Analytical derivation of capacity at diverging junctions

Freeway congestion mainly occurs at discontinuities of the road network such as merges, 2 weaving sections and diverges. Reliable tools are therefore needed to estimate the operations 3 at these discontinuities and evaluate their capacity. This paper proposes an analytical model to 4 estimate the capacity at a diverging junction according to the kinematic wave theory of 5 Lighthill, Whitham and Richards. The model simply relies on the assumption that exiting 6 vehicles drive temporarily at a speed which is lower than the free-flow speed. The slow 7 vehicles are considered as moving bottlenecks. To explain the methodology, the acceleration 8 is assumed to be infinite in a first step. But, as it is a key factor explaining the capacity drop, 9 we relax this assumption in a second step by introducing a constant acceleration rate for all 10 the vehicles. Considering the moving bottleneck theory, we compute the effective flow 11 passing the diverging junction and the corresponding relative capacity drop. The analytical 12 results are assessed with micro-simulation results