3-queue system in a 2 × 2 switch.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "a1_avg = 0.49 # average arrival rate for queue 1 (input 1 to output 2)\n",
    "a2_avg = 0.49 # average arrival rate for queue 2 (input 2 to output 1)\n",
    "a3_avg = 0.49 # average arrival rate for queue 3 (input 2 to output 2)\n",
    "\n",
    "s = np.array([1, 1, 0]) # current service configuration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# strategy 1 (maxWeight strategy):\n",
    "# during each interval [t - 1, t], choose a configuration such that the queues being served have the maximum combined size\n",
    "\n",
    "def chooseMaxWeightServiceConfiguration(s, q):\n",
    "    if q[0] + q[1] >= q[2]:\n",
    "        s[0] = s[1] = 1\n",
    "        return\n",
    "    s[2] = 1\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(a1_avg)\n",
    "    #a1 = np.random.binomial(n = 10, p = a1_avg / 10)\n",
    "    #a1 = np.random.hypergeometric(6, 94, 5)\n",
    "    a2 = np.random.poisson(a2_avg)\n",
    "    a3 = np.random.poisson(a3_avg)\n",
    "    s = np.zeros(3)\n",
    "    chooseMaxWeightServiceConfiguration(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": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Policy = MaxWeight\n",
      "Average Arrival Rate for Queue 1 = λ₁ = 0.49\n",
      "Average Arrival Rate for Queue 2 = λ₂ = 0.49\n",
      "Average Arrival Rate for Queue 3 = λ₃ = 0.49\n",
      "Service Rate μ = 1 (for all 3 queues)\n",
      "\n",
      "Steady-state Average Size of Queue 1 = ̅q₁ ≈ 11.613\n",
      "Steady-state Average Size of Queue 2 = ̅q₂ ≈ 12.058\n",
      "Steady-state Average Size of Queue 3 = ̅q₃ ≈ 24.103\n",
      "̅q₁ + ̅q₂ ≈ 23.671\n",
      "Steady-state Average Total Queue Size ≈ 47.773\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 = MaxWeight')\n",
    "print('Average Arrival Rate for Queue 1 = \\u03BB\\u2081 =', a1_avg)\n",
    "print('Average Arrival Rate for Queue 2 = \\u03BB\\u2082 =', a2_avg)\n",
    "print('Average Arrival Rate for Queue 3 = \\u03BB\\u2083 =', a3_avg)\n",
    "print('Service Rate \\u03BC = 1 (for all 3 queues)')\n",
    "print('\\nSteady-state Average Size of Queue 1 = \\u0305q\\u2081 \\u2248', round(np.average(q1_output), 3))\n",
    "print('Steady-state Average Size of Queue 2 = \\u0305q\\u2082 \\u2248', round(np.average(q2_output), 3))\n",
    "print('Steady-state Average Size of Queue 3 = \\u0305q\\u2083 \\u2248', round(np.average(q3_output), 3))\n",
    "print('\\u0305q\\u2081 + \\u0305q\\u2082 \\u2248', round(np.average(q1_output + q2_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 (maxSizeCenter strategy):\n",
    "# during each interval [t - 1, t], choose a configuration that serves the first two queues unless both of them are empty and the third one is not\n",
    "\n",
    "def chooseServeNonzeroQueuesConfiguration(s, q):\n",
    "    if q[2] == 0:\n",
    "        s[0] = s[1] = 1\n",
    "        return\n",
    "    if q[0] == 0 or q[1] == 0:\n",
    "        s[2] = 1\n",
    "        return\n",
    "    s[0] = s[1] = 1\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(a1_avg)\n",
    "    #a1 = np.random.binomial(n = 10, p = a1_avg / 10)\n",
    "    #a1 = np.random.hypergeometric(6, 94, 5)\n",
    "    a2 = np.random.poisson(a2_avg)\n",
    "    a3 = np.random.poisson(a3_avg)\n",
    "    s = np.zeros(3)\n",
    "    chooseServeNonzeroQueuesConfiguration(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 = MaxSizeCenter\n",
      "Average Arrival Rate for Queue 1 = λ₁ = 0.49\n",
