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annotate trafficintelligence/traffic_engineering.py @ 1259:3bfdb2ffd29d

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modif for plotting nserved
author Nicolas Saunier <nicolas.saunier@polymtl.ca>
date Tue, 09 Apr 2024 15:21:55 -0400
parents 770306fef827
children f10e84505443
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rev   line source
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4bd7cc69b6cd added traffic engineering utilities with first version of LaneGroups
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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 '''since the beginning of the capacity reduction'''
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94 if self.demand is None or t<0:
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95 print('Missing demand field')
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96 return None
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97 return self.demand*t
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98
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99 def nServed(self, t):
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100 '''since the beginning of the capacity reduction'''
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101 if self.capacity is None or t<0:
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102 print('Missing capacity field')
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103 return None
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104 if 0<=t<=self.reductionDuration:
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105 return self.beta*self.capacity*t
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106 elif self.reductionDuration < t:
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107 qDuration = self.queueingDuration()
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108 if t <= qDuration:
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109 return self.beta*self.capacity*self.reductionDuration+self.capacity*(t-self.reductionDuration)
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110 else:
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111 return self.beta*self.capacity*self.reductionDuration+self.capacity*(qDuration-self.reductionDuration)+self.demand*(t-qDuration)
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112
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113 def nQueued(self, t):
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114 return self.nArrived(t)-self.nServed(t)
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115
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116 def maxNQueued(self):
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117 return self.nQueued(self.reductionDuration)
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118
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119 def totalDelay(self):
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120 if self.capacity is None:
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121 print('Missing capacity field')
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122 return None
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123 return self.capacity*self.reductionDuration**2*(1-self.beta)*(self.demandCapacityRatio-self.beta)/(2*(1-self.demandCapacityRatio))
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124
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125 def averageDelay(self):
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126 return self.reductionDuration*(self.demandCapacityRatio-self.beta)/(2*self.demandCapacityRatio)
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127
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128 def averageNQueued(self):
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129 return self.totalDelay()/self.queueingDuration()
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130
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131
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132 #########################
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133 # fundamental diagrams
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134 #########################
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135
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136 class FundamentalDiagram(object):
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137 ''' '''
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138 def __init__(self, name):
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139 self.name = name
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140 self.kj = None
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141 self.kc = None
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142 self.vf = None
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143 self.qmax = None
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144
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145 def getJamDensity(self):
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146 return self.kj
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147
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148 def getCriticalDensity(self):
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149 return self.kc
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150
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151 def getCapacity(self):
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152 return self.qmax
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153
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154 def getFreeFlowSpeed(self):
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155 return self.vf
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157 def q(self, k):
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158 return k*self.v(k)
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159
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160 @staticmethod
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161 def meanHeadway(k):
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162 return 1/k
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163
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164 @staticmethod
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165 def meanSpacing(q):
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166 return 1/q
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167
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168 def plotVK(self, language='fr', units={}):
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169 densities = [k for k in arange(1, self.kj+1)]
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170 figure()
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171 plot(densities, [self.v(k) for k in densities])
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172 xlim(xmin=0)
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173 ylim(ymin=0)
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174 xlabel('Densite (veh/km)') # todo other languages and adapt to units
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175 ylabel('Vitesse (km/h)')
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176
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177 def plotQK(self, language='fr', units={}):
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178 densities = [k for k in arange(1, self.kj+1)]
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179 figure()
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180 plot(densities, [self.q(k) for k in densities])
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181 xlim(xmin=0)
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182 ylim(ymin=0)
