durée : 99.2155 grillées : 101\n",
"itération : 400 moyenne durée : 98.9101 grillées : 108\n",
"nombre moyen d'ampoules grillées : 99.88577154308618\n"
]
}
],
"source": [
"ampoule = [0 for a in range(S)]\n",
"moyenne_grille = 0\n",
"stats = []\n",
"\n",
"\n",
"for i in range(iteration):\n",
" grille = 0\n",
" mean = 0\n",
"\n",
" for n in range(S):\n",
" mean += ampoule[n]\n",
" if ampoule[n] == 0:\n",
" # remplacement d'une ampoule grillée\n",
" grille += 1\n",
" # on détermine la durée de vie de cette ampoule\n",
" # on arrondit à l'entier le plus proche\n",
" ampoule[n] = int(generate_expo(mu))\n",
" else:\n",
" # on enlève une heure à la durée de vie de l'ampoule\n",
" ampoule[n] -= 1\n",
"\n",
" mean /= S\n",
"\n",
" stats.append(dict(i=i, mean=mean, grille=grille))\n",
"\n",
" if i > 0:\n",
" moyenne_grille += grille\n",
" if i % 100 == 0:\n",
" print(\"itération : \", i, \" moyenne durée : \", mean, \" grillées :\", grille)\n",
"\n",
"moyenne_grille = float(moyenne_grille) / float(iteration - 1)\n",
"print(\"nombre moyen d'ampoules grillées :\", moyenne_grille)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" i | \n",
" mean | \n",
" grille | \n",
" grille_sum | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0 | \n",
" 0.0000 | \n",
" 10000 | \n",
" 0 | \n",
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\n",
" \n",
" | 1 | \n",
" 1 | \n",
" 98.5142 | \n",
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" 99 | \n",
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\n",
" \n",
" | 2 | \n",
" 2 | \n",
" 98.5526 | \n",
" 91 | \n",
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\n",
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\n",
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"