11_queue_simulation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# System Simulation using Simpy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "!pip3 install seaborn simpy faker"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Números aleatorios"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "mean = 5.4\n",
    "numeros = [random.expovariate(1.0 / mean) for i in range(0, 10000)]\n",
    "numeros[:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Media: 5.383617\n"
     ]
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     },
     "metadata": {
      "needs_background": "light"
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     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "from pandas import Series\n",
    "\n",
    "s = Series(numeros)\n",
    "print(\"Media: %f\" % s.mean())\n",
    "s.plot.density(figsize=(15,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Media: 5.413099\n"
     ]
    }
   ],
   "source": [
    "from numpy import random as nprnd\n",
    "numeros = nprnd.exponential(mean, 10000)\n",
    "s = Series(numeros)\n",
    "print(\"Media: %f\" % s.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Strings aleatorios"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "!pip install Faker"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Octavia de Botella\n",
      "Via de Goyo Casares 25 Piso 7 \n",
      "Alicante, 93671\n"
     ]
    }
   ],
   "source": [
    "from faker import Faker\n",
    "fake = Faker('es-ES')\n",
    "print(fake.name())\n",
    "print(fake.address())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ley de Little\n",
    "\n",
    "$L = \\lambda \\cdot W$\n",
    "\n",
    "Siendo $L$ el número medio de clientes, $\\lambda$ la tasa de llegadas y $W$ el tiempo medio de espera en el sistema.\n",
    "\n",
    "*Ejemplo*: ¿Cuántos clientes debería haber en el sistema si llegan 10 por hora y de media esperan 1.5 minutos?\n",
    "\n",
    "$L = \\lambda \\cdot W = 10 \\cdot 1.5 = 15$\n",
    "\n",
    "*Ejemplo*: calcular el tiempo medio en el sistema para una cola con 15 clientes y una tasa de llegadas de 10 clientes por minuto.\n",
    "\n",
    "$W = \\frac{L}{\\lambda} = \\frac{15}{10} = 1.5 {min.}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulación cola básica M/M/1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "!pip install simpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      " 0.0000 Rebeca se pone en cola\n",
      " 0.0000 Rebeca ha esperado 0.000000\n",
      " 0.1266 Rebeca servido en 0.126644\n",
      " 3.0602 Virgilio se pone en cola\n",
      " 3.0602 Virgilio ha esperado 0.000000\n",
      " 4.0251 Severiano se pone en cola\n",
      " 4.3231 Virgilio servido en 1.262931\n",
      " 4.3231 Severiano ha esperado 0.298059\n",
      " 8.0258 Rosa se pone en cola\n",
      " 9.9690 Severiano servido en 5.645865\n",
      " 9.9690 Rosa ha esperado 1.943146\n",
      "10.4237 Rosa servido en 0.454762\n",
      "14.7077 Ainara se pone en cola\n",
      "14.7077 Ainara ha esperado 0.000000\n",
      "14.8589 Ainara servido en 0.151251\n",
      "16.3518 Cesar se pone en cola\n",
      "16.3518 Cesar ha esperado 0.000000\n",
      "17.0920 Judith se pone en cola\n",
      "17.1727 Angélica se pone en cola\n",
      "17.8377 Dolores se pone en cola\n",
      "19.8714 Cesar servido en 3.519578\n",
      "19.8714 Judith ha esperado 2.779428\n",
      "20.9862 Ester se pone en cola\n",
      "23.8081 Judith servido en 3.936646\n",
      "23.8081 Angélica ha esperado 6.635391\n",
      "28.2571 Angélica servido en 4.449044\n",
      "28.2571 Dolores ha esperado 10.419359\n",
      "36.5458 Dolores servido en 8.288690\n",
      "36.5458 Ester ha esperado 15.559574\n",
      "36.5784 Ester servido en 0.032600\n",
      "\n",
      "Tiempo medio espera: 3.763496\n",
      "Tiempo medio servicio: 2.786801\n"
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      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
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     },
     "metadata": {
      "needs_background": "light"
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     "output_type": "display_data"
    }
   ],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import simpy\n",
    "\n",
    "t_espera = []\n",
    "t_servicio = []\n",
    "\n",
    "log = print\n",
    "# log = lambda s: 0\n",
    "\n",
    "def source(env, number, intervalo_llegadas, cola, tiempo_sistema):\n",
    "    for i in range(number):\n",
    "        c = cliente(env, fake.first_name(), cola, tiempo_sistema)\n",
    "        env.process(c)\n",
    "        t = random.expovariate(1.0 / intervalo_llegadas)\n",
    "        yield env.timeout(t)\n",
    "\n",
    "def cliente(env, nombre, cola, tiempo_sistema):\n",
