example_analytic_ac_approx.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Allen Cunneen approximation (GI/G/c model)\n",
    "\n",
    "For models with general inter-arrival and service times there are no exact analytic solutions. The Allen Cunneen formula will give some approximation results."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importing modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Erlang module\n",
    "from queuesim.analytic import ac_approx_table\n",
    "\n",
    "# Plotting modules\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.ticker as formater\n",
    "import seaborn as sns\n",
    "\n",
    "# Defining general plot style\n",
    "sns.set()\n",
    "percent_formater = formater.PercentFormatter(xmax=1, decimals=0)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mean waiting time as a function of the coefficient of variation of the service times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>lambda</th>\n",
       "      <th>mu</th>\n",
       "      <th>a</th>\n",
       "      <th>c</th>\n",
       "      <th>rho</th>\n",
       "      <th>CV[I]</th>\n",
       "      <th>CV[S]</th>\n",
       "      <th>SCV[I]</th>\n",
       "      <th>SCV[S]</th>\n",
       "      <th>E[N_Q]</th>\n",
       "      <th>E[N]</th>\n",
       "      <th>E[W]</th>\n",
       "      <th>E[V]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.01</td>\n",
       "      <td>0.0125</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>1</td>\n",
       "      <td>0.25</td>\n",
       "      <td>2.000</td>\n",
       "      <td>2.800</td>\n",
       "      <td>200.0</td>\n",
       "      <td>280.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.01</td>\n",
       "      <td>0.0125</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.6</td>\n",
       "      <td>1</td>\n",
       "      <td>0.36</td>\n",
       "      <td>2.176</td>\n",
       "      <td>2.976</td>\n",
       "      <td>217.6</td>\n",
       "      <td>297.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.01</td>\n",
       "      <td>0.0125</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.7</td>\n",
       "      <td>1</td>\n",
       "      <td>0.49</td>\n",
       "      <td>2.384</td>\n",
       "      <td>3.184</td>\n",
       "      <td>238.4</td>\n",
       "      <td>318.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.01</td>\n",
       "      <td>0.0125</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1</td>\n",
       "      <td>0.64</td>\n",
       "      <td>2.624</td>\n",
       "      <td>3.424</td>\n",
       "      <td>262.4</td>\n",
       "      <td>342.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.01</td>\n",
       "      <td>0.0125</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.9</td>\n",
       "      <td>1</td>\n",
       "      <td>0.81</td>\n",
       "      <td>2.896</td>\n",
       "      <td>3.696</td>\n",
       "      <td>289.6</td>\n",
       "      <td>369.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.01</td>\n",
       "      <td>0.0125</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1.00</td>\n",
       "      <td>3.200</td>\n",
       "      <td>4.000</td>\n",
       "      <td>320.0</td>\n",
       "      <td>400.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.01</td>\n",
       "      <td>0.0125</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1</td>\n",
       "      <td>1.21</td>\n",
       "      <td>3.536</td>\n",
       "      <td>4.336</td>\n",
       "      <td>353.6</td>\n",
       "      <td>433.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.01</td>\n",
       "      <td>0.0125</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.2</td>\n",
       "      <td>1</td>\n",
       "      <td>1.44</td>\n",
       "      <td>3.904</td>\n",
       "      <td>4.704</td>\n",
       "      <td>390.4</td>\n",
       "      <td>470.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.01</td>\n",
       "      <td>0.0125</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.3</td>\n",
       "      <td>1</td>\n",
       "      <td>1.69</td>\n",
       "      <td>4.304</td>\n",
       "      <td>5.104</td>\n",
       "      <td>430.4</td>\n",
       "      <td>510.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.01</td>\n",
