Statistical aspects of gap-acceptance theory for unsignalized intersection capacity

Abstract

We partially correct and significantly deepen the Siegloch's method (1973), which is currently used to determine the capacity of unsignalized intersections. Taking into account current knowledge about microstructure of vehicular traffic flows we suggest Generalized Inverse Gaussian distribution as a theoretically and empirically substantiated alternative to the exponential distribution of priority-stream clearances, considered in Siegloch's original methodology. Furthermore, we formulate a statistical model for gap-acceptance theory and present a series of validated theoretical calculations leading to general formulas for proportion and statistical distribution of priority-stream clearances that exactly k minor-stream vehicles have utilized for their inclusion maneuver (accepted-clearance distribution of order k). Using up-to-date empirical data-sets we test hypotheses of priority-stream clearance-distribution and analyze sample acceptanceratios and empirical distribution of accepted clearances. By means of an original concept we finally estimate an implicit acceptance-rule, with the help of which a minor-street driver is deciding on acceptance/rejection of an offered priority-clearance.