Time Gap Modeling under Mixed Traffic Condition: A Statistical Analysis

This paper attempts to model vehicular time gap, which is defined as the time interval between any two successive arrivals of vehicles at a reference point of measurement on a road segment. Such an approach is justified under the non-lane-based heterogeneous traffic conditions prevailing in developing countries such as India, characterized by many “zero” time gaps due to simultaneous arrivals within a given road width. In addition, time gap data are characterized by a significant amount of data in the tail region due to long headways. Nevertheless, many researchers of time gap modeling have used light-tailed distributions that modeled time gaps satisfactorily due to two reasons: (a) The tail data was merged into a single bin; and (b) goodness-of-fit tests such as the Chi-square test, which has many limitations, were used. Further, some researchers have suggested different distributions for the same range of traffic flows, leading to ambiguity in distribution selection. In addition, bin size, which dictates the degree of fit of any distribution, has been ascribed very less importance in time gap modeling. Hence, this paper tries to consolidate and standardize the existing research in time gap modeling research by addressing all these issues. Two new distributions, namely Generalized Pareto (GP) and Generalized Extreme Value (GEV) with better tail modeling properties, have been proposed along with other conventional distribution to model vehicular time gaps over a wide range of flow from 550 vph to 4,100 vph. Two types of goodness-of-fit tests, namely Area-based and Distance-based tests, have been used. It has been found from the study that GP distribution fits the time gap data well (overall and tails) up to a flow range of 1,500 vph based on both kinds of tests, and GEV fits the data well for the flow levels above 1,500 vph based on the area test only.