3 queues 1 server simulation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "averageNumberOfArrivalsPerUnitTime1 = 0.3\n",
    "averageNumberOfArrivalsPerUnitTime2 = 0.1\n",
    "averageNumberOfArrivalsPerUnitTime3 = 0.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# strategy 1: the server randomly serves one of the three queues during each interval\n",
    "\n",
    "# simulate 10,000,001 times, with q1(0) = q2(0) = q3(0) = 0\n",
    "# discard first 2,000,000 samples to ensure steady state\n",
    "# take samples every 100 times to ensure independence\n",
    "\n",
    "q1 = np.zeros(10000002)\n",
    "q1_output = np.zeros(80001)\n",
    "q2 = np.zeros(10000002)\n",
    "q2_output = np.zeros(80001)\n",
    "q3 = np.zeros(10000002)\n",
    "q3_output = np.zeros(80001)\n",
    "\n",
    "for t in range(1, 10000002):\n",
    "    a1 = np.random.poisson(averageNumberOfArrivalsPerUnitTime1)\n",
    "    #a1 = np.random.binomial(n = 10, p = averageNumberOfArrivalsPerUnitTime1 / 10)\n",
    "    #a1 = np.random.hypergeometric(4, 96, 5)\n",
    "    a2 = np.random.poisson(averageNumberOfArrivalsPerUnitTime2)\n",
    "    a3 = np.random.poisson(averageNumberOfArrivalsPerUnitTime3)\n",
    "    s = np.array([1, 0, 0])\n",
    "    random.shuffle(s)\n",
    "    q1[t] = max(q1[t - 1] + a1 - s[0], 0)\n",
    "    q2[t] = max(q2[t - 1] + a2 - s[1], 0)\n",
    "    q3[t] = max(q3[t - 1] + a3 - s[2], 0)\n",
    "\n",
    "for t in range(0, 80001):\n",
    "    q1_output[t] = q1[2 * 1000000 + 1 + 100 * t]\n",
    "    q2_output[t] = q2[2 * 1000000 + 1 + 100 * t]\n",
    "    q3_output[t] = q3[2 * 1000000 + 1 + 100 * t]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Policy = Random\n",
      "Average Arrival Rate for Queue 1 = λ₁ = 0.3\n",
      "Average Arrival Rate for Queue 2 = λ₂ = 0.1\n",
      "Average Arrival Rate for Queue 3 = λ₃ = 0.2\n",
      "Service Rate μ = 1 (for all 3 queues)\n",
      "\n",
      "Steady-state Average Size of Queue 1 ≈ 7.275\n",
      "Steady-state Average Size of Queue 2 ≈ 0.307\n",
      "Steady-state Average Size of Queue 3 ≈ 1.144\n",
      "Steady-state Average Total Queue Size ≈ 8.726\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1296x864 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# output for strategy 1\n",
    "\n",
    "print('Policy = Random')\n",
    "print('Average Arrival Rate for Queue 1 = \\u03BB\\u2081 =', averageNumberOfArrivalsPerUnitTime1)\n",
    "print('Average Arrival Rate for Queue 2 = \\u03BB\\u2082 =', averageNumberOfArrivalsPerUnitTime2)\n",
    "print('Average Arrival Rate for Queue 3 = \\u03BB\\u2083 =', averageNumberOfArrivalsPerUnitTime3)\n",
    "print('Service Rate \\u03BC = 1 (for all 3 queues)')\n",
    "print('\\nSteady-state Average Size of Queue 1 \\u2248', round(np.average(q1_output), 3))\n",
    "print('Steady-state Average Size of Queue 2 \\u2248', round(np.average(q2_output), 3))\n",
    "print('Steady-state Average Size of Queue 3 \\u2248', round(np.average(q3_output), 3))\n",
    "print('Steady-state Average Total Queue Size \\u2248', round(np.average(q1_output + q2_output + q3_output), 3))\n",
    "\n",
    "plt.figure(figsize = (18, 12))\n",
    "\n",
    "plt.subplot(1, 3, 1)\n",
    "\n",
    "plt.hist(q1_output, bins = np.linspace(0, int(max(q1_output)) + 1, int(max(q1_output) + 2)), density = True)\n",
