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annotate trafficintelligence/traffic_engineering.py @ 1212:af329f3330ba

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work in progress on 3D safety analysis
author Nicolas Saunier <nicolas.saunier@polymtl.ca>
date Tue, 02 May 2023 17:11:24 -0400
parents 770306fef827
children 3bfdb2ffd29d
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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 from math import ceil
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5 from numpy import e, log, arange
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6 from scipy import stats
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7
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8 from matplotlib.pyplot import figure,plot,xlabel,ylabel, xlim, ylim
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9
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10 from trafficintelligence import prediction
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11
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12 #########################
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13 # Simulation
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14 #########################
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15
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16 def generateTimeHeadways(meanTimeHeadway, simulationTime):
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17 '''Generates the time headways between arrivals
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18 given the meanTimeHeadway and the negative exponential distribution
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19 over a time interval of length simulationTime (assumed to be in same time unit as headway'''
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20 from random import expovariate
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21 headways = []
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22 totalTime = 0
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23 flow = 1/meanTimeHeadway
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24 while totalTime < simulationTime:
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25 h = expovariate(flow)
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26 headways.append(h)
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27 totalTime += h
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28 return headways
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29
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30 class RoadUser(object):
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31 '''Simple example of inheritance to plot different road users '''
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32 def __init__(self, position, velocity):
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33 'Both fields are 2D numpy arrays'
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34 self.position = position.astype(float)
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35 self.velocity = velocity.astype(float)
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36
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37 def move(self, deltaT):
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38 self.position += deltaT*self.velocity
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39
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40 def draw(self, init = False):
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41 from matplotlib.pyplot import plot
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42 if init:
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43 self.plotLine = plot(self.position[0], self.position[1], self.getDescriptor())[0]
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44 else:
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45 self.plotLine.set_data(self.position[0], self.position[1])
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47
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48 class PassengerVehicle(RoadUser):
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49 def getDescriptor(self):
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50 return 'dr'
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51
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52 class Pedestrian(RoadUser):
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53 def getDescriptor(self):
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54 return 'xb'
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55
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56 class Cyclist(RoadUser):
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57 def getDescriptor(self):
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58 return 'og'
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59
790
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60 #########################
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61 # queueing models
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62 #########################
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63
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64 class CapacityReduction(object):
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65 def __init__(self, beta, reductionDuration, demandCapacityRatio = None, demand = None, capacity = None):
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66 '''reduction duration should be positive
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67 demandCapacityRatio is demand/capacity (q/s)'''
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68 if demandCapacityRatio is None and demand is None and capacity is None:
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69 print('Missing too much information (demand, capacity and ratio)')
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70 import sys
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71 sys.exit()
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72 if 0 <= beta < 1:
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73 self.beta = beta
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74 self.reductionDuration = reductionDuration
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75
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76 if demandCapacityRatio is not None:
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77 self.demandCapacityRatio = demandCapacityRatio
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78 if demand is not None:
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79 self.demand = demand
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80 if capacity is not None:
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81 self.capacity = capacity
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82 if capacity is not None and demand is not None:
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83 self.demandCapacityRatio = float(self.demand)/self.capacity
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84 if demand <= beta*capacity:
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85 print('There is no queueing as the demand {} is inferior to the reduced capacity {}'.format(demand, beta*capacity))
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86 else:
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87 print('reduction coefficient (beta={}) is not in [0, 1['.format(beta))
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88
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89 def queueingDuration(self):
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90 return self.reductionDuration*(1-self.beta)/(1-self.demandCapacityRatio)
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91
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92 def nArrived(self, t):
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93 if self.demand is None:
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94 print('Missing demand field')
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95 return None
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96 return self.demand*t
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97
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98 def nServed(self, t):
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99 if self.capacity is None:
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100 print('Missing capacity field')
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101 return None
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102 if 0<=t<=self.reductionDuration:
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103 return self.beta*self.capacity*t
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104 elif self.reductionDuration < t <= self.queueingDuration():
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105 return self.beta*self.capacity*self.reductionDuration+self.capacity*(t-self.reductionDuration)
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106
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107 def nQueued(self, t):