      "Average Arrival Rate for Queue 2 = λ₂ = 0.49\n",
      "Average Arrival Rate for Queue 3 = λ₃ = 0.49\n",
      "Service Rate μ = 1 (for all 3 queues)\n",
      "\n",
      "Steady-state Average Size of Queue 1 = ̅q₁ ≈ 9.948\n",
      "Steady-state Average Size of Queue 2 = ̅q₂ ≈ 9.946\n",
      "Steady-state Average Size of Queue 3 = ̅q₃ ≈ 14.446\n",
      "̅q₁ + ̅q₂ ≈ 19.894\n",
      "Steady-state Average Total Queue Size = ≈ 34.34\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 = MaxSizeCenter')\n",
    "print('Average Arrival Rate for Queue 1 = \\u03BB\\u2081 =', a1_avg)\n",
    "print('Average Arrival Rate for Queue 2 = \\u03BB\\u2082 =', a2_avg)\n",
    "print('Average Arrival Rate for Queue 3 = \\u03BB\\u2083 =', a3_avg)\n",
    "print('Service Rate \\u03BC = 1 (for all 3 queues)')\n",
    "print('\\nSteady-state Average Size of Queue 1 = \\u0305q\\u2081 \\u2248', round(np.average(q1_output), 3))\n",
    "print('Steady-state Average Size of Queue 2 = \\u0305q\\u2082 \\u2248', round(np.average(q2_output), 3))\n",
    "print('Steady-state Average Size of Queue 3 = \\u0305q\\u2083 \\u2248', round(np.average(q3_output), 3))\n",
    "print('\\u0305q\\u2081 + \\u0305q\\u2082 \\u2248', round(np.average(q1_output + q2_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 (random strategy):\n",
    "# during each interval [t - 1, t], choose a random configuration\n",
    "\n",
    "def chooseRandomServiceConfiguration(s):\n",
    "    if np.random.choice(2) == 0:\n",
    "        s[0] = s[1] = 1\n",
    "        return\n",
    "    s[2] = 1\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(a1_avg)\n",
    "    #a1 = np.random.binomial(n = 10, p = a1_avg / 10)\n",
    "    #a1 = np.random.hypergeometric(6, 94, 5)\n",
    "    a2 = np.random.poisson(a2_avg)\n",
    "    a3 = np.random.poisson(a3_avg)\n",
    "    s = np.zeros(3)\n",
    "    chooseRandomServiceConfiguration(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": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Policy = Random\n",
      "Average Arrival Rate for Queue 1 = λ₁ = 0.49\n",
      "Average Arrival Rate for Queue 2 = λ₂ = 0.49\n",
      "Average Arrival Rate for Queue 3 = λ₃ = 0.49\n",
      "Service Rate μ = 1 (for all 3 queues)\n",
      "\n",
      "Steady-state Average Size of Queue 1 = ̅q₁ ≈ 35.479\n",
      "Steady-state Average Size of Queue 2 = ̅q₂ ≈ 35.567\n",
      "Steady-state Average Size of Queue 3 = ̅q₃ ≈ 37.836\n",
      "̅q₁ + ̅q₂ ≈ 71.046\n",
      "Steady-state Average Total Queue Size ≈ 108.882\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 3\n",
    "\n",
    "print('Policy = Random')\n",
    "print('Average Arrival Rate for Queue 1 = \\u03BB\\u2081 =', a1_avg)\n",
    "print('Average Arrival Rate for Queue 2 = \\u03BB\\u2082 =', a2_avg)\n",
    "print('Average Arrival Rate for Queue 3 = \\u03BB\\u2083 =', a3_avg)\n",
    "print('Service Rate \\u03BC = 1 (for all 3 queues)')\n",
    "print('\\nSteady-state Average Size of Queue 1 = \\u0305q\\u2081 \\u2248', round(np.average(q1_output), 3))\n",
    "print('Steady-state Average Size of Queue 2 = \\u0305q\\u2082 \\u2248', round(np.average(q2_output), 3))\n",
    "print('Steady-state Average Size of Queue 3 = \\u0305q\\u2083 \\u2248', round(np.average(q3_output), 3))\n",
    "print('\\u0305q\\u2081 + \\u0305q\\u2082 \\u2248', round(np.average(q1_output + q2_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()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
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