example_analytic_erlang_c.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Erlang C (M/M/c model)\n",
    "\n",
    "This is an implementation of the default Erlang C model (exponential inter-arrival and service times, `c` operators)."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importing modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Erlang module\n",
    "from queuesim.analytic import erlang_c_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 &rho;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "    }\n",
       "\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<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>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>0.016393</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>9.836066</td>\n",
       "      <td>10</td>\n",
       "      <td>0.983607</td>\n",
       "      <td>56.454792</td>\n",
       "      <td>66.290858</td>\n",
       "      <td>3443.742325</td>\n",
       "      <td>4043.742325</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.016129</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>9.677419</td>\n",
       "      <td>10</td>\n",
       "      <td>0.967742</td>\n",
       "      <td>26.564755</td>\n",
       "      <td>36.242174</td>\n",
       "      <td>1647.014815</td>\n",
       "      <td>2247.014815</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.015873</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>9.523810</td>\n",
       "      <td>10</td>\n",
       "      <td>0.952381</td>\n",
       "      <td>16.669938</td>\n",
       "      <td>26.193748</td>\n",
       "      <td>1050.206120</td>\n",
       "      <td>1650.206120</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.015625</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>9.375000</td>\n",
       "      <td>10</td>\n",
       "      <td>0.937500</td>\n",
       "      <td>11.770591</td>\n",
       "      <td>21.145591</td>\n",
       "      <td>753.317839</td>\n",
       "      <td>1353.317839</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.015385</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>9.230769</td>\n",
       "      <td>10</td>\n",
       "      <td>0.923077</td>\n",
       "      <td>8.866947</td>\n",
       "      <td>18.097717</td>\n",
       "      <td>576.351580</td>\n",
       "      <td>1176.351580</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.015152</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>9.090909</td>\n",
       "      <td>10</td>\n",
       "      <td>0.909091</td>\n",
       "      <td>6.959227</td>\n",
       "      <td>16.050136</td>\n",
       "      <td>459.308957</td>\n",
       "      <td>1059.308957</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.014925</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>8.955224</td>\n",
       "      <td>10</td>\n",
       "      <td>0.895522</td>\n",
       "      <td>5.619064</td>\n",
       "      <td>14.574288</td>\n",
       "      <td>376.477299</td>\n",
       "      <td>976.477299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.014706</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>8.823529</td>\n",
       "      <td>10</td>\n",
       "      <td>0.882353</td>\n",
       "      <td>4.632369</td>\n",
       "      <td>13.455898</td>\n",
       "      <td>315.001078</td>\n",
       "      <td>915.001078</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.014493</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>8.695652</td>\n",
       "      <td>10</td>\n",
       "      <td>0.869565</td>\n",
       "      <td>3.880276</td>\n",
       "      <td>12.575928</td>\n",
       "      <td>267.739047</td>\n",
       "      <td>867.739047</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.014286</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>8.571429</td>\n",
       "      <td>10</td>\n",
       "      <td>0.857143</td>\n",
       "      <td>3.291530</td>\n",
       "      <td>11.862959</td>\n",
       "      <td>230.407098</td>\n",
       "      <td>830.407098</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.014085</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>8.450704</td>\n",
       "      <td>10</td>\n",
       "      <td>0.845070</td>\n",
       "      <td>2.820839</td>\n",
       "      <td>11.271543</td>\n",
       "      <td>200.279553</td>\n",
       "      <td>800.279553</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.013889</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>8.333333</td>\n",
       "      <td>10</td>\n",
       "      <td>0.833333</td>\n",
       "      <td>2.438053</td>\n",
       "      <td>10.771386</td>\n",
       "      <td>175.539819</td>\n",
       "      <td>775.539819</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.013699</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>8.219178</td>\n",
       "      <td>10</td>\n",
       "      <td>0.821918</td>\n",
       "      <td>2.122339</td>\n",
       "      <td>10.341517</td>\n",
       "      <td>154.930726</td>\n",
       "      <td>754.930726</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.013514</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>8.108108</td>\n",
