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PDF (DX094490.pdf) - White Rose Etheses Online

PDF (DX094490.pdf) - White Rose Etheses Online

100 increases. At high

100 increases. At high flow situations vehicles mcve in platoons with a minimum headway between successive vehicles. This is more pronounced if headways along one lane only are observed. In such conditions, the number of very small headways reduces, the largest number of observed headways being around the value of the minimum gap. Gerlough and Huber demonstrated the disagreement between theoretical and observed headways using the probability density curve, Fig. 4.13. Because of this disagreement a number of different distributions have been used which predict fewer small headways. 4.8.2.3 The Shifted Negative Exponential Distribution This distribution introduces a minimum allowable headway, t. Equation 4.18 becomes where P(h ^ t) = etT)/(T) (eq. 4.19) - 1 t = the mean headway (sec) The shifted negative exponential distribution cumulative curve is shown in Fig. 4.14. 4.8.2.4 Schuhi's Composite Headway Model Schuhl (1955) proposed a model which assumes some vehicles in a flow to be in bunches having a minimum headway, while the rest to flow in a random manner. The probability of a headway h being less than t is -t/t -(t--r)/t P(h < t) 2 (eq. 4.22) = (1 - e)[1 - e O[1 - e where

101 0: the proportion of restrained vehicles the mean headway of the free-flowing vehicles (sec) t 2 . the mean headway of the restrained vehicles (sec) t: the minimum headway of the restrained vehicles (sec) Cowan (1975) has proposed that the minimum headway should be considered as a random variable within the bunches of restrained vehicles. 4.8.2.5 The Pearson Type III Distribution The generalised equation for the Pearson Type III (or Gamma) distribution is where ____ k -qkt f(t) = r (k) (qk) e (eq. 4.23) k: a constant q: the traffic flow (veh/sec) 1 k-i -z F(k) = I z e dz : the gamma function - z=0 When k is a positive integer (k) = (k-i)! and k-i ______ k -qkt f(t) (qk) e (eq. 4.24) (k-i) ! which is the Erlang distribution. The major advantage of the Erlang distribution is that it can describe headway distributions ranging from complete random flow (k=].) to completely regular flow (kco). Fig. 4.15 shows four of the Erlang family of curves. 4.8.3 Analysis of Collected Data The circulating flow data collected at Castle Square

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PDF (267549_VOL2.pdf) - White Rose Etheses Online
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