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As expected, probability of headway less than't's increases with the flow rate and rate of such increase is considerably high for headways 7.5 s or more.
The present study, therefore, made an attempt to develop nomographs considering the appropriate distribution models (see Table 4 and Fig. 4) for calculating the headway probabilities (probability of headway less than't's) at different flow levels (see Fig. 5).
This was further investigated by plotting the nomographs wherein probability of headway less than 7.5 s or more was observed to increase almost sharply with the flow; this attributes to frequent formation of platoons and higher amount of car following interaction.
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SEE values were found to be about 0.052 (Fig. 6a), 0.041 (Fig. 6b), 0.054 (Fig. 6c) and 0.059 (Fig. 6d) respectively indicating satisfactory agreement between the probability of headways of field data and model outcomes.
The present paper has proposed a statistical framework for modelling headways and determined the probabilities of headways at different flow levels.
Theoretically calculated probabilities of headways were plotted against those observed at field in order to compare how rational the outcomes are with respect to field observations.
Open image in new window Fig. 6 Agreement between the probabilities of headways obtained from the 'nomograph' and field data obtained from a 'pilot study': a West (nomograph) and North (pilot study) bound traffic; b West (nomograph) and South (pilot study) bound traffic; c East (nomograph) and North (pilot study) bound traffic and d East (nomograph) and South (pilot study) bound traffic.
Then, the probability of the headway in lane 2 which allows n vehicles to driving into it fitly can be expressed by Eq. (4).
In Troutbeck's microscopic model the probability of the critical headway is calculated through the maximum likelihood method which requires an iteration process.
The maximum vehicle speed, the difference of the average vehicle speed from the speed limit (different for each type of road), the average and maximum lateral deviation, the average and minimum headway as well as the probabilities of Time Exposed Headway (TEHP*) and of Time Integrated Headway (TIHP* 1 were the metrics that have been selected according to the above criteria.
Open image in new window Fig. 3 Steps in longitudinal movement procedure Step 1 Value of randomisation parameter determines the probability of deceleration based on headway and speed of the subject vehicle and the brake light status of the leader.
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