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Moving and fixed bottlenecks are moving or fixed capacity restrictions thataffect the propagation of traffic flow. They are a very important modelingapproach to describe the effects of slow vehicles and traffic signals intransportation networks. However, the computation of solutions associated withthe presence of fixed and moving bottlenecks is complex, since they bothinfluence and are influenced by traffic. In this study, we propose a fastnumerical scheme that can efficiently compute the solutions to an arbitrarynumber of fixed and moving bottlenecks, for a stretch of road modeled by theLighthill-Whitham-Richards (LWR) model with triangular fundamental diagram. Thenumerical scheme is based on a semi-analytic Lax-Hopf formula that requires avery low number of operations compared with existing schemes. We illustrate theperformance of the numerical scheme on scenarios involving multiple slowvehicles and traffic signals, and demonstrate that this scheme can be part ofan optimization loop to simultaneously optimize the schedule of severalheavy-duty vehicles and traffic signals in a city for alleviating trafficcongestion

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