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183 xlabel('Densite (veh/km)') # todo other languages and adapt to units
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184 ylabel('Debit (km/h)')
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185
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186 class GreenshieldsFD(FundamentalDiagram):
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187 '''Speed is a linear function of density'''
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188 def __init__(self, vf, kj):
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189 FundamentalDiagram.__init__(self,'Greenshields')
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190 self.vf=vf
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191 self.kj=kj
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192 self.kc=kj/2
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193 self.qmax=vf*kj/4
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194
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195 def v(self,k):
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196 from numpy import log
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197 return self.vf*(1-k/self.kj)
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198
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199
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200 class GreenbergFD(FundamentalDiagram):
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201 '''Speed is the logarithm of density'''
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202 def __init__(self, vc, kj):
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203 FundamentalDiagram.__init__(self,'Greenberg')
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204 self.vc=vc
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205 self.kj=kj
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206 self.qmax = self.kc*self.vc
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207 self.kc = self.kj/e
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208
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209 def v(self,k):
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210 return self.vc*log(self.kj/k)
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211
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212 class TriangularFD(FundamentalDiagram):
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213 def __init__(self, vf = None, kc = None, kj = None, qmax = None, w = None):
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214 FundamentalDiagram.__init__(self,'Triangular')
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215 if vf is not None and qmax is not None and kj is not None:
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216 self.vf=vf
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217 self.qmax = qmax
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218 self.kj = kj
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219 self.kc = qmax/vf
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220 self.w = qmax/(self.kc-kj)
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221
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222 def v(self, k):
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223 if k<self.kc:
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224 return self.vf
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225 else:
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226 return self.vf*self.kc*(self.kj/k-1)/(self.kj-self.kc)
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227
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228 def generateDensities(n, maxDensity):
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229 return stats.uniform.rvs(size=n)*maxDensity
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230
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231 def generateSpeedVolumes(fd, n, maxDensity, maxHGVProportion = 0, etrucks = 2.5):
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232 densities = generateDensities(n, maxDensity)
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233 speeds = [fd.v(k) for k in densities]
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234 volumes = [fd.q(k) for k in densities]
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235 if maxHGVProportion > 0:
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236 hgvProportions = stats.uniform.rvs(size=n)*maxHGVProportion # en pourcent
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237 volumes = [v/(1+(etrucks-1)*p/100) for v,p in zip(volumes, hgvProportions)]
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238 else:
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239 hgvProportions = None
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240 return speeds, volumes, hgvProportions
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241
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242 def highwayLOS(k):
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243 'returns the highway level of service for density k in veh/km'
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244 if k>=28: return 'F'
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245 elif k>=22: return 'E'
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246 elif k>=16: return 'D'
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247 elif k>=11: return 'C'
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248 elif k>=7: return 'B'
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249 else: return 'A'
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250
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251 #########################
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252 # intersection
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253 #########################
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254
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255 class FourWayIntersection(object):
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256 '''Simple class for simple intersection outline'''
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257 def __init__(self, dimension, coordX, coordY):
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258 self.dimension = dimension
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259 self.coordX = coordX
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260 self.coordY = coordY
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261
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262 def plot(self, options = 'k'):
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263 from matplotlib.pyplot import plot, axis
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264
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265 minX = min(self.dimension[0])
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266 maxX = max(self.dimension[0])
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267 minY = min(self.dimension[1])
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268 maxY = max(self.dimension[1])
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269
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270 plot([minX, self.coordX[0], self.coordX[0]], [self.coordY[0], self.coordY[0], minY],options)
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271 plot([self.coordX[1], self.coordX[1], maxX], [minY, self.coordY[0], self.coordY[0]],options)
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272 plot([minX, self.coordX[0], self.coordX[0]], [self.coordY[1], self.coordY[1], maxY],options)
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273 plot([self.coordX[1], self.coordX[1], maxX], [maxY, self.coordY[1], self.coordY[1]],options)
