Proyecto5.ipynb

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    "### Universidad de Costa Rica\n",
    "#### IE0405 - Modelos Probabilísticos de Señales y Sistemas\n",
    "### P5: Procesos M/M/s\n",
    "\n",
    "- Estudiante1: **Emmanuel Carballo Vargas**\n",
    "- Carné1: **B41424**\n",
    "\n",
    "- Estudiante2: **Francinny Marín Sibaja**\n",
    "- Carné2: **B74459**\n",
    "\n",
    "- Estudiante3: **Jose Hidalgo Castro**\n",
    "- Carné3: **B63466**\n",
    "- Grupo: **15**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Parte a:\n",
    "\n",
    "Del enunciado se obtienen los siguientes datos:\n",
    "- $\\lambda$ = 7 personas/minuto\n",
    "- $\\nu$ = 0.25 personas/minuto\n",
    "- El sistema no debe exceder 100 personas en fila durante el 95% del tiempo de servicio $\\Rightarrow$ i = 100. \n",
    "\n",
    "De manera que, se logra reconocer que es un proceso **M/M/s**, dado que se requiere que el sistema no exceda 100 personas en fila durante el 95% de tiempo, entonces:\n",
    "\n",
    "$$\n",
    "P( \\text{101 o } ) = \\sum_{i=101}^{\\infty} (1 - \\rho) \\rho^i  = 1 - \\sum_{i=0}^{100} (1 - \\rho) \\rho^i = \\rho^{100}\n",
    "$$\n",
    "\n",
    "Ahora, se sabe que $\\rho = \\lambda/s\\nu$, además, se requiere una probabilidad menor o igual al 5% (esto debido a que se busca que el 95% del tiempo no se exceda una cantidad de 100 personas en fila), por lo que se tiene que:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "P( \\text{101 o más clientes en el sistema} ) = \\rho^{100} & = \\left( \\frac{\\lambda}{s\\nu} \\right)^{100} \\leq 0.05 \\\\\n",
    "\\Rightarrow s^{100} & \\geq \\frac{\\lambda^{100}}{0.05\\nu^{100}} = \\frac{7^{100}}{0.05\\cdot 0.25^{100}} \\quad \\Rightarrow \\quad s \\geq \\sqrt[100]{\\frac{7^{100}}{0.05\\cdot 0.25^{100}} } \\Rightarrow s \\geq 28.85 \\approx 29 \n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Por lo que para cumplir el requisito se requieren de al menos 29 servidores.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Parte b:\n",
    "\n",
    "En esta sección se modifica el código provisto para simular y corroborar el resultado anterior, además se crean dos gráficas que muestran dicha simulación.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Se requiere una cantidad de 29 servidores para cumplir con los requerimientos.\n",
      "\n",
      "Simulación para 29 servidores\n",
      "Parámetro lambda = 7.0\n",
      "Parámetro nu*s = 7.25\n",
      "Tiempo con más de 100 solicitudes en fila:\n",
      "\t 0.00%\n",
      "\t Sí cumple con la especificación.\n",
      "Simulación es equivalente a 8.16 horas.\n"
     ]
    },
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulación para 26 servidores\n",
      "Parámetro lambda = 7.0\n",
      "Parámetro nu*s = 6.5\n",
      "Tiempo con más de 100 solicitudes en fila:\n",
      "\t 67.38%\n",
      "\t No cumple con la especificación.\n",
      "Simulación es equivalente a 8.74 horas.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "import numpy as np\n",
    "import math\n",
    "from scipy import stats\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def total_servidores(personas_fila, tasa_llegada, tasa_partida, porcentaje_tiempo, servidores):\n",
    "    \n",
    "    # indices a usar en las sumatorias\n",
    "    sumatoria_2 = 0\n",
    "    sumatoria_1 = 0\n",
    "\n",
    "    # Probabilidad de estado cero\n",
    "    phi_0 = 0\n",
    "\n",
    "    while sumatoria_1 < porcentaje_tiempo:\n",
    "\n",
    "        # Se calcula el rho\n",
    "        rhoo = tasa_llegada/(servidores*tasa_partida)\n",
    "\n",
    "        # Manejo de excepciones --> division por cero\n",
    "        try:\n",
    "            x = pow(servidores*rhoo,servidores)/(math.factorial(servidores)*(1-rhoo))\n",
    "        except:\n",
    "            x = pow(servidores*rhoo,servidores)/(math.factorial(servidores)*(0.0000001))\n",
    "\n",
    "        k = 0;\n",
    "        sumatoria_2 = 0 # Se reinicia la sumatoria\n",
    "\n",
    "        # Se realiza la sumatoria de Phi_0\n",
    "        while k <= (servidores-1):\n",
    "            sumatoria_2 = sumatoria_2 + ((pow(servidores*rhoo,k))/(math.factorial(k)))\n",
    "            k = k + 1 # Se incrementa el índice k\n",
    "\n",
    "        phi_0 = 1/(sumatoria_2 + x) # Se calcula Phi_0\n",
    "\n",
    "        i = 0\n",
    "        sumatoria_1 = 0 # Se reinicia la sumatoria \n",
    "\n",
    "        # Sumatoria de la probabilidad de que el estado en el sistema esté por debajo de 100 personas\n",
