{ "cells": [ { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "Asiakaspalvelupisteen jonon muodostukseen vaikuttaa kaksi tekijää:\n", "\n", "● Asiakkaiden saapuminen palvelupisteeseen.\n", "\n", "● Palvelun kesto.\n", "\n", "Asiakkaiden saapumista voidaan monissa tapauksissa mallintaa onnistuneesti eksponentiaalisella jakaumalla. Tällöin tarvitaan tieto siitä, kuinka paljon asiakkaita saapuu keskimäärin tarkasteltavassa aikavälissä.\n", "\n", "Palvelun kestoa voidaan monissa tapauksissa mallintaa onnistuneesti normaalijakaumalla. Tällöin tarvitaan palveluajan keskiarvo ja keskihajonta." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "KESKIARVO_ASIAKAS = 5 #asiakkaiden väli minuutteina\n", "KESKIARVO_PALVELU = 2 #minuuttia\n", "KESKIHAJONTA_PALVELU = 0.5\n", "ASIAKKAITA = 1000" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", " | seuraava_asiakas | \n", "saapumis_aika | \n", "palvelun_kesto | \n", "palvelun_aloitus | \n", "palvelun_lopetus | \n", "jonotus | \n", "kokonais_aika | \n", "
---|---|---|---|---|---|---|---|
0 | \n", "4.559935 | \n", "4.559935 | \n", "1.970475 | \n", "4.559935 | \n", "6.530409 | \n", "0.000000 | \n", "1.970475 | \n", "
1 | \n", "7.170075 | \n", "11.730009 | \n", "1.750567 | \n", "11.730009 | \n", "13.480576 | \n", "0.000000 | \n", "1.750567 | \n", "
2 | \n", "2.125404 | \n", "13.855414 | \n", "2.863559 | \n", "13.855414 | \n", "16.718973 | \n", "0.000000 | \n", "2.863559 | \n", "
3 | \n", "14.641087 | \n", "28.496501 | \n", "2.058293 | \n", "28.496501 | \n", "30.554794 | \n", "0.000000 | \n", "2.058293 | \n", "
4 | \n", "3.523031 | \n", "32.019532 | \n", "2.096044 | \n", "32.019532 | \n", "34.115576 | \n", "0.000000 | \n", "2.096044 | \n", "
5 | \n", "0.716269 | \n", "32.735801 | \n", "1.767038 | \n", "34.115576 | \n", "35.882613 | \n", "1.379775 | \n", "3.146812 | \n", "
6 | \n", "5.303635 | \n", "38.039436 | \n", "1.753736 | \n", "38.039436 | \n", "39.793172 | \n", "0.000000 | \n", "1.753736 | \n", "
7 | \n", "3.239577 | \n", "41.279013 | \n", "2.786673 | \n", "41.279013 | \n", "44.065686 | \n", "0.000000 | \n", "2.786673 | \n", "
8 | \n", "12.890109 | \n", "54.169123 | \n", "2.685727 | \n", "54.169123 | \n", "56.854850 | \n", "0.000000 | \n", "2.685727 | \n", "
9 | \n", "3.937489 | \n", "58.106611 | \n", "2.637670 | \n", "58.106611 | \n", "60.744281 | \n", "0.000000 | \n", "2.637670 | \n", "
10 | \n", "6.887558 | \n", "64.994169 | \n", "0.923588 | \n", "64.994169 | \n", "65.917757 | \n", "0.000000 | \n", "0.923588 | \n", "
11 | \n", "16.207476 | \n", "81.201645 | \n", "2.562661 | \n", "81.201645 | \n", "83.764306 | \n", "0.000000 | \n", "2.562661 | \n", "
12 | \n", "12.078720 | \n", "93.280365 | \n", "2.098805 | \n", "93.280365 | \n", "95.379171 | \n", "0.000000 | \n", "2.098805 | \n", "
13 | \n", "8.308787 | \n", "101.589152 | \n", "2.684418 | \n", "101.589152 | \n", "104.273571 | \n", "0.000000 | \n", "2.684418 | \n", "
14 | \n", "0.101702 | \n", "101.690854 | \n", "1.657744 | \n", "104.273571 | \n", "105.931314 | \n", "2.582716 | \n", "4.240460 | \n", "
15 | \n", "3.926541 | \n", "105.617396 | \n", "1.943939 | \n", "105.931314 | \n", "107.875253 | \n", "0.313919 | \n", "2.257858 | \n", "
16 | \n", "9.675890 | \n", "115.293285 | \n", "1.975953 | \n", "115.293285 | \n", "117.269238 | \n", "0.000000 | \n", "1.975953 | \n", "