    "plt.xlabel('Queue Size')\n",
    "plt.title('Normalized Histogram for Size of Queue 1')\n",
    "\n",
    "\n",
    "plt.subplot(1, 3, 2)\n",
    "\n",
    "plt.hist(q2_output, bins = np.linspace(0, int(max(q2_output)) + 1, int(max(q2_output) + 2)), density = True)\n",
    "plt.xlabel('Queue Size')\n",
    "plt.title('Normalized Histogram for Size of Queue 2')\n",
    "\n",
    "\n",
    "plt.subplot(1, 3, 3)\n",
    "\n",
    "plt.hist(q3_output, bins = np.linspace(0, int(max(q3_output)) + 1, int(max(q3_output) + 2)), density = True)\n",
    "plt.xlabel('Queue Size')\n",
    "plt.title('Normalized Histogram for Size of Queue 3')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# strategy 2: the server serves the shortest queue during each interval\n",
    "\n",
    "def chooseShortestQueueToServe(s, q):\n",
    "    q_nonzero = np.array([])\n",
    "    for e in q:\n",
    "        if e > 0:\n",
    "            q_nonzero = np.append(q_nonzero, e)\n",
    "    if len(q_nonzero) == 0:\n",
    "        s[0] = 1\n",
    "        return\n",
    "    for i in range(len(q)):\n",
    "        if q[i] == min(q_nonzero):\n",
    "            s[i] = 1\n",
    "            return\n",
    "\n",
    "# simulate 10,000,001 times, with q1(0) = q2(0) = q3(0) = 0\n",
    "# discard first 2,000,000 samples to ensure steady state\n",
    "# take samples every 100 times to ensure independence\n",
    "\n",
    "q1 = np.zeros(10000002)\n",
    "q1_output = np.zeros(80001)\n",
    "q2 = np.zeros(10000002)\n",
    "q2_output = np.zeros(80001)\n",
    "q3 = np.zeros(10000002)\n",
    "q3_output = np.zeros(80001)\n",
    "\n",
    "for t in range(1, 10000002):\n",
    "    a1 = np.random.poisson(averageNumberOfArrivalsPerUnitTime1)\n",
    "    #a1 = np.random.binomial(n = 10, p = averageNumberOfArrivalsPerUnitTime1 / 10)\n",
    "    #a1 = np.random.hypergeometric(4, 96, 5)\n",
    "    a2 = np.random.poisson(averageNumberOfArrivalsPerUnitTime2)\n",
    "    a3 = np.random.poisson(averageNumberOfArrivalsPerUnitTime3)\n",
    "    s = np.zeros(3)\n",
    "    chooseShortestQueueToServe(s, np.array([q1[t - 1], q2[t - 1], q3[t - 1]]))\n",
    "    q1[t] = max(q1[t - 1] + a1 - s[0], 0)\n",
    "    q2[t] = max(q2[t - 1] + a2 - s[1], 0)\n",
    "    q3[t] = max(q3[t - 1] + a3 - s[2], 0)\n",
    "\n",
    "for t in range(0, 80001):\n",
    "    q1_output[t] = q1[2 * 1000000 + 1 + 100 * t]\n",
    "    q2_output[t] = q2[2 * 1000000 + 1 + 100 * t]\n",
    "    q3_output[t] = q3[2 * 1000000 + 1 + 100 * t]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Policy = Serve-the-shortest-nonzero-queue\n",
      "Average Arrival Rate for Queue 1 = λ₁ = 0.3\n",
      "Average Arrival Rate for Queue 2 = λ₂ = 0.1\n",
      "Average Arrival Rate for Queue 3 = λ₃ = 0.2\n",
      "Service Rate μ = 1 (for all 3 queues)\n",
      "\n",
      "Steady-state Average Size of Queue 1 ≈ 0.254\n",
      "Steady-state Average Size of Queue 2 ≈ 0.136\n",
      "Steady-state Average Size of Queue 3 ≈ 0.363\n",
      "Steady-state Average Total Queue Size ≈ 0.753\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x864 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# output for strategy 2\n",
    "\n",
    "print('Policy = Serve-the-shortest-nonzero-queue')\n",