    "        while i < servidores:\n",
    "            y1 = pow(servidores*rhoo,i)/(math.factorial(i))\n",
    "            sumatoria_1 = sumatoria_1 + y1*phi_0\n",
    "            i = i + 1\n",
    "\n",
    "        while i >= servidores and i <= (personas_fila + servidores):\n",
    "            y2 = (pow(servidores,servidores)*pow(rhoo,i))/(math.factorial(servidores))\n",
    "            sumatoria_1 = sumatoria_1 + y2*phi_0\n",
    "            i = i + 1\n",
    "\n",
    "        servidores = servidores+1; # Se incrementa en 1 el número de servidores\n",
    "    print(\"Se requiere una cantidad de {} servidores para cumplir con los requerimientos.\".format(servidores-2))\n",
    "    \n",
    "def graficas(N, lam, nu_s):\n",
    "\n",
    "    # Distribución de los tiempos de llegada entre cada cliente\n",
    "    X = stats.expon(scale = 1/lam)\n",
    "\n",
    "    # Distribución de los tiempos de servicio a cada cliente\n",
    "    Y = stats.expon(scale = 1/nu_s)\n",
    "\n",
    "    # Intervalos entre llegadas (segundos desde último cliente)\n",
    "    t_intervalos = np.ceil(X.rvs(N)).astype('int')\n",
    "\n",
    "    # Tiempos de las llegadas (segundos desde el inicio)\n",
    "    t_llegadas = [t_intervalos[0]]\n",
    "    for i in range(1, len(t_intervalos)):\n",
    "        siguiente = t_llegadas[i-1] + t_intervalos[i]\n",
    "        t_llegadas.append(siguiente)\n",
    "\n",
    "    # Tiempos de servicio (segundos desde inicio de servicio)\n",
    "    t_servicio = np.ceil(Y.rvs(N)).astype('int')\n",
    "\n",
    "    # Inicialización del tiempo de inicio y fin de atención\n",
    "    inicio = t_llegadas[0]          # primera llegada\n",
    "    fin = inicio + t_servicio[0]    # primera salida\n",
    "\n",
    "    # Tiempos en que recibe atención cada i-ésimo cliente (!= que llega)\n",
    "    t_atencion = [inicio]\n",
    "    for i in range(1, N):\n",
    "        inicio = np.max((t_llegadas[i], fin))\n",
    "        fin = inicio + t_servicio[i]\n",
    "        t_atencion.append(inicio)\n",
    "\n",
    "    # Inicialización del vector temporal para registrar eventos\n",
    "    t = np.zeros(t_atencion[-1] + t_servicio[-1] + 1)\n",
    "\n",
    "    # Asignación de eventos de llegada (+1) y salida (-1) de clientes\n",
    "    for c in range(N):\n",
    "        i = t_llegadas[c]\n",
    "        t[i] += 1\n",
    "        j = t_atencion[c] + t_servicio[c]\n",
    "        t[j] -= 1\n",
    "\n",
    "    # Umbral de P o más personas en sistema (hay P - 1 en fila)\n",
    "    P = 102\n",
    "\n",
    "    # Instantes (segundos) de tiempo con P o más solicitudes en sistema\n",
    "    exceso = 0\n",
    "\n",
    "    # Proceso aleatorio (estados n = {0, 1, 2...})\n",
    "    Xt = np.zeros(t.shape)\n",
    "\n",
    "    # Inicialización de estado n\n",
    "    n = 0\n",
    "\n",
    "    # Recorrido del vector temporal y conteo de clientes (estado n)\n",
    "    for i, c in enumerate(t):\n",
    "        n += c # sumar (+1) o restar (-1) al estado\n",
    "        Xt[i] = n\n",
    "        if Xt[i] >= P: \n",
    "            exceso += 1\n",
    "\n",
    "    # Fracción de tiempo con P o más solicitudes en sistema\n",
    "    fraccion = exceso / len(t)\n",
    "\n",
    "    # Resultados\n",
    "    print('Parámetro lambda =', str(lam*60))\n",
    "    print('Parámetro nu*s =', str(nu_s*60))\n",
    "    print('Tiempo con más de {} solicitudes en fila:'.format(P-2))\n",
    "    print('\\t {:0.2f}%'.format(100*fraccion))\n",
    "    if fraccion <= 0.01:\n",
    "        print('\\t Sí cumple con la especificación.')\n",
    "    else:\n",
    "        print('\\t No cumple con la especificación.') \n",
    "    print('Simulación es equivalente a {:0.2f} horas.'.format(len(t)/3600))\n",
    "\n",
    "    # Gráfica de X(t) (estados del sistema)\n",
    "    plt.figure()\n",
    "    plt.plot(Xt)\n",
    "    plt.plot(range(len(t)), (P-1)*np.ones(t.shape))\n",
    "    plt.legend(('$X(t) = n$', '$L_q = $' + str(P-2)))\n",
    "    plt.ylabel('Clientes en el sistema, $n$')\n",
    "    plt.xlabel('Tiempo, $t$ / segundos')\n",
    "    plt.xlim((0, 5000))\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "# Se llama a las funciones con distintos parámetros:\n",
    "total_servidores(100, 7, 0.24, 0.95, 1)\n",
    "print()\n",
    "print('Simulación para 29 servidores')\n",
    "graficas(3200, 7/60, 7.25/60)\n",
    "\n",
    "print('Simulación para 26 servidores')\n",
    "graficas(3200, 7/60, 6.5/60)\n"
   ]
  }
 ],
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