       "      <td>10</td>\n",
       "      <td>0.810811</td>\n",
       "      <td>1.858848</td>\n",
       "      <td>9.966956</td>\n",
       "      <td>137.554734</td>\n",
       "      <td>737.554734</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.013333</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>10</td>\n",
       "      <td>0.800000</td>\n",
       "      <td>1.636721</td>\n",
       "      <td>9.636721</td>\n",
       "      <td>122.754045</td>\n",
       "      <td>722.754045</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.013158</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>7.894737</td>\n",
       "      <td>10</td>\n",
       "      <td>0.789474</td>\n",
       "      <td>1.447838</td>\n",
       "      <td>9.342575</td>\n",
       "      <td>110.035679</td>\n",
       "      <td>710.035679</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.012987</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>7.792208</td>\n",
       "      <td>10</td>\n",
       "      <td>0.779221</td>\n",
       "      <td>1.286013</td>\n",
       "      <td>9.078221</td>\n",
       "      <td>99.022991</td>\n",
       "      <td>699.022991</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.012821</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>7.692308</td>\n",
       "      <td>10</td>\n",
       "      <td>0.769231</td>\n",
       "      <td>1.146453</td>\n",
       "      <td>8.838761</td>\n",
       "      <td>89.423350</td>\n",
       "      <td>689.423350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.012658</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>7.594937</td>\n",
       "      <td>10</td>\n",
       "      <td>0.759494</td>\n",
       "      <td>1.025393</td>\n",
       "      <td>8.620329</td>\n",
       "      <td>81.006021</td>\n",
       "      <td>681.006021</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.012500</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>7.500000</td>\n",
       "      <td>10</td>\n",
       "      <td>0.750000</td>\n",
       "      <td>0.919834</td>\n",
       "      <td>8.419834</td>\n",
       "      <td>73.586688</td>\n",
       "      <td>673.586688</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.012346</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>7.407407</td>\n",
       "      <td>10</td>\n",
       "      <td>0.740741</td>\n",
       "      <td>0.827363</td>\n",
       "      <td>8.234770</td>\n",
       "      <td>67.016393</td>\n",
       "      <td>667.016393</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.012195</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>7.317073</td>\n",
       "      <td>10</td>\n",
       "      <td>0.731707</td>\n",
       "      <td>0.746018</td>\n",
       "      <td>8.063091</td>\n",
       "      <td>61.173496</td>\n",
       "      <td>661.173496</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0.012048</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>7.228916</td>\n",
       "      <td>10</td>\n",
       "      <td>0.722892</td>\n",
       "      <td>0.674189</td>\n",
       "      <td>7.903105</td>\n",
       "      <td>55.957727</td>\n",
       "      <td>655.957727</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.011905</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>7.142857</td>\n",
       "      <td>10</td>\n",
       "      <td>0.714286</td>\n",
       "      <td>0.610544</td>\n",
       "      <td>7.753402</td>\n",
       "      <td>51.285732</td>\n",
       "      <td>651.285732</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      lambda        mu         a   c       rho     E[N_Q]       E[N]  \\\n",
       "0   0.016393  0.001667  9.836066  10  0.983607  56.454792  66.290858   \n",
       "1   0.016129  0.001667  9.677419  10  0.967742  26.564755  36.242174   \n",
       "2   0.015873  0.001667  9.523810  10  0.952381  16.669938  26.193748   \n",
       "3   0.015625  0.001667  9.375000  10  0.937500  11.770591  21.145591   \n",
       "4   0.015385  0.001667  9.230769  10  0.923077   8.866947  18.097717   \n",
       "5   0.015152  0.001667  9.090909  10  0.909091   6.959227  16.050136   \n",
       "6   0.014925  0.001667  8.955224  10  0.895522   5.619064  14.574288   \n",
       "7   0.014706  0.001667  8.823529  10  0.882353   4.632369  13.455898   \n",
       "8   0.014493  0.001667  8.695652  10  0.869565   3.880276  12.575928   \n",
       "9   0.014286  0.001667  8.571429  10  0.857143   3.291530  11.862959   \n",
       "10  0.014085  0.001667  8.450704  10  0.845070   2.820839  11.271543   \n",
       "11  0.013889  0.001667  8.333333  10  0.833333   2.438053  10.771386   \n",
       "12  0.013699  0.001667  8.219178  10  0.821918   2.122339  10.341517   \n",
       "13  0.013514  0.001667  8.108108  10  0.810811   1.858848   9.966956   \n",
       "14  0.013333  0.001667  8.000000  10  0.800000   1.636721   9.636721   \n",
       "15  0.013158  0.001667  7.894737  10  0.789474   1.447838   9.342575   \n",
       "16  0.012987  0.001667  7.792208  10  0.779221   1.286013   9.078221   \n",