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108 return self.nArrived(t)-self.nServed(t)
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109
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110 def maxNQueued(self):
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111 return self.nQueued(self.reductionDuration)
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112
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113 def totalDelay(self):
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114 if self.capacity is None:
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115 print('Missing capacity field')
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116 return None
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117 return self.capacity*self.reductionDuration**2*(1-self.beta)*(self.demandCapacityRatio-self.beta)/(2*(1-self.demandCapacityRatio))
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118
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119 def averageDelay(self):
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120 return self.reductionDuration*(self.demandCapacityRatio-self.beta)/(2*self.demandCapacityRatio)
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121
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122 def averageNQueued(self):
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123 return self.totalDelay()/self.queueingDuration()
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124
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125
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126 #########################
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127 # fundamental diagrams
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128 #########################
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129
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130 class FundamentalDiagram(object):
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131 ''' '''
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132 def __init__(self, name):
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133 self.name = name
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134 self.kj = None
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135 self.kc = None
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136 self.vf = None
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137 self.qmax = None
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138
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139 def getJamDensity(self):
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140 return self.kj
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141
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142 def getCriticalDensity(self):
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143 return self.kc
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144
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145 def getCapacity(self):
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146 return self.qmax
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147
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148 def getFreeFlowSpeed(self):
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149 return self.vf
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150
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151 def q(self, k):
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152 return k*self.v(k)
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153
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154 @staticmethod
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155 def meanHeadway(k):
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156 return 1/k
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157
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158 @staticmethod
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159 def meanSpacing(q):
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160 return 1/q
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161
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162 def plotVK(self, language='fr', units={}):
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163 densities = [k for k in arange(1, self.kj+1)]
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164 figure()
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165 plot(densities, [self.v(k) for k in densities])
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166 xlim(xmin=0)
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167 ylim(ymin=0)
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168 xlabel('Densite (veh/km)') # todo other languages and adapt to units
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169 ylabel('Vitesse (km/h)')
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170
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171 def plotQK(self, language='fr', units={}):
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172 densities = [k for k in arange(1, self.kj+1)]
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173 figure()
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174 plot(densities, [self.q(k) for k in densities])
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175 xlim(xmin=0)
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176 ylim(ymin=0)
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177 xlabel('Densite (veh/km)') # todo other languages and adapt to units
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178 ylabel('Debit (km/h)')
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179
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180 class GreenshieldsFD(FundamentalDiagram):
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181 '''Speed is a linear function of density'''
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182 def __init__(self, vf, kj):
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183 FundamentalDiagram.__init__(self,'Greenshields')
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184 self.vf=vf
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185 self.kj=kj
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186 self.kc=kj/2
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187 self.qmax=vf*kj/4
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188
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189 def v(self,k):
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190 from numpy import log
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191 return self.vf*(1-k/self.kj)
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192
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193
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194 class GreenbergFD(FundamentalDiagram):
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195 '''Speed is the logarithm of density'''
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196 def __init__(self, vc, kj):
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197 FundamentalDiagram.__init__(self,'Greenberg')
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198 self.vc=vc
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199 self.kj=kj
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200 self.qmax = self.kc*self.vc
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201 self.kc = self.kj/e
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202
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203 def v(self,k):
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204 return self.vc*log(self.kj/k)
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205
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206 class TriangularFD(FundamentalDiagram):
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207 def __init__(self, vf = None, kc = None, kj = None, qmax = None, w = None):
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208 FundamentalDiagram.__init__(self,'Triangular')
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209 if vf is not None and qmax is not None and kj is not None:
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210 self.vf=vf
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211 self.qmax = qmax
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212 self.kj = kj
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213 self.kc = qmax/vf
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214 self.w = qmax/(self.kc-kj)
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215
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216 def v(self, k):
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217 if k<self.kc:
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218 return self.vf
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219 else:
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220 return self.vf*self.kc*(self.kj/k-1)/(self.kj-self.kc)
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221
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222 def generateDensities(n, maxDensity):
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223 return stats.uniform.rvs(size=n)*maxDensity
