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@nickstanisha
Last active February 7, 2016 21:09
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Solution and extension of this FiveThirtyEight riddle: http://fivethirtyeight.com/features/how-many-cars-will-get-stuck-in-traffic/
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from __future__ import division\n",
"import pickle\n",
"import numpy as np"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Problem Solution\n",
"Writing out all permutations for small values of N, you will notice a pattern that the Nth solution always seems to be 1/N greater than the N-1th solution. Below, this suspicion is confirmed by rolling the dice for 10^6 trials and counting the number of groups for different values of N."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def get_expected_values(N):\n",
" \"\"\" Returns expected number of groups for the number of \n",
" cars up to and including N\n",
" \"\"\"\n",
" exp = np.zeros(N+1)\n",
" for i in xrange(N+1):\n",
" if i < 2:\n",
" exp[i] = i\n",
" else:\n",
" exp[i] = exp[i-1] + (1/i)\n",
" return exp\n",
"\n",
"expected_values = get_expected_values(1000)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def get_num_groups(speeds):\n",
" \"\"\" Given an iterable object of floats representing speeds,\n",
" return the number of groups that will form.\n",
" \n",
" NOTE: speeds[0] == the front-most car\n",
" \"\"\"\n",
" if len(speeds) == 0:\n",
" return 0\n",
" num_groups = 0\n",
" slowest = speeds[0]\n",
" for car in speeds:\n",
" if car <= slowest:\n",
" num_groups += 1\n",
" slowest = car\n",
" return num_groups\n",
"\n",
"def avg_groups(N, n_trials=1000000):\n",
" convergence = np.zeros(n_trials)\n",
" \n",
" for i in xrange(n_trials):\n",
" speeds = np.random.rand(N)\n",
" convergence[i] = get_num_groups(speeds)\n",
" \n",
" return np.cumsum(convergence)/(np.arange(n_trials) + 1)\n",
"\n",
"def final_speeds(speeds):\n",
" if len(speeds) == 0:\n",
" return speeds\n",
" slowest = speeds[0]\n",
" for i in xrange(len(speeds)):\n",
" if speeds[i] > slowest:\n",
" speeds[i] = slowest\n",
" else:\n",
" slowest = speeds[i]\n",
" return speeds\n",
"\n",
"def speed_trials(N, n_trials=1000):\n",
" all_speeds = np.empty((n_trials, N))\n",
" for i in xrange(n_trials):\n",
" speeds = np.random.rand(N)\n",
" all_speeds[i] = final_speeds(speeds)\n",
" return all_speeds"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"try:\n",
" with open('one_lane_avg_groups.p', 'rb') as infile:\n",
" data = pickle.load(infile)\n",
" with open('one_lane_speeds.p', 'rb') as infile:\n",
" one_lane_speeds = pickle.load(infile)\n",
"except:\n",
" data = dict()\n",
" all_speeds = dict()\n",
" for N in [4, 10, 30, 100, 300, 1000]:\n",
" data[N] = avg_groups(N)\n",
" all_speeds[N] = speed_trials(N)\n",
" with open('one_lane_avg_groups.p', 'wb') as outfile:\n",
" pickle.dump(data, outfile)\n",
" with open('one_lane_speeds.p', 'wb') as outfile:\n",
" pickle.dump(all_speeds, outfile)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import matplotlib\n",
"from matplotlib import pyplot as plt\n",
"import seaborn as sns\n",
"\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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4hCQ1oTmSxtEcuU7myHUyT66VOXKdzEtNje1zPnl5hE4IIYQYoiTICyGEEEOUBHkhhBBi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\nLDo6ZztTWfItI/+qRv6NRQV0kf8bkYgOYjDnIYi5dCXWcLosXHJdRp3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LSlk2p4jWrkC6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o8AmFkD8IY8xzWi79+zjfKyGG85d8W4577p2EY6BpM8c7CH23fs552rF4feEa8/meLBfQepjEU5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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x13df98d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig,ax = plt.subplots(figsize=(8,8))\n",
