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geraintpalmergeraintpalmer
committedJul 12, 2016
Add notebooks for priority queues and baulking functions
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‎Baulking Functions - I.ipynb

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Baulking Functions - I"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### This notebook will illustrate a simple deterministic example, designed to show the difference between baulking and queueing capacities"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"import ciw"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"def my_baulking_function(n):\n",
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" if n < 3:\n",
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" return 0.0\n",
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" return 1.0"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"params_dict = {\n",
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" 'Arrival_distributions': [['Deterministic', 5.0], ['Deterministic', 23.0]],\n",
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" 'Service_distributions': [['Deterministic', 21.0], ['Deterministic', 1.5]],\n",
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" 'Transition_matrices': [[0.0, 0.0], [1.0, 0.0]],\n",
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" 'Number_of_servers': [1, 1],\n",
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" 'Baulking_functions': [my_baulking_function, None]\n",
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"}"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Now if we run this to time t=48, we will get the following chain of events:"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"| Time | Queue Node 1 | In Service Node 1 | Queue Node 2 | In Service Node 2 | Customer Finished a Service | Baulked Customers |\n",
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"|------|--------------|-------------------|--------------|-------------------|-----------------------------|-------------------|\n",
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"| 0 | | | | | | |\n",
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"| 5 | | 1 | | | | |\n",
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"| 10 | 2 | 1 | | | | |\n",
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"| 15 | 3, 2 | 1 | | | | |\n",
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"| 20 | 3, 2 | 1 | | | | 4 |\n",
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"| 23 | 3, 2 | 1 | | 5 | | 4 |\n",
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"| 24.5 | 5, 3, 2 | 1 | | | 5 | 4 |\n",
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"| 25 | 5, 3, 2 | 1 | | | 5 | 4, 6 |\n",
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"| 26 | 5, 3 | 2 | | | 5, 1 | 4, 6 |\n",
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"| 30 | 5, 3 | 2 | | | 5, 1 | 4, 6, 7 |\n",
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"| 35 | 5, 3 | 2 | | | 5, 1 | 4, 6, 7, 8 |\n",
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"| 40 | 5, 3 | 2 | | | 5, 1 | 4, 6, 7, 8, 9 |\n",
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"| 45 | 5, 3 | 2 | | | 5, 1 | 4, 6, 7, 8, 9, 10 |\n",
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"| 46 | 5, 3 | 2 | | 11 | 5, 1 | 4, 6, 7, 8, 9, 10 |\n",
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"| 47 | 5 | 3 | | 11 | 5, 1, 2 | 4, 6, 7, 8, 9, 10 |\n",
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"| 47.5 | 11, 5 | 3 | | | 5, 1, 2, 11 | 4, 6, 7, 8, 9, 10 |\n",
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"| 48 | | | | | | |"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### We would therefore expect the following results:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"expected_baulking_dictionary = {1:{0:[20.0, 25.0, 30.0, 35.0, 40.0, 45.0]}, 2:{0:[]}}\n",
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"expected_ids_of_completed_customers = set([5, 1, 2, 11])\n",
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"expected_waits_of_completed_customers = set([0.0, 0.0, 0.0, 16])\n",
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"expected_arrival_dates_of_completed_customers = set([5.0, 10.0, 23.0, 46.0])\n",
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"expected_service_start_dates_of_completed_customers = set([5.0, 23.0, 26.0, 46.0])\n",
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"expected_service_end_dates_of_completed_customers = set([24.5, 26.0, 47.0, 47.5])"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Let's check:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"N = ciw.create_network(params_dict)\n",
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"Q = ciw.Simulation(N)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"Q.simulate_until_max_time(48)\n",
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"recs = Q.get_all_records()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"True"
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]
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},
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"execution_count": 7,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"Q.baulked_dict == expected_baulking_dictionary"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"True"
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]
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},
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"execution_count": 8,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"set([r.id_number for r in recs]) == expected_ids_of_completed_customers"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"True"
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]
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},
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"execution_count": 9,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"set([r.waiting_time for r in recs]) == expected_waits_of_completed_customers"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"True"
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]
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},
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"execution_count": 10,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"set([r.arrival_date for r in recs]) == expected_arrival_dates_of_completed_customers"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"True"
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]
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},
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"execution_count": 11,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"set([r.service_start_date for r in recs]) == expected_service_start_dates_of_completed_customers"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"True"
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]
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},
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"execution_count": 12,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"set([r.service_end_date for r in recs]) == expected_service_end_dates_of_completed_customers"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.5.1"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}