    "print('Average Arrival Rate for Queue 1 = \\u03BB\\u2081 =', averageNumberOfArrivalsPerUnitTime1)\n",
    "print('Average Arrival Rate for Queue 2 = \\u03BB\\u2082 =', averageNumberOfArrivalsPerUnitTime2)\n",
    "print('Average Arrival Rate for Queue 3 = \\u03BB\\u2083 =', averageNumberOfArrivalsPerUnitTime3)\n",
    "print('Service Rate \\u03BC = 1 (for all 3 queues)')\n",
    "print('\\nSteady-state Average Size of Queue 1 \\u2248', round(np.average(q1_output), 3))\n",
    "print('Steady-state Average Size of Queue 2 \\u2248', round(np.average(q2_output), 3))\n",
    "print('Steady-state Average Size of Queue 3 \\u2248', round(np.average(q3_output), 3))\n",
    "print('Steady-state Average Total Queue Size \\u2248', round(np.average(q1_output + q2_output + q3_output), 3))\n",
    "\n",
    "plt.figure(figsize = (18, 12))\n",
    "\n",
    "plt.subplot(1, 3, 1)\n",
    "\n",
    "plt.hist(q1_output, bins = np.linspace(0, int(max(q1_output)) + 1, int(max(q1_output) + 2)), density = True)\n",
    "plt.xlabel('Queue Size')\n",
    "plt.title('Normalized Histogram for Size of Queue 1')\n",
    "\n",
    "\n",
    "plt.subplot(1, 3, 2)\n",
    "\n",
    "plt.hist(q2_output, bins = np.linspace(0, int(max(q2_output)) + 1, int(max(q2_output) + 2)), density = True)\n",
    "plt.xlabel('Queue Size')\n",
    "plt.title('Normalized Histogram for Size of Queue 2')\n",
    "\n",
    "\n",
    "plt.subplot(1, 3, 3)\n",
    "\n",
    "plt.hist(q3_output, bins = np.linspace(0, int(max(q3_output)) + 1, int(max(q3_output) + 2)), density = True)\n",
    "plt.xlabel('Queue Size')\n",
    "plt.title('Normalized Histogram for Size of Queue 3')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# strategy 3: the server serves the longest queue during each interval\n",
    "\n",
    "def chooseLongestQueueToServe(s, q):\n",
    "    for i in range(len(q)):\n",
    "        if q[i] == max(q):\n",
    "            s[i] = 1\n",
    "            return\n",
    "\n",
    "# simulate 10,000,001 times, with q1(0) = q2(0) = q3(0) = 0\n",
    "# discard first 2,000,000 samples to ensure steady state\n",
    "# take samples every 100 times to ensure independence\n",
    "\n",
    "q1 = np.zeros(10000002)\n",
    "q1_output = np.zeros(80001)\n",
    "q2 = np.zeros(10000002)\n",
    "q2_output = np.zeros(80001)\n",
    "q3 = np.zeros(10000002)\n",
    "q3_output = np.zeros(80001)\n",
    "\n",
    "for t in range(1, 10000002):\n",
    "    a1 = np.random.poisson(averageNumberOfArrivalsPerUnitTime1)\n",
    "    #a1 = np.random.binomial(n = 10, p = averageNumberOfArrivalsPerUnitTime1 / 10)\n",
    "    #a1 = np.random.hypergeometric(4, 96, 5)\n",
    "    a2 = np.random.poisson(averageNumberOfArrivalsPerUnitTime2)\n",
    "    a3 = np.random.poisson(averageNumberOfArrivalsPerUnitTime3)\n",
    "    s = np.zeros(3)\n",
    "    chooseLongestQueueToServe(s, np.array([q1[t - 1], q2[t - 1], q3[t - 1]]))\n",
    "    q1[t] = max(q1[t - 1] + a1 - s[0], 0)\n",
    "    q2[t] = max(q2[t - 1] + a2 - s[1], 0)\n",
    "    q3[t] = max(q3[t - 1] + a3 - s[2], 0)\n",
    "\n",
    "for t in range(0, 80001):\n",
    "    q1_output[t] = q1[2 * 1000000 + 1 + 100 * t]\n",
    "    q2_output[t] = q2[2 * 1000000 + 1 + 100 * t]\n",
    "    q3_output[t] = q3[2 * 1000000 + 1 + 100 * t]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Policy = Serve-the-longest-queue\n",