"\n",
"for N in sorted(data.keys(), key=lambda x: -x):\n",
" ax.plot(data[N]/expected_values[N],label='N={}'.format(N))\n",
"\n",
"ax.legend(loc='upper right')\n",
"ax.set_xscale('log')\n",
"ax.grid(True)\n",
"ax.set_ylabel('Empirical/Expected Average Number of Groups')\n",
"ax.set_xlabel('Number of Simulation Iterations')\n",
"ax.set_title('Convergence of Average Number of Groups')\n",
"\n",
"fig.savefig('convergence.png', bbox_inches='tight')"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"# Extension: Left Lane, Average Speed and Groups\n",
"Let's extend this problem by adding another lane designated for faster drivers. The model for the fast lane works like this\n",
"\n",
"* There is a minimum speed you must be travelling to qualify for the left lane\n",
"* You may enter the left lane only if the person in front of you is travelling slower than you are\n",
"* You cannot leave the left lane once you've chosen to move there"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def split_speeds(speeds, ll_minimum):\n",
" l_speed = list()\n",
" r_speed = list()\n",
" \n",
" slowest = speeds[0]\n",
" for car in speeds:\n",
" if car > slowest:\n",
" if car > ll_minimum:\n",
" l_speed.append(car)\n",
" else:\n",
" r_speed.append(car)\n",
" else:\n",
" slowest = car\n",
" r_speed.append(car)\n",
" return (l_speed, r_speed)\n",
"\n",
"def two_lane_speed_trials(ll_minimum, N=100, n_trials=100):\n",
" all_ll_speeds = [list() for _ in xrange(n_trials)]\n",
" all_rl_speeds = [list() for _ in xrange(n_trials)]\n",
" \n",
" for i in xrange(n_trials):\n",
" speeds = np.random.rand(N)\n",
" l_speed, r_speed = split_speeds(speeds, ll_minimum)\n",
" all_ll_speeds[i] = final_speeds(l_speed)\n",
" all_rl_speeds[i] = final_speeds(r_speed)\n",
" return (all_ll_speeds, all_rl_speeds)\n",
"\n",
"def two_lane_avg_groups(ll_minimum, N=100, n_trials=10000):\n",
" convergence = np.zeros(n_trials)\n",
" \n",
" for i in xrange(n_trials):\n",
" speeds = np.random.rand(N)\n",
" l_speed, r_speed = split_speeds(speeds, ll_minimum)\n",
" convergence[i] = get_num_groups(l_speed) + get_num_groups(r_speed)\n",
" \n",
" return np.cumsum(convergence)/(np.arange(n_trials) + 1)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"try:\n",
" with open('two_lane_avg_groups.p', 'rb') as infile:\n",
" two_lane_group_data = pickle.load(infile)\n",
" with open('two_lane_speeds.p', 'rb') as infile:\n",
" two_lane_speeds = pickle.load(infile)\n",
"except:\n",
" two_lane_group_data = dict()\n",
" two_lane_speeds = dict()\n",
" for ll_minimum in np.linspace(0.05, 0.95, 19):\n",
" two_lane_group_data[ll_minimum] = two_lane_avg_groups(ll_minimum)\n",
" two_lane_speeds[ll_minimum] = two_lane_speed_trials(ll_minimum)\n",
" with open('two_lane_avg_groups.p', 'wb') as outfile:\n",
" pickle.dump(two_lane_group_data, outfile)\n",
" with open('two_lane_speeds.p', 'wb') as outfile:\n",
" pickle.dump(two_lane_speeds, outfile)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Mathematical Justification of Left-Lane Behavior\n",
"We know that for an infinite number of cars in a single lane, the average speed will approach the slowest speed in the pack. So what is the probability that that speed is very small?\n",
"\n",
"It is clear that the probability that the minimum value is small is 1 minus the probability that none of the speeds are small.\n",
