On the numerical treatment of moving bottlenecks

This paper shows how moving obstructions in (kinematic wave) traffic streams can be modeled with “off-the shelf” computer programs. It shows that if a moving obstruction is replaced by a sequence of fixed obstructions at nearby locations with the same “capacity”, then the error in vehicle number converges uniformly to zero as the maximum separation between the moving and fixed bottlenecks is reduced. This result implies that average flows, densities, accumulations and delays can be predicted as accurately as desired with this method. Thus, any convergent finite difference scheme can be used to model moving bottlenecks. The approach can be used with non-concave fundamental diagrams and multiple bottlenecks, even if they pass each other. Examples are given. It is assumed that the bottleneck trajectories are exogenous to the model. However, by introducing suitable car-following laws and interaction rules, slow trucks and busses embedded in the traffic stream can be modeled endogenously.