Stochastic Processes of Moving Bottlenecks

Abstract

This paper presents a general framework for developing formulas to estimate the capacity of freeway bottlenecks caused by the presence of slow vehicles. These underperforming vehicles may represent trucks on an uphill grade, cautious lane changers at a weaving section, or any other stream of vehicles moving consistently—at least for a short period of time—more slowly than prevailing traffic. From modeling of the underperforming stream as simplified yet realistic stochastic processes, closed-form expressions for the segment's capacity can be obtained. Four such processes are presented and exemplified for the case of short uphill grades, a type of facility where existing capacity formulas fail. The proposed models—which do not need calibration—improve current estimates, and one in particular explains existing data with remarkable accuracy.