       "17  0.012821  0.001667  7.692308  10  0.769231   1.146453   8.838761   \n",
       "18  0.012658  0.001667  7.594937  10  0.759494   1.025393   8.620329   \n",
       "19  0.012500  0.001667  7.500000  10  0.750000   0.919834   8.419834   \n",
       "20  0.012346  0.001667  7.407407  10  0.740741   0.827363   8.234770   \n",
       "21  0.012195  0.001667  7.317073  10  0.731707   0.746018   8.063091   \n",
       "22  0.012048  0.001667  7.228916  10  0.722892   0.674189   7.903105   \n",
       "23  0.011905  0.001667  7.142857  10  0.714286   0.610544   7.753402   \n",
       "\n",
       "           E[W]         E[V]  \n",
       "0   3443.742325  4043.742325  \n",
       "1   1647.014815  2247.014815  \n",
       "2   1050.206120  1650.206120  \n",
       "3    753.317839  1353.317839  \n",
       "4    576.351580  1176.351580  \n",
       "5    459.308957  1059.308957  \n",
       "6    376.477299   976.477299  \n",
       "7    315.001078   915.001078  \n",
       "8    267.739047   867.739047  \n",
       "9    230.407098   830.407098  \n",
       "10   200.279553   800.279553  \n",
       "11   175.539819   775.539819  \n",
       "12   154.930726   754.930726  \n",
       "13   137.554734   737.554734  \n",
       "14   122.754045   722.754045  \n",
       "15   110.035679   710.035679  \n",
       "16    99.022991   699.022991  \n",
       "17    89.423350   689.423350  \n",
       "18    81.006021   681.006021  \n",
       "19    73.586688   673.586688  \n",
       "20    67.016393   667.016393  \n",
       "21    61.173496   661.173496  \n",
       "22    55.957727   655.957727  \n",
       "23    51.285732   651.285732  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Arrival rate range\n",
    "l_range = [1 / mean_i for mean_i in range(61, 85)]\n",
    "\n",
    "# Service rate\n",
    "mu = 1 / 600\n",
    "\n",
    "# Number of operators\n",
    "c = 10\n",
    "\n",
    "# Erlang C results for different values of lambda\n",
    "results = erlang_c_table([(l, mu, c) for l in l_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, 'Erlang C model at different utilizations')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(16, 9))\n",
    "\n",
    "ax.plot(results[\"rho\"], results[\"E[W]\"], 'r')\n",
    "ax.tick_params(axis='y', labelcolor='r')\n",
    "ax.set_xlabel(\"Utilization $\\\\rho$\")\n",
    "ax.set_ylabel(\"E[W]\", color='r')\n",
    "ax.xaxis.set_major_formatter(percent_formater)\n",
    "\n",
    "ax.set_title(\"Erlang C model at different utilizations\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mean waiting time as a function of c\n",
    "\n",
    "* Now the utilization will be fixed at &rho;=80%.\n",
    "* The service rate will also stay fixed at &mu;=1/600.\n",
    "* The arrival rate will be adjusted when changing c to keep &rho; fixed: &lambda;=&rho;*&mu;*c."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<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>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>0.001333</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1</td>\n",
       "      <td>0.8</td>\n",
       "      <td>3.200000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>2400.000000</td>\n",
       "      <td>3000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.002667</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>1.6</td>\n",
       "      <td>2</td>\n",
       "      <td>0.8</td>\n",
       "      <td>2.844444</td>\n",
       "      <td>4.444444</td>\n",
       "      <td>1066.666667</td>\n",
       "      <td>1666.666667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.004000</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>2.4</td>\n",
       "      <td>3</td>\n",
       "      <td>0.8</td>\n",
       "      <td>2.588764</td>\n",
       "      <td>4.988764</td>\n",
       "      <td>647.191011</td>\n",
       "      <td>1247.191011</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.005333</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>3.2</td>\n",
       "      <td>4</td>\n",
       "      <td>0.8</td>\n",
       "      <td>2.385730</td>\n",
       "      <td>5.585730</td>\n",
       "      <td>447.324354</td>\n",
       "      <td>1047.324354</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.006667</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5</td>\n",
       "      <td>0.8</td>\n",
       "      <td>2.216450</td>\n",
       "      <td>6.216450</td>\n",
       "      <td>332.467532</td>\n",
       "      <td>932.467532</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.008000</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>4.8</td>\n",
       "      <td>6</td>\n",
       "      <td>0.8</td>\n",
       "      <td>2.071088</td>\n",
       "      <td>6.871088</td>\n",
       "      <td>258.886000</td>\n",
       "      <td>858.886000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.009333</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>5.6</td>\n",
       "      <td>7</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.943750</td>\n",
       "      <td>7.543750</td>\n",