       "      <td>0.0125</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>1</td>\n",
       "      <td>1.96</td>\n",
       "      <td>4.736</td>\n",
       "      <td>5.536</td>\n",
       "      <td>473.6</td>\n",
       "      <td>553.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.01</td>\n",
       "      <td>0.0125</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.5</td>\n",
       "      <td>1</td>\n",
       "      <td>2.25</td>\n",
       "      <td>5.200</td>\n",
       "      <td>6.000</td>\n",
       "      <td>520.0</td>\n",
       "      <td>600.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "    lambda      mu    a  c  rho  CV[I]  CV[S]  SCV[I]  SCV[S]  E[N_Q]   E[N]  \\\n",
       "0     0.01  0.0125  0.8  1  0.8    1.0    0.5       1    0.25   2.000  2.800   \n",
       "1     0.01  0.0125  0.8  1  0.8    1.0    0.6       1    0.36   2.176  2.976   \n",
       "2     0.01  0.0125  0.8  1  0.8    1.0    0.7       1    0.49   2.384  3.184   \n",
       "3     0.01  0.0125  0.8  1  0.8    1.0    0.8       1    0.64   2.624  3.424   \n",
       "4     0.01  0.0125  0.8  1  0.8    1.0    0.9       1    0.81   2.896  3.696   \n",
       "5     0.01  0.0125  0.8  1  0.8    1.0    1.0       1    1.00   3.200  4.000   \n",
       "6     0.01  0.0125  0.8  1  0.8    1.0    1.1       1    1.21   3.536  4.336   \n",
       "7     0.01  0.0125  0.8  1  0.8    1.0    1.2       1    1.44   3.904  4.704   \n",
       "8     0.01  0.0125  0.8  1  0.8    1.0    1.3       1    1.69   4.304  5.104   \n",
       "9     0.01  0.0125  0.8  1  0.8    1.0    1.4       1    1.96   4.736  5.536   \n",
       "10    0.01  0.0125  0.8  1  0.8    1.0    1.5       1    2.25   5.200  6.000   \n",
       "\n",
       "     E[W]   E[V]  \n",
       "0   200.0  280.0  \n",
       "1   217.6  297.6  \n",
       "2   238.4  318.4  \n",
       "3   262.4  342.4  \n",
       "4   289.6  369.6  \n",
       "5   320.0  400.0  \n",
       "6   353.6  433.6  \n",
       "7   390.4  470.4  \n",
       "8   430.4  510.4  \n",
       "9   473.6  553.6  \n",
       "10  520.0  600.0  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Arrival rate\n",
    "l = 1 / 100\n",
    "\n",
    "# Service rate\n",
    "mu = 1 / 80\n",
    "\n",
    "# Number of operators\n",
    "c = 1\n",
    "\n",
    "# Coefficient of variation of the inter-arrival times\n",
    "cv_i = 1  # exponential distribution has always cv_i = 1\n",
    "\n",
    "# Coefficient of variation of the service times range\n",
    "cv_s_range = [i / 10 for i in range(5, 16)]\n",
    "\n",
    "# Allen Cunneen results for different values of cv_s\n",
    "results = ac_approx_table([(l, mu, c, cv_i**2, cv_s**2) for cv_s in cv_s_range])\n",
    "\n",
    "# Display results table\n",
    "results"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Optional: Interactive diagram mode\n",
    "# Run \"pip install ipympl\" first\n",
    "# %matplotlib ipympl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Allen Cunneen model at coefficients of variation of the service times')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1152x648 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(16, 9))\n",
    "\n",
    "ax.plot(results[\"CV[S]\"], results[\"E[W]\"], 'r')\n",
    "ax.tick_params(axis='y', labelcolor='r')\n",
    "ax.set_xlabel(\"Coefficient of variation of the service times CV[S]\")\n",
    "ax.set_ylabel(\"E[W]\", color='r')\n",
    "ax.xaxis.set_major_formatter(percent_formater)\n",
    "\n",
    "ax = ax.twinx()\n",
    "ax.plot(results[\"CV[S]\"], results[\"rho\"], 'g')\n",
    "ax.tick_params(axis='y', labelcolor='g')\n",
    "ax.set_ylabel(\"Utilization $\\\\rho$\", color='g')\n",
    "ax.yaxis.set_major_formatter(percent_formater)\n",
    "\n",
    "ax.set_title(\"Allen Cunneen model at different coefficients of variation of the service times\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mean waiting time is increasing at increasing variations of the service times (at fixed utilization)."
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "50353b016531f30848d54ac32cae776bc182aa8d1967b29e76fe0c76333975c2"
  },
  "kernelspec": {
   "display_name": "Python 3.9.7 64-bit",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}