17 | \n", "3.250767 | \n", "118.544052 | \n", "1.941022 | \n", "118.544052 | \n", "120.485074 | \n", "0.000000 | \n", "1.941022 | \n", "
18 | \n", "8.665241 | \n", "127.209293 | \n", "1.322388 | \n", "127.209293 | \n", "128.531681 | \n", "0.000000 | \n", "1.322388 | \n", "
19 | \n", "5.277812 | \n", "132.487105 | \n", "2.391272 | \n", "132.487105 | \n", "134.878377 | \n", "0.000000 | \n", "2.391272 | \n", "
20 | \n", "5.039594 | \n", "137.526699 | \n", "2.022646 | \n", "137.526699 | \n", "139.549345 | \n", "0.000000 | \n", "2.022646 | \n", "
21 | \n", "3.944090 | \n", "141.470789 | \n", "1.160414 | \n", "141.470789 | \n", "142.631204 | \n", "0.000000 | \n", "1.160414 | \n", "
22 | \n", "4.229980 | \n", "145.700769 | \n", "1.353824 | \n", "145.700769 | \n", "147.054593 | \n", "0.000000 | \n", "1.353824 | \n", "
23 | \n", "0.925151 | \n", "146.625920 | \n", "2.340526 | \n", "147.054593 | \n", "149.395120 | \n", "0.428673 | \n", "2.769200 | \n", "
24 | \n", "2.306118 | \n", "148.932038 | \n", "1.134182 | \n", "149.395120 | \n", "150.529301 | \n", "0.463082 | \n", "1.597263 | \n", "
25 | \n", "0.299353 | \n", "149.231391 | \n", "2.667097 | \n", "150.529301 | \n", "153.196398 | \n", "1.297910 | \n", "3.965007 | \n", "
26 | \n", "0.225853 | \n", "149.457244 | \n", "2.107281 | \n", "153.196398 | \n", "155.303679 | \n", "3.739154 | \n", "5.846434 | \n", "
27 | \n", "0.847106 | \n", "150.304351 | \n", "2.081570 | \n", "155.303679 | \n", "157.385249 | \n", "4.999328 | \n", "7.080898 | \n", "
28 | \n", "10.233806 | \n", "160.538156 | \n", "1.934800 | \n", "160.538156 | \n", "162.472957 | \n", "0.000000 | \n", "1.934800 | \n", "
29 | \n", "0.616380 | \n", "161.154536 | \n", "2.640670 | \n", "162.472957 | \n", "165.113627 | \n", "1.318420 | \n", "3.959090 | \n", "
... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "
970 | \n", "7.102974 | \n", "4964.656230 | \n", "2.428474 | \n", "4964.656230 | \n", "4967.084704 | \n", "0.000000 | \n", "2.428474 | \n", "
971 | \n", "0.138565 | \n", "4964.794795 | \n", "2.744121 | \n", "4967.084704 | \n", "4969.828825 | \n", "2.289909 | \n", "5.034030 | \n", "
972 | \n", "3.011328 | \n", "4967.806123 | \n", "2.080804 | \n", "4969.828825 | \n", "4971.909629 | \n", "2.022702 | \n", "4.103506 | \n", "
973 | \n", "16.542482 | \n", "4984.348605 | \n", "1.713767 | \n", "4984.348605 | \n", "4986.062372 | \n", "0.000000 | \n", "1.713767 | \n", "
974 | \n", "3.610126 | \n", "4987.958731 | \n", "1.303616 | \n", "4987.958731 | \n", "4989.262347 | \n", "0.000000 | \n", "1.303616 | \n", "
975 | \n", "0.523492 | \n", "4988.482223 | \n", "1.887123 | \n", "4989.262347 | \n", "4991.149470 | \n", "0.780124 | \n", "2.667247 | \n", "
976 | \n", "5.928719 | \n", "4994.410942 | \n", "1.555162 | \n", "4994.410942 | \n", "4995.966104 | \n", "0.000000 | \n", "1.555162 | \n", "
977 | \n", "17.111571 | \n", "5011.522513 | \n", "1.243976 | \n", "5011.522513 | \n", "5012.766489 | \n", "0.000000 | \n", "1.243976 | \n", "
978 | \n", "7.167799 | \n", "5018.690312 | \n", "1.888549 | \n", "5018.690312 | \n", "5020.578861 | \n", "0.000000 | \n", "1.888549 | \n", "
979 | \n", "3.154027 | \n", "5021.844339 | \n", "1.980424 | \n", "5021.844339 | \n", "5023.824763 | \n", "0.000000 | \n", "1.980424 | \n", "