       "      <td>208.258976</td>\n",
       "      <td>808.258976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.010667</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>6.4</td>\n",
       "      <td>8</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.830580</td>\n",
       "      <td>8.230580</td>\n",
       "      <td>171.616847</td>\n",
       "      <td>771.616847</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.012000</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>7.2</td>\n",
       "      <td>9</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.728889</td>\n",
       "      <td>8.928889</td>\n",
       "      <td>144.074099</td>\n",
       "      <td>744.074099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.013333</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>8.0</td>\n",
       "      <td>10</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.636721</td>\n",
       "      <td>9.636721</td>\n",
       "      <td>122.754045</td>\n",
       "      <td>722.754045</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.014667</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>8.8</td>\n",
       "      <td>11</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.552595</td>\n",
       "      <td>10.352595</td>\n",
       "      <td>105.858784</td>\n",
       "      <td>705.858784</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.016000</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>9.6</td>\n",
       "      <td>12</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.475366</td>\n",
       "      <td>11.075366</td>\n",
       "      <td>92.210378</td>\n",
       "      <td>692.210378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.017333</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>10.4</td>\n",
       "      <td>13</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.404121</td>\n",
       "      <td>11.804121</td>\n",
       "      <td>81.006959</td>\n",
       "      <td>681.006959</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.018667</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>11.2</td>\n",
       "      <td>14</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.338121</td>\n",
       "      <td>12.538121</td>\n",
       "      <td>71.685076</td>\n",
       "      <td>671.685076</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.020000</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>12.0</td>\n",
       "      <td>15</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.276762</td>\n",
       "      <td>13.276762</td>\n",
       "      <td>63.838085</td>\n",
       "      <td>663.838085</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.021333</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>12.8</td>\n",
       "      <td>16</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.219536</td>\n",
       "      <td>14.019536</td>\n",
       "      <td>57.165734</td>\n",
       "      <td>657.165734</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.022667</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>13.6</td>\n",
       "      <td>17</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.166017</td>\n",
       "      <td>14.766017</td>\n",
       "      <td>51.441911</td>\n",
       "      <td>651.441911</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.024000</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>14.4</td>\n",
       "      <td>18</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.115841</td>\n",
       "      <td>15.515841</td>\n",
       "      <td>46.493378</td>\n",
       "      <td>646.493378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.025333</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>15.2</td>\n",
       "      <td>19</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.068696</td>\n",
       "      <td>16.268696</td>\n",
       "      <td>42.185379</td>\n",
       "      <td>642.185379</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.026667</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>16.0</td>\n",
       "      <td>20</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.024311</td>\n",
       "      <td>17.024311</td>\n",
       "      <td>38.411669</td>\n",
       "      <td>638.411669</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.028000</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>16.8</td>\n",
       "      <td>21</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.982449</td>\n",
       "      <td>17.782449</td>\n",
       "      <td>35.087467</td>\n",
       "      <td>635.087467</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.029333</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>17.6</td>\n",
       "      <td>22</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.942902</td>\n",
       "      <td>18.542902</td>\n",
       "      <td>32.144385</td>\n",
       "      <td>632.144385</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0.030667</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>18.4</td>\n",
       "      <td>23</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.905486</td>\n",