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224
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225 def generateSpeedVolumes(fd, n, maxDensity, maxHGVProportion = 0, etrucks = 2.5):
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226 densities = generateDensities(n, maxDensity)
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227 speeds = [fd.v(k) for k in densities]
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228 volumes = [fd.q(k) for k in densities]
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229 if maxHGVProportion > 0:
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230 hgvProportions = stats.uniform.rvs(size=n)*maxHGVProportion # en pourcent
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231 volumes = [v/(1+(etrucks-1)*p/100) for v,p in zip(volumes, hgvProportions)]
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232 else:
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233 hgvProportions = None
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234 return speeds, volumes, hgvProportions
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235
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236 def highwayLOS(k):
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237 'returns the highway level of service for density k in veh/km'
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238 if k>=28: return 'F'
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239 elif k>=22: return 'E'
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240 elif k>=16: return 'D'
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241 elif k>=11: return 'C'
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242 elif k>=7: return 'B'
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243 else: return 'A'
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244
33
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245 #########################
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246 # intersection
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247 #########################
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248
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249 class FourWayIntersection(object):
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250 '''Simple class for simple intersection outline'''
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251 def __init__(self, dimension, coordX, coordY):
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252 self.dimension = dimension
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253 self.coordX = coordX
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254 self.coordY = coordY
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255
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256 def plot(self, options = 'k'):
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257 from matplotlib.pyplot import plot, axis
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258
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259 minX = min(self.dimension[0])
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260 maxX = max(self.dimension[0])
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261 minY = min(self.dimension[1])
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262 maxY = max(self.dimension[1])
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263
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264 plot([minX, self.coordX[0], self.coordX[0]], [self.coordY[0], self.coordY[0], minY],options)
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265 plot([self.coordX[1], self.coordX[1], maxX], [minY, self.coordY[0], self.coordY[0]],options)
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266 plot([minX, self.coordX[0], self.coordX[0]], [self.coordY[1], self.coordY[1], maxY],options)
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267 plot([self.coordX[1], self.coordX[1], maxX], [maxY, self.coordY[1], self.coordY[1]],options)
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268 axis('equal')
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269
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270 #########################
33
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271 # traffic signals
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272 #########################
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273
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274 class Volume(object):
33
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275 '''Class to represent volumes with varied vehicule types '''
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276 def __init__(self, volume, types = ['pc'], proportions = [1], equivalents = [1], nLanes = 1):
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277 '''mvtEquivalent is the equivalent if the movement is right of left turn'''
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278
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279 # check the sizes of the lists
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280 if sum(proportions) == 1:
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281 self.volume = volume
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282 self.types = types
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283 self.proportions = proportions
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284 self.equivalents = equivalents
314
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285 self.nLanes = nLanes
33
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286 else:
302
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287 print('Proportions do not sum to 1')
33
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288 pass
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289
314
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290 def checkProtected(self, opposedThroughMvt):
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291 '''Checks if this left movement should be protected,
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292 ie if one of the main two conditions on left turn is verified'''
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293 return self.volume >= 200 or self.volume*opposedThroughMvt.volume/opposedThroughMvt.nLanes > 50000
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294
205
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295 def getPCUVolume(self):
33
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296 '''Returns the passenger-car equivalent for the input volume'''
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297 v = 0
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298 for p, e in zip(self.proportions, self.equivalents):
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299 v += p*e
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300 return v*self.volume
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301
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302 class IntersectionMovement(object):
33
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303 '''Represents an intersection movement
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304 with a volume, a type (through, left or right)
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305 and an equivalent for movement type'''
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diff changeset
306 def __init__(self, volume, mvtEquivalent = 1):
33
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307 self.volume = volume
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308 self.mvtEquivalent = mvtEquivalent
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309
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310 def getTVUVolume(self):
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diff changeset
311 return self.mvtEquivalent*self.volume.getPCUVolume()
33
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312
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diff changeset
313 class LaneGroup(object):
33
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314 '''Class that represents a group of mouvements'''
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315
34
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316 def __init__(self, movements, nLanes):
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317 self.movements = movements
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318 self.nLanes = nLanes
33
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319
34
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diff changeset
320 def getTVUVolume(self):
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diff changeset
321 return sum([mvt.getTVUVolume() for mvt in self.movements])
33
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322
206
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diff changeset
323 def getCharge(self, saturationVolume):
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diff changeset
324 return self.getTVUVolume()/(self.nLanes*saturationVolume)
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diff changeset
325
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diff changeset
