Parameter and density estimation from real-world traffic data: A kinetic compartmental approach

Abstract

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.

Short-term traffic prediction using physics-aware neural networks

“…Remark 2.3. The TRM can be derived by assimilating the traffic flow dynamic (on the discretized road) to a chemical reaction network [19,25]. More precisely, each cell is modeled as a compartment containing two (homogeneously-distributed) fictional chemical reactants: molecules of occupied space O j and molecules of free space F j .…”

“…As for the coefficients C j et q j , they are seen as respectively reaction rates between compartments and external intakes or outtakes of reactants (cf. [25] for details).…”

“…We propose to use the TRM RNN in Section 3.2 to model the evolution of the traffic along the road between t −Np+1 and t N f . We hence consider a TRM defined on the discretized road, and to comply with the CFL condition (4), we follow the multilevel approach proposed in [25] and consider a time step ∆t for the TRM given by ∆t = ∆T /P t where P t is an integer such that…”

“…Such a choice ensures that ∆t and ∆x satisfy the CFL condition (4), and therefore the stability of the TRM [19,25].…”

“…This scheme models flow dynamics along a discretized road as a chain of chemical reactions happening between adjacent cells (now seen as compartments containing "fictional" chemical reactants). This scheme was shown to be able to reproduce complex traffic pattern observed when performing state and parameter estimation from real-world traffic data [25]. It also allows to assimilate the space-time varying parameters of the macroscopic traffic model to dimensionless and bounded parameters that are interpreted as the reaction rates of the chemical reactions mentioned above.…”