980 | \n", "10.400865 | \n", "5032.245204 | \n", "2.148101 | \n", "5032.245204 | \n", "5034.393305 | \n", "0.000000 | \n", "2.148101 | \n", "
981 | \n", "0.204477 | \n", "5032.449681 | \n", "2.214375 | \n", "5034.393305 | \n", "5036.607680 | \n", "1.943624 | \n", "4.157999 | \n", "
982 | \n", "1.020533 | \n", "5033.470214 | \n", "1.290481 | \n", "5036.607680 | \n", "5037.898161 | \n", "3.137466 | \n", "4.427948 | \n", "
983 | \n", "1.700163 | \n", "5035.170377 | \n", "2.548396 | \n", "5037.898161 | \n", "5040.446557 | \n", "2.727784 | \n", "5.276180 | \n", "
984 | \n", "4.861728 | \n", "5040.032105 | \n", "1.653602 | \n", "5040.446557 | \n", "5042.100159 | \n", "0.414452 | \n", "2.068054 | \n", "
985 | \n", "4.912337 | \n", "5044.944442 | \n", "1.842041 | \n", "5044.944442 | \n", "5046.786483 | \n", "0.000000 | \n", "1.842041 | \n", "
986 | \n", "6.195677 | \n", "5051.140119 | \n", "2.012578 | \n", "5051.140119 | \n", "5053.152697 | \n", "0.000000 | \n", "2.012578 | \n", "
987 | \n", "4.246305 | \n", "5055.386424 | \n", "3.641099 | \n", "5055.386424 | \n", "5059.027523 | \n", "0.000000 | \n", "3.641099 | \n", "
988 | \n", "0.351196 | \n", "5055.737619 | \n", "2.405110 | \n", "5059.027523 | \n", "5061.432633 | \n", "3.289904 | \n", "5.695014 | \n", "
989 | \n", "6.389141 | \n", "5062.126760 | \n", "1.465794 | \n", "5062.126760 | \n", "5063.592554 | \n", "0.000000 | \n", "1.465794 | \n", "
990 | \n", "0.332100 | \n", "5062.458860 | \n", "1.876872 | \n", "5063.592554 | \n", "5065.469426 | \n", "1.133695 | \n", "3.010566 | \n", "
991 | \n", "4.218615 | \n", "5066.677475 | \n", "2.249977 | \n", "5066.677475 | \n", "5068.927451 | \n", "0.000000 | \n", "2.249977 | \n", "
992 | \n", "44.402375 | \n", "5111.079850 | \n", "1.959461 | \n", "5111.079850 | \n", "5113.039311 | \n", "0.000000 | \n", "1.959461 | \n", "
993 | \n", "11.676260 | \n", "5122.756110 | \n", "1.253784 | \n", "5122.756110 | \n", "5124.009894 | \n", "0.000000 | \n", "1.253784 | \n", "
994 | \n", "2.951483 | \n", "5125.707593 | \n", "2.392283 | \n", "5125.707593 | \n", "5128.099877 | \n", "0.000000 | \n", "2.392283 | \n", "
995 | \n", "1.418355 | \n", "5127.125948 | \n", "2.397739 | \n", "5128.099877 | \n", "5130.497616 | \n", "0.973929 | \n", "3.371668 | \n", "
996 | \n", "1.772244 | \n", "5128.898192 | \n", "1.610387 | \n", "5130.497616 | \n", "5132.108002 | \n", "1.599424 | \n", "3.209810 | \n", "
997 | \n", "0.498313 | \n", "5129.396505 | \n", "2.140898 | \n", "5132.108002 | \n", "5134.248901 | \n", "2.711497 | \n", "4.852395 | \n", "
998 | \n", "6.645040 | \n", "5136.041545 | \n", "2.460836 | \n", "5136.041545 | \n", "5138.502382 | \n", "0.000000 | \n", "2.460836 | \n", "
999 | \n", "10.574862 | \n", "5146.616407 | \n", "2.721448 | \n", "5146.616407 | \n", "5149.337855 | \n", "0.000000 | \n", "2.721448 | \n", "
1000 rows × 7 columns
\n", "\n", " | jonotus | \n", "kokonais_aika | \n", "
---|---|---|
count | \n", "1000.000000 | \n", "1000.000000 | \n", "
mean | \n", "0.719808 | \n", "2.700317 | \n", "
std | \n", "1.245056 | \n", "1.332166 | \n", "
min | \n", "0.000000 | \n", "0.668122 | \n", "
25% | \n", "0.000000 | \n", "1.858800 | \n", "
50% | \n", "0.000000 | \n", "2.314290 | \n", "
75% | \n", "1.122697 | \n", "3.137720 | \n", "
max | \n", "10.021099 | \n", "11.976497 | \n", "