Mercurial Hosting > traffic-intelligence
annotate python/traffic_engineering.py @ 897:f5a49b603e8b
minor
author | Nicolas Saunier <nicolas.saunier@polymtl.ca> |
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date | Wed, 14 Jun 2017 01:11:56 -0400 |
parents | 9f8e9fb5621b |
children | 2cd1ce245024 |
rev | line source |
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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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7 |
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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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added function to generate headways based on flow or mean headway over some simulation period
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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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43 |
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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 |
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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 |
198
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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 |
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181 ######################### |
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182 # intersection |
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183 ######################### |
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184 |
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185 class FourWayIntersection(object): |
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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): |
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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 |
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221 self.nLanes = nLanes |
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222 else: |
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223 print('Proportions do not sum to 1') |
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224 pass |
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225 |
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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 |
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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''' |
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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 |
34 | 252 def __init__(self, movements, nLanes): |
253 self.movements = movements | |
254 self.nLanes = nLanes | |
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255 |
34 | 256 def getTVUVolume(self): |
257 return sum([mvt.getTVUVolume() for mvt in self.movements]) | |
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258 |
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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) |
34 | 268 |
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269 class Cycle(object): |
34 | 270 '''Class to compute optimal cycle and the split of effective green times''' |
271 def __init__(self, phases, lostTime, saturationVolume): | |
272 '''phases is a list of phases | |
273 a phase is a list of lanegroups''' | |
274 self.phases = phases | |
275 self.lostTime = lostTime | |
276 self.saturationVolume = saturationVolume | |
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277 |
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278 def computeCriticalCharges(self): |
314
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279 self.criticalCharges = [max([lg.getCharge(self.saturationVolume) for lg in phase]) for phase in self.phases] |
34 | 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 |
34 | 291 |
292 def computeEffectiveGreen(self): | |
314
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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 |
34 | 296 self.effectiveGreens = [round(c*effectiveGreenTime/self.criticalCharge,1) for c in self.criticalCharges] |
297 return self.effectiveGreens | |
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: |
36 | 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''' |
796 | 312 return 0.5*cycleLength*(1-float(effectiveGreen)/cycleLength)**2/(1-float(effectiveGreen*saturationDegree)/cycleLength) |
313 | |
314 def randomDelay(volume, saturationDegree): | |
315 '''Computes the random delay = queueing time for M/D/1''' | |
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) |
493
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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): |
789 | 332 'for decelerations, a < 0' |
333 return TPR-(vf-v0)/a | |
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334 |
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335 def distanceChangingSpeed(v0, vf, a, TPR): |
789 | 336 'for decelerations, a < 0' |
337 return TPR*v0-(vf**2-v0**2)/(2*a) |