      "Average Arrival Rate for Queue 1 = λ₁ = 0.3\n",
      "Average Arrival Rate for Queue 2 = λ₂ = 0.1\n",
      "Average Arrival Rate for Queue 3 = λ₃ = 0.2\n",
      "Service Rate μ = 1 (for all 3 queues)\n",
      "\n",
      "Steady-state Average Size of Queue 1 ≈ 0.225\n",
      "Steady-state Average Size of Queue 2 ≈ 0.162\n",
      "Steady-state Average Size of Queue 3 ≈ 0.361\n",
      "Steady-state Average Total Queue Size ≈ 0.748\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1296x864 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# output for strategy 3\n",
    "\n",
    "print('Policy = Serve-the-longest-queue')\n",
    "print('Average Arrival Rate for Queue 1 = \\u03BB\\u2081 =', averageNumberOfArrivalsPerUnitTime1)\n",
    "print('Average Arrival Rate for Queue 2 = \\u03BB\\u2082 =', averageNumberOfArrivalsPerUnitTime2)\n",
    "print('Average Arrival Rate for Queue 3 = \\u03BB\\u2083 =', averageNumberOfArrivalsPerUnitTime3)\n",
    "print('Service Rate \\u03BC = 1 (for all 3 queues)')\n",
    "print('\\nSteady-state Average Size of Queue 1 \\u2248', round(np.average(q1_output), 3))\n",
    "print('Steady-state Average Size of Queue 2 \\u2248', round(np.average(q2_output), 3))\n",
    "print('Steady-state Average Size of Queue 3 \\u2248', round(np.average(q3_output), 3))\n",
    "print('Steady-state Average Total Queue Size \\u2248', round(np.average(q1_output + q2_output + q3_output), 3))\n",
    "\n",
    "plt.figure(figsize = (18, 12))\n",
    "\n",
    "plt.subplot(1, 3, 1)\n",
    "\n",
    "plt.hist(q1_output, bins = np.linspace(0, int(max(q1_output)) + 1, int(max(q1_output) + 2)), density = True)\n",
    "plt.xlabel('Queue Size')\n",
    "plt.title('Normalized Histogram for Size of Queue 1')\n",
    "\n",
    "\n",
    "plt.subplot(1, 3, 2)\n",
    "\n",
    "plt.hist(q2_output, bins = np.linspace(0, int(max(q2_output)) + 1, int(max(q2_output) + 2)), density = True)\n",
    "plt.xlabel('Queue Size')\n",
    "plt.title('Normalized Histogram for Size of Queue 2')\n",
    "\n",
    "\n",
    "plt.subplot(1, 3, 3)\n",
    "\n",
    "plt.hist(q3_output, bins = np.linspace(0, int(max(q3_output)) + 1, int(max(q3_output) + 2)), density = True)\n",
    "plt.xlabel('Queue Size')\n",
    "plt.title('Normalized Histogram for Size of Queue 3')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "averageNumberOfArrivalsPerUnitTime1 = 0.05\n",
    "averageNumberOfArrivalsPerUnitTime2 = 0.61\n",
    "averageNumberOfArrivalsPerUnitTime3 = 0.33\n",
    "\n",
    "# strategy 3: the server serves the longest queue during each interval\n",
    "\n",
    "def chooseLongestQueueToServe(s, q):\n",
    "    for i in range(len(q)):\n",
    "        if q[i] == max(q):\n",
    "            s[i] = 1\n",
    "            return\n",
    "\n",
    "# simulate 10,000,001 times, with q1(0) = q2(0) = q3(0) = 0\n",
    "# discard first 2,000,000 samples to ensure steady state\n",
    "# take samples every 100 times to ensure independence\n",
    "\n",
    "q1 = np.zeros(10000002)\n",
    "q1_output = np.zeros(80001)\n",
    "q2 = np.zeros(10000002)\n",
    "q2_output = np.zeros(80001)\n",
    "q3 = np.zeros(10000002)\n",
    "q3_output = np.zeros(80001)\n",
    "\n",
    "for t in range(1, 10000002):\n",