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274 axis('equal')
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275
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276 #########################
33
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277 # traffic signals
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278 #########################
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279
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diff changeset
280 class Volume(object):
33
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281 '''Class to represent volumes with varied vehicule types '''
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282 def __init__(self, volume, types = ['pc'], proportions = [1], equivalents = [1], nLanes = 1):
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283 '''mvtEquivalent is the equivalent if the movement is right of left turn'''
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284
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285 # check the sizes of the lists
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286 if sum(proportions) == 1:
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287 self.volume = volume
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288 self.types = types
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289 self.proportions = proportions
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290 self.equivalents = equivalents
314
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291 self.nLanes = nLanes
33
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292 else:
302
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diff changeset
293 print('Proportions do not sum to 1')
33
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294 pass
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295
314
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296 def checkProtected(self, opposedThroughMvt):
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297 '''Checks if this left movement should be protected,
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298 ie if one of the main two conditions on left turn is verified'''
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299 return self.volume >= 200 or self.volume*opposedThroughMvt.volume/opposedThroughMvt.nLanes > 50000
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diff changeset
300
205
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diff changeset
301 def getPCUVolume(self):
33
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302 '''Returns the passenger-car equivalent for the input volume'''
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303 v = 0
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304 for p, e in zip(self.proportions, self.equivalents):
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305 v += p*e
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306 return v*self.volume
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307
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diff changeset
308 class IntersectionMovement(object):
33
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309 '''Represents an intersection movement
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310 with a volume, a type (through, left or right)
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311 and an equivalent for movement type'''
205
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diff changeset
312 def __init__(self, volume, mvtEquivalent = 1):
33
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313 self.volume = volume
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314 self.mvtEquivalent = mvtEquivalent
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315
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316 def getTVUVolume(self):
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diff changeset
317 return self.mvtEquivalent*self.volume.getPCUVolume()
33
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318
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diff changeset
319 class LaneGroup(object):
33
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320 '''Class that represents a group of mouvements'''
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321
34
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diff changeset
322 def __init__(self, movements, nLanes):
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323 self.movements = movements
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diff changeset
324 self.nLanes = nLanes
33
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325
34
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diff changeset
326 def getTVUVolume(self):
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diff changeset
327 return sum([mvt.getTVUVolume() for mvt in self.movements])
33
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328
206
82b4101d9a2f re-arranged and commnted signal cycle calculations
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parents: 205
diff changeset
329 def getCharge(self, saturationVolume):
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parents: 205
diff changeset
330 return self.getTVUVolume()/(self.nLanes*saturationVolume)
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parents: 205
diff changeset
331
82b4101d9a2f re-arranged and commnted signal cycle calculations
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diff changeset
332 def optimalCycle(lostTime, criticalCharge):
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diff changeset
333 return (1.5*lostTime+5)/(1-criticalCharge)
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parents: 205
diff changeset
334
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diff changeset
335 def minimumCycle(lostTime, criticalCharge, degreeSaturation=1.):
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parents: 205
diff changeset
336 'degree of saturation can be used as the peak hour factor too'
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diff changeset
337 return lostTime/(1-criticalCharge/degreeSaturation)
34
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diff changeset
338
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diff changeset
339 class Cycle(object):
34
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diff changeset
340 '''Class to compute optimal cycle and the split of effective green times'''
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diff changeset
341 def __init__(self, phases, lostTime, saturationVolume):
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diff changeset
342 '''phases is a list of phases
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diff changeset
343 a phase is a list of lanegroups'''
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diff changeset
344 self.phases = phases
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diff changeset
345 self.lostTime = lostTime
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diff changeset
346 self.saturationVolume = saturationVolume
33
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347
206
82b4101d9a2f re-arranged and commnted signal cycle calculations
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parents: 205
diff changeset
348 def computeCriticalCharges(self):
314
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parents: 302
diff changeset
349 self.criticalCharges = [max([lg.getCharge(self.saturationVolume) for lg in phase]) for phase in self.phases]
34
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parents: 33
diff changeset
350 self.criticalCharge = sum(self.criticalCharges)
206
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parents: 205
diff changeset
351
82b4101d9a2f re-arranged and commnted signal cycle calculations
