Prediction of minor stream delays at a limited priority freeway merge

Abstract

This paper presents the development and application of a limited priority gap acceptance model to freeway merging. In the limited priority model, drivers in the major stream at a merge area may incur delay in restoring small headways to a larger, sustainable minimum headway between them and the vehicle in front. This allows minor stream drivers to accept smaller gaps. The headway distributions are assumed to be distributed according to Cowan’s M3 model, whose terms were calibrated for this system. Minor stream minimum follow-on time was calibrated, and a realistic range of the critical gap identified. An equation was developed for minimum average minor stream delay. A function was identified to model the relationship between minor stream average delay and degree of saturation. The shape parameter of this function was calibrated using simulated traffic flow data, under three different minor stream arrival pattern regimes. The model provides a useful means of comparing performance, through average minor stream delay, for varying minor and major stream flow rates and minor stream critical gap, under arrival patterns that differ due to traffic control upstream of the on-ramp. Minor stream delay is a particularly useful measure of effectiveness for uncongested freeway merging as it relates directly to the distance required to merge. Observations from the model developed provide physical evidence that minor stream drivers incur lesser delay, or have a better chance of merging quickly, when they arrive at constant intervals as is the case under constant departure ramp metering, than when they arrive in bunches downstream of a signalised intersection, or even a semi-bunched state downstream of an unsignalised intersection.