‎Baulking Functions - II.ipynb

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Baulking Functions - II"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### This example is more involved that Baulking Functions - I, and shows the flexibility of the baulking functions functionality"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"import ciw\n",
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"import math"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"def baulking_function_A(n):\n",
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" if n < 3:\n",
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" return 0.0\n",
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" if n < 7:\n",
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" return 0.5\n",
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" if n < 11:\n",
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" return 1.0"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"def baulking_function_B(n):\n",
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" return 1.0 - (1.0 / n)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"def baulking_function_C(n):\n",
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" if n < 10:\n",
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" return math.exp(-n)\n",
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" return 0.0"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Baulking functions can be as complicated as you like, as long as they take in a positive integer (number of customers at the node), and return a probability (a float between 0.0 and 1.0).\n",
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"### This example will show how different baulking functions can be assigned to different node - customer class pairs. We will even combine baulking with queueing capacities. Networks can be as complicated as you like... we could even have added priorities too, but let's stick with baulking and queue capacities for now."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"params_dict = {\n",
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" 'Arrival_distributions': {'Class 0': [['Exponential', 8.0], ['Exponential', 4.0]],\n",
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" 'Class 1': [['Exponential', 6.0], ['Exponential', 5.0]]},\n",
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" 'Service_distributions': {'Class 0': [['Exponential', 10.0], ['Exponential', 7.0]],\n",
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" 'Class 1': [['Exponential', 6.0], ['Exponential', 4.0]]},\n",
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" 'Transition_matrices': {'Class 0': [[0.0, 0.3], [0.3, 0.3]],\n",
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" 'Class 1': [[0.2, 0.1], [0.0, 0.2]]},\n",
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" 'Number_of_servers': [2, 2],\n",
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" 'Baulking_functions': {'Class 0': [baulking_function_A, None],\n",
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" 'Class 1': [baulking_function_B, baulking_function_C]}\n",
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"}"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"N = ciw.create_network(params_dict)\n",
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"Q = ciw.Simulation(N)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 17,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"ename": "ZeroDivisionError",
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"evalue": "float division by zero",
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"output_type": "error",
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"traceback": [
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"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
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"\u001b[0;31mZeroDivisionError\u001b[0m Traceback (most recent call last)",
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"\u001b[0;32m<ipython-input-17-d373bed3e80b>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mQ\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msimulate_until_max_time\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
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"\u001b[0;32m/Users/geraintianpalmer/Documents/Ciw/ciw/simulation.py\u001b[0m in \u001b[0;36msimulate_until_max_time\u001b[0;34m(self, max_simulation_time)\u001b[0m\n\u001b[1;32m 245\u001b[0m \u001b[0mcurrent_time\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnext_active_node\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnext_event_date\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 246\u001b[0m \u001b[0;32mwhile\u001b[0m \u001b[0mcurrent_time\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0mmax_simulation_time\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 247\u001b[0;31m \u001b[0mnext_active_node\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhave_event\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 248\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mnode\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtransitive_nodes\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 249\u001b[0m \u001b[0mnode\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mupdate_next_event_date\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcurrent_time\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;32m/Users/geraintianpalmer/Documents/Ciw/ciw/arrival_node.py\u001b[0m in \u001b[0;36mhave_event\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 71\u001b[0m priority_class)\n\u001b[1;32m 72\u001b[0m \u001b[0mnext_node\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msimulation\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtransitive_nodes\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnext_node\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 73\u001b[0;31m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrelease_individual\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnext_node\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnext_individual\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 74\u001b[0m self.event_dates_dict[self.next_node][\n\u001b[1;32m 75\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnext_class\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mincrement_time\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;32m/Users/geraintianpalmer/Documents/Ciw/ciw/arrival_node.py\u001b[0m in \u001b[0;36mrelease_individual\u001b[0;34m(self, next_node, next_individual)\u001b[0m\n\u001b[1;32m 123\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrecord_rejection\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnext_node\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 124\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 125\u001b[0;31m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdecide_baulk\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnext_node\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnext_individual\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 126\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 127\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0msend_individual\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnext_node\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnext_individual\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;32m/Users/geraintianpalmer/Documents/Ciw/ciw/arrival_node.py\u001b[0m in \u001b[0;36mdecide_baulk\u001b[0;34m(self, next_node, next_individual)\u001b[0m\n\u001b[1;32m 40\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 41\u001b[0m \u001b[0mrnd_num\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrandom\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 42\u001b[0;31m \u001b[0;32mif\u001b[0m \u001b[0mrnd_num\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0mnext_node\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbaulking_functions\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnext_class\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnext_node\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnumber_of_individuals\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 43\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrecord_baulk\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnext_node\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 44\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;32m<ipython-input-3-9946f13f7a01>\u001b[0m in \u001b[0;36mbaulking_function_B\u001b[0;34m(n)\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mbaulking_function_B\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0;36m1.0\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m1.0\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
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"\u001b[0;31mZeroDivisionError\u001b[0m: float division by zero"
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]
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}
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],
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"source": [
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"Q.simulate_until_max_time(100)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 18,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"0.006737946999085467"
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]
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},
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"execution_count": 18,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"math.exp(-5)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"source": []
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"codemirror_mode": {
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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}
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},
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"nbformat_minor": 0
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}

