|
| 1 | +{ |
| 2 | + "cells": [ |
| 3 | + { |
| 4 | + "cell_type": "markdown", |
| 5 | + "metadata": {}, |
| 6 | + "source": [ |
| 7 | + "# Baulking Functions - I" |
| 8 | + ] |
| 9 | + }, |
| 10 | + { |
| 11 | + "cell_type": "markdown", |
| 12 | + "metadata": {}, |
| 13 | + "source": [ |
| 14 | + "### This notebook will illustrate a simple deterministic example, designed to show the difference between baulking and queueing capacities" |
| 15 | + ] |
| 16 | + }, |
| 17 | + { |
| 18 | + "cell_type": "code", |
| 19 | + "execution_count": 1, |
| 20 | + "metadata": { |
| 21 | + "collapsed": true |
| 22 | + }, |
| 23 | + "outputs": [], |
| 24 | + "source": [ |
| 25 | + "import ciw" |
| 26 | + ] |
| 27 | + }, |
| 28 | + { |
| 29 | + "cell_type": "code", |
| 30 | + "execution_count": 2, |
| 31 | + "metadata": { |
| 32 | + "collapsed": true |
| 33 | + }, |
| 34 | + "outputs": [], |
| 35 | + "source": [ |
| 36 | + "def my_baulking_function(n):\n", |
| 37 | + " if n < 3:\n", |
| 38 | + " return 0.0\n", |
| 39 | + " return 1.0" |
| 40 | + ] |
| 41 | + }, |
| 42 | + { |
| 43 | + "cell_type": "code", |
| 44 | + "execution_count": 3, |
| 45 | + "metadata": { |
| 46 | + "collapsed": true |
| 47 | + }, |
| 48 | + "outputs": [], |
| 49 | + "source": [ |
| 50 | + "params_dict = {\n", |
| 51 | + " 'Arrival_distributions': [['Deterministic', 5.0], ['Deterministic', 23.0]],\n", |
| 52 | + " 'Service_distributions': [['Deterministic', 21.0], ['Deterministic', 1.5]],\n", |
| 53 | + " 'Transition_matrices': [[0.0, 0.0], [1.0, 0.0]],\n", |
| 54 | + " 'Number_of_servers': [1, 1],\n", |
| 55 | + " 'Baulking_functions': [my_baulking_function, None]\n", |
| 56 | + "}" |
| 57 | + ] |
| 58 | + }, |
| 59 | + { |
| 60 | + "cell_type": "markdown", |
| 61 | + "metadata": {}, |
| 62 | + "source": [ |
| 63 | + "### Now if we run this to time t=48, we will get the following chain of events:" |
| 64 | + ] |
| 65 | + }, |
| 66 | + { |
| 67 | + "cell_type": "markdown", |
| 68 | + "metadata": {}, |
| 69 | + "source": [ |
| 70 | + "| Time | Queue Node 1 | In Service Node 1 | Queue Node 2 | In Service Node 2 | Customer Finished a Service | Baulked Customers |\n", |
| 71 | + "|------|--------------|-------------------|--------------|-------------------|-----------------------------|-------------------|\n", |
| 72 | + "| 0 | | | | | | |\n", |
| 73 | + "| 5 | | 1 | | | | |\n", |
| 74 | + "| 10 | 2 | 1 | | | | |\n", |
| 75 | + "| 15 | 3, 2 | 1 | | | | |\n", |
| 76 | + "| 20 | 3, 2 | 1 | | | | 4 |\n", |
| 77 | + "| 23 | 3, 2 | 1 | | 5 | | 4 |\n", |
| 78 | + "| 24.5 | 5, 3, 2 | 1 | | | 5 | 4 |\n", |
| 79 | + "| 25 | 5, 3, 2 | 1 | | | 5 | 4, 6 |\n", |
| 80 | + "| 26 | 5, 3 | 2 | | | 5, 1 | 4, 6 |\n", |
| 81 | + "| 30 | 5, 3 | 2 | | | 5, 1 | 4, 6, 7 |\n", |
| 82 | + "| 35 | 5, 3 | 2 | | | 5, 1 | 4, 6, 7, 8 |\n", |
| 83 | + "| 40 | 5, 3 | 2 | | | 5, 1 | 4, 6, 7, 8, 9 |\n", |
| 84 | + "| 45 | 5, 3 | 2 | | | 5, 1 | 4, 6, 7, 8, 9, 10 |\n", |
| 85 | + "| 46 | 5, 3 | 2 | | 11 | 5, 1 | 4, 6, 7, 8, 9, 10 |\n", |
| 86 | + "| 47 | 5 | 3 | | 11 | 5, 1, 2 | 4, 6, 7, 8, 9, 10 |\n", |
