Cache refresh traffic estimation using a k-sided die

cache-traffic.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from scipy import stats, integrate\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "trials done\n"
     ]
    }
   ],
   "source": [
    "epochs = 10000\n",
    "trials = np.reshape(np.random.randint(0, 31, 3000 * epochs), (epochs, -1))\n",
    "print(\"trials done\")\n",
    "counts_per_epoch=np.apply_along_axis(np.bincount, axis = 1, arr = trials)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000,)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max_count_per_epoch = np.apply_along_axis(max, axis=1, arr = counts_per_epoch)\n",
    "max_count_per_epoch.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "118"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max_count_per_epoch[3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 0.0222,  0.2088,  0.5403,  0.7504,  0.9064,  0.9725,  0.9893,\n",
       "         0.9963,  0.9994,  1.    ]),\n",
       " array([ 106. ,  109.7,  113.4,  117.1,  120.8,  124.5,  128.2,  131.9,\n",
       "         135.6,  139.3,  143. ]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa380eb38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(max_count_per_epoch, cumulative=True, normed=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}