‎Priority Queues.ipynb

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Priority Queues"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Import Ciw"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"import ciw\n",
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"from random import seed\n",
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"from numpy import mean, random"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### We will simulate an M/M/1 queue with two priority classes. The two classes will have the same service rate (1.0) but different arrival rates (0.2 and 0.6 respectively). The first class will have higher priority than the second. Let's build the parameters dictionary:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"params_dict = {\n",
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" 'Arrival_distributions': {'Class 0': [['Exponential', 0.2]],\n",
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" 'Class 1': [['Exponential', 0.6]]},\n",
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" 'Service_distributions': {'Class 0': [['Exponential', 1.0]],\n",
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" 'Class 1': [['Exponential', 1.0]]},\n",
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" 'Transition_matrices': {'Class 0': [[0.0]],\n",
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" 'Class 1': [[0.0]]},\n",
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" 'Number_of_servers': [1],\n",
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" 'Priority_classes': {'Class 0': 0,\n",
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" 'Class 1': 1}\n",
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"\n",
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" }"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### This corresponds to Example 4.3 in http://www.win.tue.nl/~iadan/que/h4.pdf, we shall compare the results obtained analytically to the results obtained using Ciw. Analytically we expect the average time in the system for those in Class 0 to be 2.0, and for those in Class 1 to be 6.0."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### We shall run 150 trials, running each trial for a maximum time of 500, and a warm-up time of 100 will be used."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"throughput_class0 = []\n",
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"throughput_class1 = []"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"random.seed(20)\n",
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"seed(20)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"for iteration in range(150):\n",
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" N = ciw.create_network(params_dict)\n",
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" Q = ciw.Simulation(N)\n",
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" Q.simulate_until_max_time(500)\n",
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" recs = Q.get_all_records()\n",
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" throughput_class0.append(mean([r.waiting_time + r.service_time for r in recs if r.customer_class==0 if r.arrival_date > 100]))\n",
111+
" throughput_class1.append(mean([r.waiting_time + r.service_time for r in recs if r.customer_class==1 if r.arrival_date > 100]))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"1.98638760088\n"
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]
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}
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],
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"source": [
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"print(mean(throughput_class0))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"5.91798349036\n"
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]
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}
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],
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"source": [
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"print(mean(throughput_class1))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.5.1"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
183+
}

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