| 87 | + "| 47.5 | 11, 5 | 3 | | | 5, 1, 2, 11 | 4, 6, 7, 8, 9, 10 |\n", |
| 88 | + "| 48 | | | | | | |" |
| 89 | + ] |
| 90 | + }, |
| 91 | + { |
| 92 | + "cell_type": "markdown", |
| 93 | + "metadata": {}, |
| 94 | + "source": [ |
| 95 | + "### We would therefore expect the following results:" |
| 96 | + ] |
| 97 | + }, |
| 98 | + { |
| 99 | + "cell_type": "code", |
| 100 | + "execution_count": 4, |
| 101 | + "metadata": { |
| 102 | + "collapsed": true |
| 103 | + }, |
| 104 | + "outputs": [], |
| 105 | + "source": [ |
| 106 | + "expected_baulking_dictionary = {1:{0:[20.0, 25.0, 30.0, 35.0, 40.0, 45.0]}, 2:{0:[]}}\n", |
| 107 | + "expected_ids_of_completed_customers = set([5, 1, 2, 11])\n", |
| 108 | + "expected_waits_of_completed_customers = set([0.0, 0.0, 0.0, 16])\n", |
| 109 | + "expected_arrival_dates_of_completed_customers = set([5.0, 10.0, 23.0, 46.0])\n", |
| 110 | + "expected_service_start_dates_of_completed_customers = set([5.0, 23.0, 26.0, 46.0])\n", |
| 111 | + "expected_service_end_dates_of_completed_customers = set([24.5, 26.0, 47.0, 47.5])" |
| 112 | + ] |
| 113 | + }, |
| 114 | + { |
| 115 | + "cell_type": "markdown", |
| 116 | + "metadata": {}, |
| 117 | + "source": [ |
| 118 | + "### Let's check:" |
| 119 | + ] |
| 120 | + }, |
| 121 | + { |
| 122 | + "cell_type": "code", |
| 123 | + "execution_count": 5, |
| 124 | + "metadata": { |
| 125 | + "collapsed": false |
| 126 | + }, |
| 127 | + "outputs": [], |
| 128 | + "source": [ |
| 129 | + "N = ciw.create_network(params_dict)\n", |
| 130 | + "Q = ciw.Simulation(N)" |
| 131 | + ] |
| 132 | + }, |
| 133 | + { |
| 134 | + "cell_type": "code", |
| 135 | + "execution_count": 6, |
| 136 | + "metadata": { |
| 137 | + "collapsed": true |
| 138 | + }, |
| 139 | + "outputs": [], |
| 140 | + "source": [ |
| 141 | + "Q.simulate_until_max_time(48)\n", |
| 142 | + "recs = Q.get_all_records()" |
| 143 | + ] |
| 144 | + }, |
| 145 | + { |
| 146 | + "cell_type": "code", |
| 147 | + "execution_count": 7, |
| 148 | + "metadata": { |
| 149 | + "collapsed": false |
| 150 | + }, |
| 151 | + "outputs": [ |
| 152 | + { |
| 153 | + "data": { |
| 154 | + "text/plain": [ |
| 155 | + "True" |
| 156 | + ] |
| 157 | + }, |
| 158 | + "execution_count": 7, |
| 159 | + "metadata": {}, |
| 160 | + "output_type": "execute_result" |
| 161 | + } |
| 162 | + ], |
| 163 | + "source": [ |
| 164 | + "Q.baulked_dict == expected_baulking_dictionary" |
| 165 | + ] |
| 166 | + }, |
| 167 | + { |
| 168 | + "cell_type": "code", |
| 169 | + "execution_count": 8, |
| 170 | + "metadata": { |
| 171 | + "collapsed": false |
| 172 | + }, |
| 173 | + "outputs": [ |
| 174 | + { |
| 175 | + "data": { |
| 176 | + "text/plain": [ |
| 177 | + "True" |
| 178 | + ] |
| 179 | + }, |
| 180 | + "execution_count": 8, |
| 181 | + "metadata": {}, |
| 182 | + "output_type": "execute_result" |
| 183 | + } |
| 184 | + ], |
| 185 | + "source": [ |
| 186 | + "set([r.id_number for r in recs]) == expected_ids_of_completed_customers" |
| 187 | + ] |
| 188 | + }, |
| 189 | + { |
| 190 | + "cell_type": "code", |
| 191 | + "execution_count": 9, |
| 192 | + "metadata": { |
| 193 | + "collapsed": false |
