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# JnBrymn/EARRRL Notebook.ipynb

Created Mar 18, 2021
 { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# EARRRL - The Estimated Average Recent Request Rate Limiter\n", "\n", "Here are the corresponding blog posts:\n", "* [Basic concept and practical implementation and usage](http://blog.jnbrymn.com/2021/03/18/estimated-average-recent-request-rate-limiter.html)\n", "* [Mathematical analysis](http://blog.jnbrymn.com/2021/03/18/estimated-average-recent-request-rate-limiter-math.html)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib\n", "import matplotlib.pyplot as plt\n", "from pylab import rcParams\n", "import numpy as np\n", "plt.style.use('seaborn-whitegrid')\n", "rcParams['figure.figsize'] = 10, 5\n", "font = {'family' : 'normal',\n", " 'weight' : 'bold',\n", " 'size' : 12}\n", "\n", "matplotlib.rc('font', **font)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# NOTE\n", "I called EARRRL as CEWMA initially (Continuous Exponentially Weighted Moving Average)... and now I'm too lazy to fix it." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import time\n", "import math\n", "\n", "class CEWMA:\n", " def __init__(self, halflife):\n", " self.N = 0\n", " self.T = 0\n", " self.lambd = -math.log(0.5)/halflife\n", " \n", " def update(self, num_hits, now_timestamp):\n", " delta_t = self.T - now_timestamp\n", " self.R = num_hits + self.N*math.exp(self.lambd*delta_t)\n", " self.T = now_timestamp\n", " \n", " def evaluate(self, now_timestamp):\n", " delta_t = self.T - now_timestamp\n", " return self.N*self.lambd * math.exp(self.lambd*delta_t)\n", " " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def hit_train(start_time, delta_t, end_time):\n", " \"\"\"returns list of (hit_count, time)\"\"\"\n", " return [start_time+delta_t*i for i in range(math.ceil((end_time-start_time)/delta_t))]" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[10, 13, 16, 19]" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hit_train(start_time=10, delta_t=3, end_time=20)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def simulate_cewma_value(cewma, hit_times, sim_end_t):\n", " sim_delta_t = 0.01\n", " i = 0\n", " t = 0\n", " times = []\n", " values = []\n", " while True :\n", " if t > sim_end_t:\n", " break\n", " if len(hit_times) > i and hit_times[i] <= t:\n", " cewma.update(1, hit_times[i])\n", " i += 1\n", " times.append(t)\n", " values.append(cewma.evaluate(t))\n", " t += sim_delta_t\n", " return times, values" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "findfont: Font family ['normal'] not found. Falling back to DejaVu Sans.\n", "findfont: Font family ['normal'] not found. Falling back to DejaVu Sans.\n", "findfont: Font family ['normal'] not found. Falling back to DejaVu Sans.\n" ] }, { "data": { "image/png": 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\n", 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