       "      <td>19.305486</td>\n",
       "      <td>29.526717</td>\n",
       "      <td>629.526717</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.032000</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>19.2</td>\n",
       "      <td>24</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.870038</td>\n",
       "      <td>20.070038</td>\n",
       "      <td>27.188679</td>\n",
       "      <td>627.188679</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.033333</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>20.0</td>\n",
       "      <td>25</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.836411</td>\n",
       "      <td>20.836411</td>\n",
       "      <td>25.092339</td>\n",
       "      <td>625.092339</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      lambda        mu     a   c  rho    E[N_Q]       E[N]         E[W]  \\\n",
       "0   0.001333  0.001667   0.8   1  0.8  3.200000   4.000000  2400.000000   \n",
       "1   0.002667  0.001667   1.6   2  0.8  2.844444   4.444444  1066.666667   \n",
       "2   0.004000  0.001667   2.4   3  0.8  2.588764   4.988764   647.191011   \n",
       "3   0.005333  0.001667   3.2   4  0.8  2.385730   5.585730   447.324354   \n",
       "4   0.006667  0.001667   4.0   5  0.8  2.216450   6.216450   332.467532   \n",
       "5   0.008000  0.001667   4.8   6  0.8  2.071088   6.871088   258.886000   \n",
       "6   0.009333  0.001667   5.6   7  0.8  1.943750   7.543750   208.258976   \n",
       "7   0.010667  0.001667   6.4   8  0.8  1.830580   8.230580   171.616847   \n",
       "8   0.012000  0.001667   7.2   9  0.8  1.728889   8.928889   144.074099   \n",
       "9   0.013333  0.001667   8.0  10  0.8  1.636721   9.636721   122.754045   \n",
       "10  0.014667  0.001667   8.8  11  0.8  1.552595  10.352595   105.858784   \n",
       "11  0.016000  0.001667   9.6  12  0.8  1.475366  11.075366    92.210378   \n",
       "12  0.017333  0.001667  10.4  13  0.8  1.404121  11.804121    81.006959   \n",
       "13  0.018667  0.001667  11.2  14  0.8  1.338121  12.538121    71.685076   \n",
       "14  0.020000  0.001667  12.0  15  0.8  1.276762  13.276762    63.838085   \n",
       "15  0.021333  0.001667  12.8  16  0.8  1.219536  14.019536    57.165734   \n",
       "16  0.022667  0.001667  13.6  17  0.8  1.166017  14.766017    51.441911   \n",
       "17  0.024000  0.001667  14.4  18  0.8  1.115841  15.515841    46.493378   \n",
       "18  0.025333  0.001667  15.2  19  0.8  1.068696  16.268696    42.185379   \n",
       "19  0.026667  0.001667  16.0  20  0.8  1.024311  17.024311    38.411669   \n",
       "20  0.028000  0.001667  16.8  21  0.8  0.982449  17.782449    35.087467   \n",
       "21  0.029333  0.001667  17.6  22  0.8  0.942902  18.542902    32.144385   \n",
       "22  0.030667  0.001667  18.4  23  0.8  0.905486  19.305486    29.526717   \n",
       "23  0.032000  0.001667  19.2  24  0.8  0.870038  20.070038    27.188679   \n",
       "24  0.033333  0.001667  20.0  25  0.8  0.836411  20.836411    25.092339   \n",
       "\n",
       "           E[V]  \n",
       "0   3000.000000  \n",
       "1   1666.666667  \n",
       "2   1247.191011  \n",
       "3   1047.324354  \n",
       "4    932.467532  \n",
       "5    858.886000  \n",
       "6    808.258976  \n",
       "7    771.616847  \n",
       "8    744.074099  \n",
       "9    722.754045  \n",
       "10   705.858784  \n",
       "11   692.210378  \n",
       "12   681.006959  \n",
       "13   671.685076  \n",
       "14   663.838085  \n",
       "15   657.165734  \n",
       "16   651.441911  \n",
       "17   646.493378  \n",
       "18   642.185379  \n",
       "19   638.411669  \n",
       "20   635.087467  \n",
       "21   632.144385  \n",
       "22   629.526717  \n",
       "23   627.188679  \n",
       "24   625.092339  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fixed utilization\n",
    "rho = 0.8\n",
    "\n",
    "# Service rate\n",
    "mu = 1 / 600\n",
    "\n",
    "# Number of operators range\n",
    "c_range = range(1, 26)\n",
    "\n",
    "# Erlang C results for different values of c\n",
    "results = erlang_c_table([(rho * mu * c, mu, c) for c in c_range])\n",
    "\n",
    "# Display results table\n",
    "results"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Erlang C model at different numbers of operators (and the same utilization in all cases)')"
      ]
     },
     "execution_count": 6,
     "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[\"c\"], results[\"E[W]\"], 'r')\n",
    "ax.tick_params(axis='y', labelcolor='r')\n",
    "ax.set_xlabel(\"Number of operators $c$\")\n",
    "ax.set_ylabel(\"E[W]\", color='r')\n",
    "\n",
    "ax = ax.twinx()\n",
    "ax.plot(results[\"c\"], 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(\"Erlang C model at different numbers of operators (and the same utilization in all cases)\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On a larger system (with more operators) the mean waiting time will be lower (at the same utilization) (Economy of scale)."
   ]
  }
 ],
 "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
}