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annotate python/traffic_engineering.py @ 925:974077e23804

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update on setup script (not tested)
author Nicolas Saunier <nicolas.saunier@polymtl.ca>
date Mon, 10 Jul 2017 01:38:12 -0400
parents 9f8e9fb5621b
children 2cd1ce245024
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1 #! /usr/bin/env python
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2 ''' Traffic Engineering Tools and Examples'''
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3
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4 import prediction
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5
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6 from math import ceil
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8
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9 #########################
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10 # Simulation
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11 #########################
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12
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13 def generateTimeHeadways(meanTimeHeadway, simulationTime):
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14 '''Generates the time headways between arrivals
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15 given the meanTimeHeadway and the negative exponential distribution
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16 over a time interval of length simulationTime (assumed to be in same time unit as headway'''
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17 from random import expovariate
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18 headways = []
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19 totalTime = 0
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20 flow = 1/meanTimeHeadway
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21 while totalTime < simulationTime:
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22 h = expovariate(flow)
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23 headways.append(h)
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24 totalTime += h
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25 return headways
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26
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27 class RoadUser(object):
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28 '''Simple example of inheritance to plot different road users '''
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29 def __init__(self, position, velocity):
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30 'Both fields are 2D numpy arrays'
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31 self.position = position.astype(float)
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32 self.velocity = velocity.astype(float)
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33
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34 def move(self, deltaT):
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35 self.position += deltaT*self.velocity
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36
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37 def draw(self, init = False):
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38 from matplotlib.pyplot import plot
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39 if init:
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40 self.plotLine = plot(self.position[0], self.position[1], self.getDescriptor())[0]
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41 else:
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42 self.plotLine.set_data(self.position[0], self.position[1])
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44
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45 class PassengerVehicle(RoadUser):
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46 def getDescriptor(self):
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47 return 'dr'
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48
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49 class Pedestrian(RoadUser):
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50 def getDescriptor(self):
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51 return 'xb'
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52
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53 class Cyclist(RoadUser):
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54 def getDescriptor(self):
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55 return 'og'
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56
790
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57 #########################
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58 # queueing models
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59 #########################
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60
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61 class CapacityReduction(object):
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62 def __init__(self, beta, reductionDuration, demandCapacityRatio = None, demand = None, capacity = None):
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63 '''reduction duration should be positive
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64 demandCapacityRatio is demand/capacity (q/s)'''
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65 if demandCapacityRatio is None and demand is None and capacity is None:
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66 print('Missing too much information (demand, capacity and ratio)')
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67 import sys
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68 sys.exit()
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69 if 0 <= beta < 1:
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70 self.beta = beta
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71 self.reductionDuration = reductionDuration
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72
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73 if demandCapacityRatio is not None:
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74 self.demandCapacityRatio = demandCapacityRatio
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75 if demand is not None:
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76 self.demand = demand
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77 if capacity is not None:
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78 self.capacity = capacity
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79 if capacity is not None and demand is not None:
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80 self.demandCapacityRatio = float(self.demand)/self.capacity
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81 if demand <= beta*capacity:
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82 print('There is no queueing as the demand {} is inferior to the reduced capacity {}'.format(demand, beta*capacity))
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83 else:
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84 print('reduction coefficient (beta={}) is not in [0, 1['.format(beta))
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85
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86 def queueingDuration(self):
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87 return self.reductionDuration*(1-self.beta)/(1-self.demandCapacityRatio)
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88
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89 def nArrived(self, t):
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90 if self.demand is None:
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91 print('Missing demand field')
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92 return None
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93 return self.demand*t
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94
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95 def nServed(self, t):
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96 if self.capacity is None:
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97 print('Missing capacity field')
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98 return None
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99 if 0<=t<=self.reductionDuration:
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100 return self.beta*self.capacity*t
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101 elif self.reductionDuration < t <= self.queueingDuration():
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102 return self.beta*self.capacity*self.reductionDuration+self.capacity*(t-self.reductionDuration)
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103
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104 def nQueued(self, t):
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105 return self.nArrived(t)-self.nServed(t)
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106
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107 def maxNQueued(self):
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108 return self.nQueued(self.reductionDuration)
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109
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110 def totalDelay(self):
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111 if self.capacity is None:
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112 print('Missing capacity field')
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113 return None
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114 return self.capacity*self.reductionDuration**2*(1-self.beta)*(self.demandCapacityRatio-self.beta)/(2*(1-self.demandCapacityRatio))