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parents: 205
diff changeset
352 def computeOptimalCycle(self):
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parents: 205
diff changeset
353 self.computeCriticalCharges()
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diff changeset
354 self.C = optimalCycle(self.lostTime, self.criticalCharge)
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diff changeset
355 return self.C
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parents: 205
diff changeset
356
82b4101d9a2f re-arranged and commnted signal cycle calculations
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parents: 205
diff changeset
357 def computeMinimumCycle(self, degreeSaturation=1.):
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parents: 205
diff changeset
358 self.computeCriticalCharges()
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diff changeset
359 self.C = minimumCycle(self.lostTime, self.criticalCharge, degreeSaturation)
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parents: 205
diff changeset
360 return self.C
34
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parents: 33
diff changeset
361
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parents: 33
diff changeset
362 def computeEffectiveGreen(self):
314
539e2b4cfaa3 modified for 4740 tps
Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 302
diff changeset
363 #from numpy import round
206
82b4101d9a2f re-arranged and commnted signal cycle calculations
Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 205
diff changeset
364 #self.computeCycle() # in case it was not done before
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Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 205
diff changeset
365 effectiveGreenTime = self.C-self.lostTime
34
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parents: 33
diff changeset
366 self.effectiveGreens = [round(c*effectiveGreenTime/self.criticalCharge,1) for c in self.criticalCharges]
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parents: 33
diff changeset
367 return self.effectiveGreens
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parents: 33
diff changeset
368
33
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parents:
diff changeset
369
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parents:
diff changeset
370 def computeInterGreen(perceptionReactionTime, initialSpeed, intersectionLength, vehicleAverageLength = 6, deceleration = 3):
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parents:
diff changeset
371 '''Computes the intergreen time (yellow/amber plus all red time)
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parents:
diff changeset
372 Deceleration is positive
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parents:
diff changeset
373 All variables should be in the same units'''
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parents:
diff changeset
374 if deceleration > 0:
36
571b11304ec9 corrected bug
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parents: 34
diff changeset
375 return [perceptionReactionTime+float(initialSpeed)/(2*deceleration), float(intersectionLength+vehicleAverageLength)/initialSpeed]
33
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parents:
diff changeset
376 else:
992
2cd1ce245024 update to python 3
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parents: 796
diff changeset
377 print('Issue deceleration should be strictly positive')
33
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parents:
diff changeset
378 return None
37
911b52744ceb added uniform delay function
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parents: 36
diff changeset
379
911b52744ceb added uniform delay function
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parents: 36
diff changeset
380 def uniformDelay(cycleLength, effectiveGreen, saturationDegree):
911b52744ceb added uniform delay function
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parents: 36
diff changeset
381 '''Computes the uniform delay'''
796
Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 790
diff changeset
382 return 0.5*cycleLength*(1-float(effectiveGreen)/cycleLength)**2/(1-float(effectiveGreen*saturationDegree)/cycleLength)
Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 790
diff changeset
383
Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 790
diff changeset
384 def randomDelay(volume, saturationDegree):
Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 790
diff changeset
385 '''Computes the random delay = queueing time for M/D/1'''
Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 790
diff changeset
386 return saturationDegree**2/(2*volume*(1-saturationDegree))
87
f234154207d4 distance and time to change speed
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parents: 73
diff changeset
387
790
944949c8ef3e minor name change
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parents: 789
diff changeset
388 def incrementalDelay(T, X, c, k=0.5, I=1):
944949c8ef3e minor name change
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parents: 789
diff changeset
389 '''Computes the incremental delay (HCM)
493
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Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 479
diff changeset
390 T in hours
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Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 479
diff changeset
391 c capacity of the lane group
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Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 479
diff changeset
392 k default for fixed time signal
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Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 479
diff changeset
393 I=1 for isolated intersection (Poisson arrival)'''
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Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 479
diff changeset
394 from math import sqrt
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Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 479
diff changeset
395 return 900*T*(X - 1 + sqrt((X - 1)**2 + 8*k*I*X/(c*T)))
850ed17c7b2f added some computation of delay
Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 479
diff changeset
396
87
f234154207d4 distance and time to change speed
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parents: 73
diff changeset
397 #########################
f234154207d4 distance and time to change speed
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diff changeset
398 # misc
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Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 73
diff changeset
399 #########################
f234154207d4 distance and time to change speed
Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 73
diff changeset
400
f234154207d4 distance and time to change speed
Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 73
diff changeset
401 def timeChangingSpeed(v0, vf, a, TPR):
789
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parents: 665
diff changeset
402 'for decelerations, a < 0'
3666342dabe2 minor changes
Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 665
diff changeset
403 return TPR-(vf-v0)/a
87
f234154207d4 distance and time to change speed
Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 73
diff changeset
404
f234154207d4 distance and time to change speed
Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 73
diff changeset
405 def distanceChangingSpeed(v0, vf, a, TPR):
789
3666342dabe2 minor changes
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parents: 665
diff changeset
406 'for decelerations, a < 0'
1165
c5863e04d302 corrected bug
Nicolas Saunier <nicolas.saunier@polymtl.ca>
parents: 1029
diff changeset
407 return TPR*v0+(vf**2-v0**2)/(2*a)