  Efficient and exact algorithms are important for performing fast and accurate
traffic network simulations with macroscopic traffic models. In this paper, we
extend the semi-analytical Lax-Hopf algorithm in order to compute link inflows
and outflows with the LWR model. Our proposed Fax Lax-Hopf algorithm has a very
low computational complexity. We demonstrate that some of the original
algorithm's operations (associated with the initial conditions) can be
discarded, leading to a faster computation of boundary demand/supplies in
network simulation problems, for general concave fundamental diagrams.
Moreover, the computational cost can be further reduced for triangular
Fundamental Diagrams and specific space-time discretizations. The resulting
formulation has a performance comparable to the Link Transmission Model and,
since it solves the original LWR model for a wide range of FD shapes, with any
initial configuration, it is suitable to solve a broad range of traffic
operations problems. As part of the analysis, we compare the performance of the
proposed scheme to other well-known computational methods.

Analysis of PDEs