  The main motivation of this work is to assess the validity of a LWR traffic
flow model to model measurements obtained from trajectory data, and propose
extensions of this model to improve it. A formulation for a discrete dynamical
system is proposed aiming at reproducing the evolution in time of the density
of vehicles along a road, as observed in the measurements. This system is
formulated as a chemical reaction network where road cells are interpreted as
compartments, the transfer of vehicles from one cell to the other is seen as a
chemical reaction between adjacent compartment and the density of vehicles is
seen as a concentration of reactant. Several degrees of flexibility on the
parameters of this system, which basically consist of the reaction rates
between the compartments, can be considered: a constant value or a function
depending on time and/or space. Density measurements coming from trajectory
data are then interpreted as observations of the states of this system at
consecutive times. Optimal reaction rates for the system are then obtained by
minimizing the discrepancy between the output of the system and the state
measurements. This approach was tested both on simulated and real data, proved
successful in recreating the complexity of traffic flows despite the
assumptions on the flux-density relation.
