Analytical Derivation of Capacity at Diverging Junctions

Freeway congestion occurs mainly at discontinuities of the road network, such as merges, weaving sections, and diverges. Reliable tools are needed for estimating the operations at these discontinuities and evaluating their capacity. This paper proposes an analytical model that estimates the capacity at a diverging junction according to the kinematic wave theory of Lighthill, Whitham, and Richards. The model assumes that exiting vehicles drive temporarily at a speed that is lower than the free-flow speed. The slow vehicles are considered moving bottlenecks. In the methodology, the acceleration is assumed to be infinite in a first step. But, because it is a key factor in explaining the capacity drop, this assumption is relaxed in a second step through a constant acceleration rate used for all the vehicles. In this study, the moving bottleneck theory is used to compute the effective flow passing the diverging junction and the corresponding relative capacity drop. The analytical results are assessed with microsimulation results.