    "    llegada = env.now\n",
    "    log('%7.4f %s se pone en cola' % (llegada, nombre))\n",
    "\n",
    "    with cola.request() as req:        \n",
    "        yield req\n",
    "        \n",
    "        espera = env.now - llegada\n",
    "        t_espera.append(espera)\n",
    "        log('%7.4f %s ha esperado %f' % (env.now, nombre, espera))\n",
    "        \n",
    "        inicio_servicio = env.now\n",
    "        tiempo_servicio = random.expovariate(1.0 / tiempo_sistema)\n",
    "        yield env.timeout(tiempo_servicio)\n",
    "        t_servicio.append(tiempo_servicio)\n",
    "        log('%7.4f %s servido en %f' % (env.now, nombre, tiempo_servicio))\n",
    "\n",
    "        \n",
    "TOTAL_CLIENTES = 10\n",
    "TIEMPO_SISTEMA = 5\n",
    "INTERVALO_LLEGADAS = 3\n",
    "\n",
    "random.seed(42)\n",
    "env = simpy.Environment()\n",
    "cola = simpy.Resource(env, capacity=1)\n",
    "env.process(source(env, TOTAL_CLIENTES, INTERVALO_LLEGADAS, cola, TIEMPO_SISTEMA))\n",
    "env.run()\n",
    "\n",
    "print(\"\\nTiempo medio espera: %f\" % Series(t_espera).mean())\n",
    "print(\"Tiempo medio servicio: %f\" % Series(t_servicio).mean())\n",
    "\n",
    "f, a = plt.subplots(1, 2, figsize=(15,5))\n",
    "Series(t_espera).plot(ax=a[0], linewidth=1)\n",
    "sns.distplot(Series(t_espera), ax=a[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Queue dumping"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " 0.0000 Cliente 0 se pone en cola\n",
      " 0.0000 Cliente 0 ha esperado 0.000000\n",
      " 3.0602 Cliente 1 se pone en cola\n",
      " 3.8179 Cliente 2 se pone en cola\n",
      " 3.8595 Cliente 0 servido en 3.859489\n",
      " 3.8595 Cliente 1 ha esperado 0.799308\n",
      " 4.9509 Cliente 1 servido en 1.091429\n",
      " 4.9509 Cliente 2 ha esperado 1.132978\n",
      " 7.2055 Cliente 3 se pone en cola\n",
      " 7.2962 Cliente 4 se pone en cola\n",
      " 8.3493 Cliente 4 DESISTE despues de 1.053072\n",
      " 8.6427 Cliente 3 DESISTE despues de 1.437276\n",
      " 9.4080 Cliente 5 se pone en cola\n",
      "10.0730 Cliente 6 se pone en cola\n",
      "11.5139 Cliente 6 DESISTE despues de 1.440881\n",
      "11.5275 Cliente 2 servido en 6.576554\n",
      "11.5275 Cliente 5 ha esperado 2.119516\n",
      "12.4350 Cliente 7 se pone en cola\n",
      "13.4480 Cliente 7 DESISTE despues de 1.012998\n",
      "17.4082 Cliente 8 se pone en cola\n",
      "19.8045 Cliente 8 DESISTE despues de 2.396279\n",
      "22.2052 Cliente 5 servido en 10.677704\n",
      "22.3251 Cliente 9 se pone en cola\n",
      "22.3251 Cliente 9 ha esperado 0.000000\n",
      "60.1434 Cliente 9 servido en 37.818272\n",
      "Tiempo medio espera: 1.139231\n",
      "Tiempo medio servicio: 12.004690\n"
     ]
    }
   ],
   "source": [
    "RANDOM_SEED = 42\n",
    "NEW_CUSTOMERS = 10\n",
    "INTERVAL_CUSTOMERS = 3.0\n",
    "MIN_PATIENCE = 1\n",
    "MAX_PATIENCE = 3\n",
    "\n",
    "t_espera = []\n",
    "t_servicio = []\n",
    "\n",
    "def source(env, number, interval, counter):\n",
    "    for i in range(number):\n",
    "        c = customer(env, 'Cliente %d' % i, counter, time_in_bank=12.0)\n",
    "        env.process(c)\n",
    "        t = random.expovariate(1.0 / interval)\n",
    "        yield env.timeout(t)\n",
    "\n",
    "def customer(env, name, counter, time_in_bank):\n",
    "    llegada = env.now\n",
    "    print('%7.4f %s se pone en cola' % (llegada, name))\n",
    "\n",
    "    with counter.request() as req:\n",
    "        patience = random.uniform(MIN_PATIENCE, MAX_PATIENCE)\n",
    "        results = yield req | env.timeout(patience)\n",
    "\n",
    "        espera = env.now - llegada\n",
    "        t_espera.append(espera)\n",
    "        \n",
    "        if req in results:\n",
    "            inicio_servicio = env.now\n",
    "            print('%7.4f %s ha esperado %f' % (env.now, name, espera))\n",
    "            tib = random.expovariate(1.0 / time_in_bank)\n",
    "            yield env.timeout(tib)\n",
    "            servicio = env.now - inicio_servicio\n",
    "            t_servicio.append(servicio)\n",
    "            print('%7.4f %s servido en %f' % (env.now, name, servicio))\n",
    "        else:\n",
    "            print('%7.4f %s DESISTE despues de %f' % (env.now, name, espera))\n",
    "\n",
    "random.seed(RANDOM_SEED)\n",
    "env = simpy.Environment()\n",
    "counter = simpy.Resource(env, capacity=1)\n",
    "env.process(source(env, NEW_CUSTOMERS, INTERVAL_CUSTOMERS, counter))\n",
    "env.run()\n",
    "\n",
    "print(\"Tiempo medio espera: %f\" % Series(t_espera).mean())\n",
    "print(\"Tiempo medio servicio: %f\" % Series(t_servicio).mean())"
   ]
  }
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