A fast semi-analytic algorithm for computing solutions associated with multiple moving or fixed bottlenecks: Application to joint scheduling and signal timing

Moving and fixed bottlenecks are moving or fixed capacity restrictions that affect the propagation of traffic flow. They are a very important modeling approach to describe the effects of slow vehicles and traffic signals in transportation networks. However, the computation of solutions associated with the presence of fixed and moving bottlenecks is complex, since they both influence and are influenced by traffic. In this study, we propose a fast numerical scheme that can efficiently compute the solutions to an arbitrary number of fixed and moving bottlenecks, for a stretch of road modeled by the Lighthill-Whitham-Richards (LWR) model with triangular fundamental diagram. The numerical scheme is based on a semi-analytic Lax-Hopf formula that requires a very low number of operations compared with existing schemes. We illustrate the performance of the numerical scheme on scenarios involving multiple slow vehicles and traffic signals, and demonstrate that this scheme can be part of an optimization loop to simultaneously optimize the schedule of several heavy-duty vehicles and traffic signals in a city for alleviating traffic congestion