    "    a1 = np.random.poisson(averageNumberOfArrivalsPerUnitTime1)\n",
    "    #a1 = np.random.binomial(n = 10, p = averageNumberOfArrivalsPerUnitTime1 / 10)\n",
    "    #a1 = np.random.hypergeometric(4, 96, 5)\n",
    "    a2 = np.random.poisson(averageNumberOfArrivalsPerUnitTime2)\n",
    "    a3 = np.random.poisson(averageNumberOfArrivalsPerUnitTime3)\n",
    "    s = np.zeros(3)\n",
    "    chooseLongestQueueToServe(s, np.array([q1[t - 1], q2[t - 1], q3[t - 1]]))\n",
    "    q1[t] = max(q1[t - 1] + a1 - s[0], 0)\n",
    "    q2[t] = max(q2[t - 1] + a2 - s[1], 0)\n",
    "    q3[t] = max(q3[t - 1] + a3 - s[2], 0)\n",
    "\n",
    "for t in range(0, 80001):\n",
    "    q1_output[t] = q1[2 * 1000000 + 1 + 100 * t]\n",
    "    q2_output[t] = q2[2 * 1000000 + 1 + 100 * t]\n",
    "    q3_output[t] = q3[2 * 1000000 + 1 + 100 * t]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Policy = Serve-the-longest-queue\n",
      "Average Arrival Rate for Queue 1 = λ₁ = 0.05\n",
      "Average Arrival Rate for Queue 2 = λ₂ = 0.61\n",
      "Average Arrival Rate for Queue 3 = λ₃ = 0.33\n",
      "Service Rate μ = 1 (for all 3 queues)\n",
      "\n",
      "Steady-state Average Size of Queue 1 ≈ 15.635\n",
      "Steady-state Average Size of Queue 2 ≈ 18.012\n",
      "Steady-state Average Size of Queue 3 ≈ 17.962\n",
      "Steady-state Average Total Queue Size ≈ 51.609\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1296x864 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# output for strategy 3\n",
    "\n",
    "print('Policy = Serve-the-longest-queue')\n",
    "print('Average Arrival Rate for Queue 1 = \\u03BB\\u2081 =', averageNumberOfArrivalsPerUnitTime1)\n",
    "print('Average Arrival Rate for Queue 2 = \\u03BB\\u2082 =', averageNumberOfArrivalsPerUnitTime2)\n",
    "print('Average Arrival Rate for Queue 3 = \\u03BB\\u2083 =', averageNumberOfArrivalsPerUnitTime3)\n",
    "print('Service Rate \\u03BC = 1 (for all 3 queues)')\n",
    "print('\\nSteady-state Average Size of Queue 1 \\u2248', round(np.average(q1_output), 3))\n",
    "print('Steady-state Average Size of Queue 2 \\u2248', round(np.average(q2_output), 3))\n",
    "print('Steady-state Average Size of Queue 3 \\u2248', round(np.average(q3_output), 3))\n",
    "print('Steady-state Average Total Queue Size \\u2248', round(np.average(q1_output + q2_output + q3_output), 3))\n",
    "\n",
    "plt.figure(figsize = (18, 12))\n",
    "\n",
    "plt.subplot(1, 3, 1)\n",
    "\n",
    "plt.hist(q1_output, bins = np.linspace(0, int(max(q1_output)) + 1, int(max(q1_output) + 2)), density = True)\n",
    "plt.xlabel('Queue Size')\n",
    "plt.title('Normalized Histogram for Size of Queue 1')\n",
    "\n",
    "\n",
    "plt.subplot(1, 3, 2)\n",
    "\n",
    "plt.hist(q2_output, bins = np.linspace(0, int(max(q2_output)) + 1, int(max(q2_output) + 2)), density = True)\n",
    "plt.xlabel('Queue Size')\n",
    "plt.title('Normalized Histogram for Size of Queue 2')\n",
    "\n",
    "\n",
    "plt.subplot(1, 3, 3)\n",
    "\n",
    "plt.hist(q3_output, bins = np.linspace(0, int(max(q3_output)) + 1, int(max(q3_output) + 2)), density = True)\n",
    "plt.xlabel('Queue Size')\n",
    "plt.title('Normalized Histogram for Size of Queue 3')\n",
    "\n",
    "plt.show()"
   ]
  }
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