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115
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116 def averageDelay(self):
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117 return self.reductionDuration*(self.demandCapacityRatio-self.beta)/(2*self.demandCapacityRatio)
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118
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119 def averageNQueued(self):
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120 return self.totalDelay()/self.queueingDuration()
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121
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122
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123 #########################
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124 # fundamental diagram
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125 #########################
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126
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127 class FundamentalDiagram(object):
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128 ''' '''
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129 def __init__(self, name):
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130 self.name = name
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131
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132 def q(self, k):
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133 return k*self.v(k)
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134
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135 @staticmethod
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136 def meanHeadway(k):
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137 return 1/k
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138
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139 @staticmethod
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140 def meanSpacing(q):
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141 return 1/q
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142
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143 def plotVK(self, language='fr', units={}):
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144 from numpy import arange
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145 from matplotlib.pyplot import figure,plot,xlabel,ylabel
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146 densities = [k for k in arange(1, self.kj+1)]
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147 figure()
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148 plot(densities, [self.v(k) for k in densities])
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149 xlabel('Densite (veh/km)') # todo other languages and adapt to units
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150 ylabel('Vitesse (km/h)')
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151
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152 def plotQK(self, language='fr', units={}):
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153 from numpy import arange
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154 from matplotlib.pyplot import figure,plot,xlabel,ylabel
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155 densities = [k for k in arange(1, self.kj+1)]
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156 figure()
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157 plot(densities, [self.q(k) for k in densities])
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158 xlabel('Densite (veh/km)') # todo other languages and adapt to units
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159 ylabel('Debit (km/h)')
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160
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161 class GreenbergFD(FundamentalDiagram):
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162 '''Speed is the logarithm of density'''
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163 def __init__(self, vc, kj):
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164 FundamentalDiagram.__init__(self,'Greenberg')
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165 self.vc=vc
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166 self.kj=kj
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167
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168 def v(self,k):
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169 from numpy import log
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170 return self.vc*log(self.kj/k)
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171
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172 def criticalDensity(self):
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173 from numpy import e
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174 self.kc = self.kj/e
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175 return self.kc
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176
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177 def capacity(self):
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178 self.qmax = self.kc*self.vc
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179 return self.qmax
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180
33
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181 #########################
116
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182 # intersection
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183 #########################
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184
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185 class FourWayIntersection(object):
116
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186 '''Simple class for simple intersection outline'''
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187 def __init__(self, dimension, coordX, coordY):
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188 self.dimension = dimension
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189 self.coordX = coordX
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190 self.coordY = coordY
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191
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192 def plot(self, options = 'k'):
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193 from matplotlib.pyplot import plot, axis
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194
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195 minX = min(self.dimension[0])
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196 maxX = max(self.dimension[0])
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197 minY = min(self.dimension[1])
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198 maxY = max(self.dimension[1])
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199
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200 plot([minX, self.coordX[0], self.coordX[0]], [self.coordY[0], self.coordY[0], minY],options)
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201 plot([self.coordX[1], self.coordX[1], maxX], [minY, self.coordY[0], self.coordY[0]],options)
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202 plot([minX, self.coordX[0], self.coordX[0]], [self.coordY[1], self.coordY[1], maxY],options)
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203 plot([self.coordX[1], self.coordX[1], maxX], [maxY, self.coordY[1], self.coordY[1]],options)
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204 axis('equal')
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205
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206 #########################
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207 # traffic signals
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208 #########################
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209
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210 class Volume(object):
33
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211 '''Class to represent volumes with varied vehicule types '''
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212 def __init__(self, volume, types = ['pc'], proportions = [1], equivalents = [1], nLanes = 1):
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213 '''mvtEquivalent is the equivalent if the movement is right of left turn'''
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214
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215 # check the sizes of the lists
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216 if sum(proportions) == 1:
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217 self.volume = volume
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218 self.types = types
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219 self.proportions = proportions
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220 self.equivalents = equivalents
314
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221 self.nLanes = nLanes
33
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222 else:
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223 print('Proportions do not sum to 1')
33
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224 pass
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225
314
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226 def checkProtected(self, opposedThroughMvt):
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227 '''Checks if this left movement should be protected,
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228 ie if one of the main two conditions on left turn is verified'''
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229 return self.volume >= 200 or self.volume*opposedThroughMvt.volume/opposedThroughMvt.nLanes > 50000
