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PDF (DX094490.pdf) - White Rose Etheses Online

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68 and their method

68 and their method estimates the proportion of drivers in each gap range having critical gap less than or equal to the middle value of the range. Troutbeck (1975) compared this method with the ones included in Miller's (1971) comparison and determined that it is not better than the NLE or Ashworth's method. This method has the disadvantage that in certain conditions it can result in negative values. Troutbeck showed that the mean critical gap in the Ramsey-Routledge method is equal to the mean accepted gap minus the reciprocal of the flow (or the average offered gap). Figure 4.3 shows the histograms used in this method. The critical gap has been related to the speed of the approaching vehicles (Cooper et al (1976), Cooper et al (1977) ). In these studies the accepted and rejected gaps were classified according to the speeds of the approaching vehicles and log-normal , gap acceptance function was fitted to the data in each 5 mile/hour speed-band. Median accepted , gaps for each speed, V 1 were expressed in terms of both time, T, and distance, D (=VT). The median accepted gap is expressed in terms of a constant time and a constant distance. They note that in their method it was not possible to remove the flow bias and derive 'absolute' gap acceptance functions. 4.2.4 Gap Acceptance Theoretical Nodels The value of the critical gap has been associated with a number of theoretical models of the acceptance behaviour of minor road vehicles. Plank (1982) has grouped all these models into four categories, as follows: Model (1) The gap-acceptance distribution is a step function. All drivers have the same critical gap, and

69 consistently accept all gaps greater than or equal to the critical gap, and reject all gaps less than the critical gap. This is the model used by Tanner (1962). Model (2) Individual drivers follow a step function gap-acceptance distribution, but the critical value is a variable distributed over the population of drivers, i.e. the drivers are consistent but not homogeneous. This is the model used by Ashworth (1968, 1969, 1970) and by Miller (1971). Model (3) The minimum acceptable headway is described by a probability distribution but is the same for all drivers, i.e. they are homogeneous but not consistent. This is the model used by Herman and Weiss (1961) and by Blunienfeld and Weiss (1978, 1979). Model (4) Each driver has a gap acceptance dis- tribution given by F(t;w) where parameter F(t) is the prob- ability of accepting a gap of size t, while parameter w has a distribution over the driver population, i.e. the drivers are neither homogeneous, nor consistent. Model (4) is the most sophisticated and will most accurately describe the true situation. However, Plank suggests that any of the other models will still yield reasonable results with less practical and mathematical difficulty. Ashworth and Bottom (1977) showed that Model (3) is a more appropriate simplification than Model (2), since the major source of variability in gap acceptance is within drivers rather than between them. Blumenfeld and Weiss (1978, 19791 support this conclusion. They also compare the statistics for Models (2) and (4) as well as for Models (1) and (3). They conclude

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