"\n",
"$$Pr\\{min(X_1, X_2, ..., X_N) < \\epsilon\\} = 1 - Pr\\{X_1 > \\epsilon \\cap X_2 > \\epsilon\\ \\cap\\ ... \\cap\\ X_N > \\epsilon\\}$$\n",
"\n",
"Since X1 ... XN are identically distributed, this probability is\n",
"\n",
"$$ Pr\\{min(X_1, X_2, ..., X_N) < \\epsilon\\} = 1 - (Pr\\{X > \\epsilon\\})^N $$\n",
"\n",
"which approaches 1 as N approaches infinity. In other words, the average speed of a singe lane WILL converge to the minimum speed for that lane, which is why it's important to specify a minimum speed for the left lane.\n",
"\n",
"Since this relationship holds for both lanes, we would expect the average speed overall to equal the weighted average of both lane's minimum speeds\n",
"\n",
"$$ v_{avg} = Pr\\{X > v_{min}\\}\\times v_{min} + Pr\\{X < v_{min}\\}\\times 0 = Pr\\{X > v_{min}\\}\\times v_{min} $$\n",
"\n",
"where v_min is the minimum left-lane velocity. This behavior is confirmed below for a unifomly distributed X and multiple values of N."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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atGhR7LQGDRpw6qmnJqysyZMnHzKMOLhR8UaPHs3zzz+f0CrOa6+9lsmTJzN8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\nmszMzMzMzFpw0mRmZmZmZtbC/wFtknjJdmjXRgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x13df90f0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import operator\n",
"\n",
"def flatten(listoflists):\n",
" return [item for sublist in listoflists for item in sublist]\n",
"\n",
"x, left_avg, right_avg, avg = list(), list(), list(), list()\n",
"for key in sorted(two_lane_speeds):\n",
" x.append(key)\n",
" \n",
" l_speeds, r_speeds = [flatten(i) for i in two_lane_speeds[key]]\n",
" left_avg.append(np.mean(l_speeds))\n",
" right_avg.append(np.mean(r_speeds))\n",
" avg.append(np.mean(l_speeds+r_speeds))\n",
"\n",
"fig,ax = plt.subplots(figsize=(14, 7))\n",
"\n",
"ax.set_axis_bgcolor('white')\n",
"ax.plot(x, right_avg, '--', color=(0.4, 0.4, 0.4))\n",
"ax.plot(x, left_avg, '--', color=(0.4, 0.4, 0.4))\n",
"ax.fill_between(x, right_avg, left_avg, color='gray', alpha=0.05)\n",
"ax.scatter(x, avg, label='All Travellers', color=(0.7, 0.7, 0.7), s=80)\n",
"index, value = max(enumerate(avg), key=operator.itemgetter(1))\n",
"ax.scatter(x[index], value, label='Maximum', color='red', s=80)\n",
"\n",
"ax.legend(loc='upper left', fontsize=12)\n",
"ax.text(0.45, 0.65, 'Fast Lane Travellers', fontsize=12)\n",
"ax.text(0.525, 0.08, 'Slow Lane Travellers', fontsize=12)\n",
"ax.grid(color=(0.9, 0.9, 0.9))\n",
"ax.set_ylim([-0.01, 1.001])\n",
"ax.set_xlim([0, 1.001])\n",
"\n",
"for tick in ax.xaxis.get_major_ticks() + ax.yaxis.get_major_ticks():\n",
" tick.label.set_fontsize(12)\n",
"\n",
"ax.set_ylabel('Average Vehicle Speed', fontsize=14, fontweight='bold')\n",
"ax.set_xlabel('Minimum Left-Lane Travelling Speed', fontsize=14, fontweight='bold')\n",
"ax.set_title('Average Vehicle Speed vs Minimum Left-Lane Travelling Speed (N=100)', fontsize=14, fontweight='bold')\n",
"\n",
"fig.savefig('n100_speed.png', bbox_inches='tight')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Confirmation of this behavior for several values of N"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"x = sorted(two_lane_speeds.keys())\n",
"avg_speed_data = dict()\n",
"\n",
"for N in [10000] + sorted(data.keys(), key=lambda x: -x):\n",
" avg_speed_data[N] = list()\n",
" for ll_minimum in sorted(two_lane_speeds.keys()):\n",
" l_speed, r_speed = [flatten(i) for i in two_lane_speed_trials(ll_minimum, N=N)]\n",