| 194 | + }, |
| 195 | + "outputs": [ |
| 196 | + { |
| 197 | + "data": { |
| 198 | + "text/plain": [ |
| 199 | + "True" |
| 200 | + ] |
| 201 | + }, |
| 202 | + "execution_count": 9, |
| 203 | + "metadata": {}, |
| 204 | + "output_type": "execute_result" |
| 205 | + } |
| 206 | + ], |
| 207 | + "source": [ |
| 208 | + "set([r.waiting_time for r in recs]) == expected_waits_of_completed_customers" |
| 209 | + ] |
| 210 | + }, |
| 211 | + { |
| 212 | + "cell_type": "code", |
| 213 | + "execution_count": 10, |
| 214 | + "metadata": { |
| 215 | + "collapsed": false |
| 216 | + }, |
| 217 | + "outputs": [ |
| 218 | + { |
| 219 | + "data": { |
| 220 | + "text/plain": [ |
| 221 | + "True" |
| 222 | + ] |
| 223 | + }, |
| 224 | + "execution_count": 10, |
| 225 | + "metadata": {}, |
| 226 | + "output_type": "execute_result" |
| 227 | + } |
| 228 | + ], |
| 229 | + "source": [ |
| 230 | + "set([r.arrival_date for r in recs]) == expected_arrival_dates_of_completed_customers" |
| 231 | + ] |
| 232 | + }, |
| 233 | + { |
| 234 | + "cell_type": "code", |
| 235 | + "execution_count": 11, |
| 236 | + "metadata": { |
| 237 | + "collapsed": false |
| 238 | + }, |
| 239 | + "outputs": [ |
| 240 | + { |
| 241 | + "data": { |
| 242 | + "text/plain": [ |
| 243 | + "True" |
| 244 | + ] |
| 245 | + }, |
| 246 | + "execution_count": 11, |
| 247 | + "metadata": {}, |
| 248 | + "output_type": "execute_result" |
| 249 | + } |
| 250 | + ], |
| 251 | + "source": [ |
| 252 | + "set([r.service_start_date for r in recs]) == expected_service_start_dates_of_completed_customers" |
| 253 | + ] |
| 254 | + }, |
| 255 | + { |
| 256 | + "cell_type": "code", |
| 257 | + "execution_count": 12, |
| 258 | + "metadata": { |
| 259 | + "collapsed": false |
| 260 | + }, |
| 261 | + "outputs": [ |
| 262 | + { |
| 263 | + "data": { |
| 264 | + "text/plain": [ |
| 265 | + "True" |
| 266 | + ] |
| 267 | + }, |
| 268 | + "execution_count": 12, |
| 269 | + "metadata": {}, |
| 270 | + "output_type": "execute_result" |
| 271 | + } |
| 272 | + ], |
| 273 | + "source": [ |
| 274 | + "set([r.service_end_date for r in recs]) == expected_service_end_dates_of_completed_customers" |
| 275 | + ] |
| 276 | + }, |
| 277 | + { |
| 278 | + "cell_type": "code", |
| 279 | + "execution_count": null, |
| 280 | + "metadata": { |
| 281 | + "collapsed": true |
| 282 | + }, |
| 283 | + "outputs": [], |
| 284 | + "source": [] |
| 285 | + } |
| 286 | + ], |
| 287 | + "metadata": { |
| 288 | + "kernelspec": { |
| 289 | + "display_name": "Python 3", |
| 290 | + "language": "python", |
| 291 | + "name": "python3" |
| 292 | + }, |
| 293 | + "language_info": { |
| 294 | + "codemirror_mode": { |
| 295 | + "name": "ipython", |
| 296 | + "version": 3 |
| 297 | + }, |
| 298 | + "file_extension": ".py", |
| 299 | + "mimetype": "text/x-python", |
| 300 | + "name": "python", |
| 301 | + "nbconvert_exporter": "python", |
| 302 | + "pygments_lexer": "ipython3", |
| 303 | + "version": "3.5.1" |
| 304 | + } |
| 305 | + }, |
| 306 | + "nbformat": 4, |
| 307 | + "nbformat_minor": 0 |
| 308 | +} |
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