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230
205
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231 def getPCUVolume(self):
33
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232 '''Returns the passenger-car equivalent for the input volume'''
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233 v = 0
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234 for p, e in zip(self.proportions, self.equivalents):
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235 v += p*e
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236 return v*self.volume
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237
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238 class IntersectionMovement(object):
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239 '''Represents an intersection movement
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240 with a volume, a type (through, left or right)
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241 and an equivalent for movement type'''
205
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242 def __init__(self, volume, mvtEquivalent = 1):
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243 self.volume = volume
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244 self.mvtEquivalent = mvtEquivalent
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245
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246 def getTVUVolume(self):
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247 return self.mvtEquivalent*self.volume.getPCUVolume()
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248
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249 class LaneGroup(object):
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250 '''Class that represents a group of mouvements'''
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251
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252 def __init__(self, movements, nLanes):
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253 self.movements = movements
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254 self.nLanes = nLanes
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255
34
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256 def getTVUVolume(self):
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257 return sum([mvt.getTVUVolume() for mvt in self.movements])
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258
206
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259 def getCharge(self, saturationVolume):
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260 return self.getTVUVolume()/(self.nLanes*saturationVolume)
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261
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262 def optimalCycle(lostTime, criticalCharge):
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263 return (1.5*lostTime+5)/(1-criticalCharge)
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264
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265 def minimumCycle(lostTime, criticalCharge, degreeSaturation=1.):
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266 'degree of saturation can be used as the peak hour factor too'
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267 return lostTime/(1-criticalCharge/degreeSaturation)
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268
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269 class Cycle(object):
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270 '''Class to compute optimal cycle and the split of effective green times'''
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271 def __init__(self, phases, lostTime, saturationVolume):
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272 '''phases is a list of phases
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273 a phase is a list of lanegroups'''
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274 self.phases = phases
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275 self.lostTime = lostTime
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276 self.saturationVolume = saturationVolume
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277
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278 def computeCriticalCharges(self):
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279 self.criticalCharges = [max([lg.getCharge(self.saturationVolume) for lg in phase]) for phase in self.phases]
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280 self.criticalCharge = sum(self.criticalCharges)
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281
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282 def computeOptimalCycle(self):
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283 self.computeCriticalCharges()
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284 self.C = optimalCycle(self.lostTime, self.criticalCharge)
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285 return self.C
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286
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287 def computeMinimumCycle(self, degreeSaturation=1.):
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288 self.computeCriticalCharges()
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289 self.C = minimumCycle(self.lostTime, self.criticalCharge, degreeSaturation)
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290 return self.C
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291
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292 def computeEffectiveGreen(self):
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293 #from numpy import round
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294 #self.computeCycle() # in case it was not done before
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295 effectiveGreenTime = self.C-self.lostTime
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296 self.effectiveGreens = [round(c*effectiveGreenTime/self.criticalCharge,1) for c in self.criticalCharges]
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297 return self.effectiveGreens
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298
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299
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300 def computeInterGreen(perceptionReactionTime, initialSpeed, intersectionLength, vehicleAverageLength = 6, deceleration = 3):
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301 '''Computes the intergreen time (yellow/amber plus all red time)
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302 Deceleration is positive
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303 All variables should be in the same units'''
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304 if deceleration > 0:
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305 return [perceptionReactionTime+float(initialSpeed)/(2*deceleration), float(intersectionLength+vehicleAverageLength)/initialSpeed]
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306 else:
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307 print 'Issue deceleration should be strictly positive'
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308 return None
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309
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310 def uniformDelay(cycleLength, effectiveGreen, saturationDegree):
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311 '''Computes the uniform delay'''
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312 return 0.5*cycleLength*(1-float(effectiveGreen)/cycleLength)**2/(1-float(effectiveGreen*saturationDegree)/cycleLength)
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313
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314 def randomDelay(volume, saturationDegree):
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315 '''Computes the random delay = queueing time for M/D/1'''
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316 return saturationDegree**2/(2*volume*(1-saturationDegree))
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317
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318 def incrementalDelay(T, X, c, k=0.5, I=1):
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319 '''Computes the incremental delay (HCM)
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320 T in hours
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321 c capacity of the lane group
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322 k default for fixed time signal
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323 I=1 for isolated intersection (Poisson arrival)'''
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324 from math import sqrt
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325 return 900*T*(X - 1 + sqrt((X - 1)**2 + 8*k*I*X/(c*T)))
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326
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327 #########################
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328 # misc
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329 #########################
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330
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331 def timeChangingSpeed(v0, vf, a, TPR):
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332 'for decelerations, a < 0'
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333 return TPR-(vf-v0)/a
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334
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335 def distanceChangingSpeed(v0, vf, a, TPR):
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336 'for decelerations, a < 0'
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337 return TPR*v0-(vf**2-v0**2)/(2*a)