" avg_speed_data[N].append(np.mean(l_speed + r_speed))"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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DSCzk3GZnGNR21f5jgcnufhpBRnRYwjHx+vRvEazuGZ+MdUi4vxy4PvxZTiIY0tBRBCCc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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x22051d68>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.cm as cm\n",
"\n",
"colors = cm.rainbow(np.linspace(0, 1, len(avg_speed_data)+1))\n",
"\n",
"fig, ax = plt.subplots(figsize=(9,6))\n",
"\n",
"ax.plot(x, [(1-i)*i for i in x], '--', label='Expected (Large N)', color=(0.4, 0.4, 0.4))\n",
"for N, c in zip(sorted(data.keys()) + [10000], colors):\n",
" ax.scatter(x, avg_speed_data[N], color=c, label='N={}'.format(N))\n",
"\n",
"\n",
"#ax.legend(loc='upper right', ncol=2, bbox_to_anchor=(1.01, 1.01))\n",
"ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))\n",
"ax.set_axis_bgcolor((0.98, 0.98, 0.98))\n",
"#ax.set_ylim([0, 0.65])\n",
"ax.grid(True, color=(0.9, 0.9, 0.9))\n",
"ax.set_ylabel('Average Vehicle Speed')\n",
"ax.set_xlabel('Minimum Left-Lane Travelling Speed (arbitrary units)')\n",
"\n",
"fig.savefig('vehicle_speed.png', bbox_inches='tight')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Conclusions"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"SPEED_LIMITS = [0, 0.25, 0.5, 0.75, 1]\n",
"N = 1000\n",
"n_trials = 10000\n",
"\n",
"l_speeds, r_speeds, groups = dict(), dict(), dict()\n",
"\n",
"for speed in SPEED_LIMITS:\n",
" l_speeds[speed], r_speeds[speed] = [flatten(i) for i in two_lane_speed_trials(speed, N=N)]\n",
" groups[speed] = np.zeros(n_trials)\n",
" \n",
" for i in xrange(n_trials):\n",
" speeds = np.random.rand(N)\n",
" l_speed, r_speed = split_speeds(speeds, speed)\n",
" groups[speed][i] = get_num_groups(l_speed) + get_num_groups(r_speed)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Min. Left Lane Speed N_left N_right N_group Average Speed\n",
"0 0.00 992.56 7.44 18.18 0.02\n",
"1 0.25 750.08 249.92 15.03 0.19\n",
"2 0.50 497.81 502.19 14.37 0.26\n",
"3 0.75 251.26 748.74 13.56 0.19\n",
"4 1.00 0.00 1000.00 7.49 0.01\n"
]
}
],
"source": [
"from collections import OrderedDict\n",
"import pandas as pd\n",
"columns = ('Min. Left Lane Speed', 'N_left', 'N_right', 'N_group', 'Average Speed')\n",
"rows = (['%.2f' % x for x in SPEED_LIMITS],\n",
" ['%.2f' % (len(l_speeds[x])/100) for x in SPEED_LIMITS],\n",
" ['%.2f' % (len(r_speeds[x])/100) for x in SPEED_LIMITS],\n",
" ['%.2f' % np.mean(groups[x]) for x in SPEED_LIMITS],\n",
" ['%.2f' % np.mean(l_speeds[x] + r_speeds[x]) for x in SPEED_LIMITS])\n",
"\n",
"print pd.DataFrame(OrderedDict(zip(columns, rows)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The cars can proceed down the highway with the fastest expected speed if the left lane is reserved exclusively for people who travel faster than average. This is also the configuration that most evenly balances the traffic across both lanes.\n",
"\n",
"If all cars are permitted to move to the left lane, then the average number of groups increases. Since more groups == less traffic (a traffic jam is one huge group) a selfish driver might think that it's in their best interest to move to the left lane even if they are slow. However, as the minimum left lane speed is decreased, there are diminishing returns in the number of groups and substantial losses in average speed of all N cars."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.11"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
@nickstanisha
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