  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