326 def optimalCycle(lostTime, criticalCharge):
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diff changeset
327 return (1.5*lostTime+5)/(1-criticalCharge)
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parents: 205
diff changeset
328
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diff changeset
329 def minimumCycle(lostTime, criticalCharge, degreeSaturation=1.):
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parents: 205
diff changeset
330 'degree of saturation can be used as the peak hour factor too'
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diff changeset
331 return lostTime/(1-criticalCharge/degreeSaturation)
34
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diff changeset
332
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diff changeset
333 class Cycle(object):
34
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diff changeset
334 '''Class to compute optimal cycle and the split of effective green times'''
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diff changeset
335 def __init__(self, phases, lostTime, saturationVolume):
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diff changeset
336 '''phases is a list of phases
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diff changeset
337 a phase is a list of lanegroups'''
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diff changeset
338 self.phases = phases
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diff changeset
339 self.lostTime = lostTime
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diff changeset
340 self.saturationVolume = saturationVolume
33
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341
206
82b4101d9a2f re-arranged and commnted signal cycle calculations
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diff changeset
342 def computeCriticalCharges(self):
314
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diff changeset
343 self.criticalCharges = [max([lg.getCharge(self.saturationVolume) for lg in phase]) for phase in self.phases]
34
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diff changeset
344 self.criticalCharge = sum(self.criticalCharges)
206
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diff changeset
345
82b4101d9a2f re-arranged and commnted signal cycle calculations
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diff changeset
346 def computeOptimalCycle(self):
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diff changeset
347 self.computeCriticalCharges()
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diff changeset
348 self.C = optimalCycle(self.lostTime, self.criticalCharge)
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diff changeset
349 return self.C
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diff changeset
350
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diff changeset
351 def computeMinimumCycle(self, degreeSaturation=1.):
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diff changeset
352 self.computeCriticalCharges()
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diff changeset
353 self.C = minimumCycle(self.lostTime, self.criticalCharge, degreeSaturation)
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diff changeset
354 return self.C
34
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parents: 33
diff changeset
355
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diff changeset
356 def computeEffectiveGreen(self):
314
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parents: 302
diff changeset
357 #from numpy import round
206
82b4101d9a2f re-arranged and commnted signal cycle calculations
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diff changeset
358 #self.computeCycle() # in case it was not done before
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parents: 205
diff changeset
359 effectiveGreenTime = self.C-self.lostTime
34
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diff changeset
360 self.effectiveGreens = [round(c*effectiveGreenTime/self.criticalCharge,1) for c in self.criticalCharges]
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diff changeset
361 return self.effectiveGreens
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diff changeset
362
33
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parents:
diff changeset
363
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parents:
diff changeset
364 def computeInterGreen(perceptionReactionTime, initialSpeed, intersectionLength, vehicleAverageLength = 6, deceleration = 3):
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parents:
diff changeset
365 '''Computes the intergreen time (yellow/amber plus all red time)
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parents:
diff changeset
366 Deceleration is positive
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diff changeset
367 All variables should be in the same units'''
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parents:
diff changeset
368 if deceleration > 0:
36
571b11304ec9 corrected bug
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parents: 34
diff changeset
369 return [perceptionReactionTime+float(initialSpeed)/(2*deceleration), float(intersectionLength+vehicleAverageLength)/initialSpeed]
33
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diff changeset
370 else:
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parents: 796
diff changeset
371 print('Issue deceleration should be strictly positive')
33
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diff changeset
372 return None
37
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parents: 36
diff changeset
373
911b52744ceb added uniform delay function
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parents: 36
diff changeset
374 def uniformDelay(cycleLength, effectiveGreen, saturationDegree):
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diff changeset
375 '''Computes the uniform delay'''
796
Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 790
diff changeset
376 return 0.5*cycleLength*(1-float(effectiveGreen)/cycleLength)**2/(1-float(effectiveGreen*saturationDegree)/cycleLength)
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parents: 790
diff changeset
377
Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 790
diff changeset
378 def randomDelay(volume, saturationDegree):
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diff changeset
379 '''Computes the random delay = queueing time for M/D/1'''
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diff changeset
380 return saturationDegree**2/(2*volume*(1-saturationDegree))
87
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parents: 73
diff changeset
381
790
944949c8ef3e minor name change
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diff changeset
382 def incrementalDelay(T, X, c, k=0.5, I=1):
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parents: 789
diff changeset
383 '''Computes the incremental delay (HCM)
493
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Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 479
diff changeset
384 T in hours
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Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 479
diff changeset
385 c capacity of the lane group
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parents: 479
diff changeset
386 k default for fixed time signal
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parents: 479
diff changeset
387 I=1 for isolated intersection (Poisson arrival)'''
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Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 479
diff changeset
388 from math import sqrt
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parents: 479
diff changeset
389 return 900*T*(X - 1 + sqrt((X - 1)**2 + 8*k*I*X/(c*T)))
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parents: 479
diff changeset
390
87
f234154207d4 distance and time to change speed
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diff changeset
391 #########################
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diff changeset
392 # misc
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diff changeset
393 #########################
f234154207d4 distance and time to change speed
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diff changeset
394
f234154207d4 distance and time to change speed
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diff changeset
395 def timeChangingSpeed(v0, vf, a, TPR):
789
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parents: 665
diff changeset
396 'for decelerations, a < 0'
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diff changeset
397 return TPR-(vf-v0)/a
87
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parents: 73
diff changeset
398
f234154207d4 distance and time to change speed
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diff changeset
399 def distanceChangingSpeed(v0, vf, a, TPR):
789
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parents: 665
diff changeset
400 'for decelerations, a < 0'
1165
c5863e04d302 corrected bug
Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 1029
diff changeset
401 return TPR*v0+(vf**2-v0**2)/(2*a)