Data-Driven Models for Traffic Flow at Junctions

The simulation of traffic flow on networks requires knowledge on the behavior across traffic intersections. For macroscopic models based on hyperbolic conservation laws there exist nowadays many ad-hoc models describing this behavior. Based on real-world car trajectory data we propose a new class of data-driven models with the requirements of being consistent to networked hyperbolic traffic flow models. To this end the new models combine artificial neural networks with a parametrization of the solution space to the half-Riemann problem at the junction. A method for deriving density and flux corresponding to the traffic close to the junction for data-driven models is presented. The models parameter are fitted to obtain suitable boundary conditions for macroscopic first and second-order traffic flow models. The prediction of various models are compared considering also existing coupling rules at the junction. Numerical results imposing the data-fitted coupling models on a traffic network are presented exhibiting accurate predictions of the new models.Comment: 27 pages, 9 figures, 6 table

A characteristic particle method for traffic flow simulations on highway networks

A characteristic particle method for the simulation of first order macroscopic traffic models on road networks is presented. The approach is based on the method "particleclaw", which solves scalar one dimensional hyperbolic conservations laws exactly, except for a small error right around shocks. The method is generalized to nonlinear network flows, where particle approximations on the edges are suitably coupled together at the network nodes. It is demonstrated in numerical examples that the resulting particle method can approximate traffic jams accurately, while only devoting a few degrees of freedom to each edge of the network.Comment: 15 pages, 5 figures. Accepted to the proceedings of the Sixth International Workshop Meshfree Methods for PDE 201

Asymmetric exclusion process with next-nearest-neighbor interaction: some comments on traffic flow and a nonequilibrium reentrance transition

We study the steady-state behavior of a driven non-equilibrium lattice gas of hard-core particles with next-nearest-neighbor interaction. We calculate the exact stationary distribution of the periodic system and for a particular line in the phase diagram of the system with open boundaries where particles can enter and leave the system. For repulsive interactions the dynamics can be interpreted as a two-speed model for traffic flow. The exact stationary distribution of the periodic continuous-time system turns out to coincide with that of the asymmetric exclusion process (ASEP) with discrete-time parallel update. However, unlike in the (single-speed) ASEP, the exact flow diagram for the two-speed model resembles in some important features the flow diagram of real traffic. The stationary phase diagram of the open system obtained from Monte Carlo simulations can be understood in terms of a shock moving through the system and an overfeeding effect at the boundaries, thus confirming theoretical predictions of a recently developed general theory of boundary-induced phase transitions. In the case of attractive interaction we observe an unexpected reentrance transition due to boundary effects.Comment: 12 pages, Revtex, 7 figure

A destination-preserving model for simulating Wardrop equilibria in traffic flow on networks

In this paper we propose a LWR-like model for traffic flow on networks which allows one to track several groups of drivers, each of them being characterized only by their destination in the network. The path actually followed to reach the destination is not assigned a priori, and can be chosen by the drivers during the journey, taking decisions at junctions. The model is then used to describe three possible behaviors of drivers, associated to three different ways to solve the route choice problem: 1. Drivers ignore the presence of the other vehicles; 2. Drivers react to the current distribution of traffic, but they do not forecast what will happen at later times; 3. Drivers take into account the current and future distribution of vehicles. Notice that, in the latter case, we enter the field of differential games, and, if a solution exists, it likely represents a global equilibrium among drivers. Numerical simulations highlight the differences between the three behaviors and suggest the existence of multiple Wardrop equilibria

Proportional fairness and its relationship with multi-class queueing networks

We consider multi-class single-server queueing networks that have a product form stationary distribution. A new limit result proves a sequence of such networks converges weakly to a stochastic flow level model. The stochastic flow level model found is insensitive. A large deviation principle for the stationary distribution of these multi-class queueing networks is also found. Its rate function has a dual form that coincides with proportional fairness. We then give the first rigorous proof that the stationary throughput of a multi-class single-server queueing network converges to a proportionally fair allocation. This work combines classical queueing networks with more recent work on stochastic flow level models and proportional fairness. One could view these seemingly different models as the same system described at different levels of granularity: a microscopic, queueing level description; a macroscopic, flow level description and a teleological, optimization description.Comment: Published in at http://dx.doi.org/10.1214/09-AAP612 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org