Traffic flow is a very prominent example of a driven non-equilibrium system. A characteristic phenomenon of traffic dynamics is the spontaneous and abrupt drop of the average velocity on a stretch of road leading to congestion. Such a traffic breakdown corresponds to a boundary-induced phase transition from free flow to congested traffic. In this paper, we study the ability of selected microscopic traffic models to reproduce a traffic breakdown, and we investigate its spatiotemporal dynamics. For our analysis, we use empirical traffic data from stationary loop detectors on a German Autobahn showing a spontaneous breakdown. We then present several methods to assess the results and compare the models with each other. In addition, we will also discuss some important modeling aspects and their impact on the resulting spatiotemporal pattern. The investigation of different downstream boundary conditions, for example, shows that the physical origin of the traffic breakdown may be artificially induced by the setup of the boundaries.
A similar behavior is known from one-dimensional driven particle systems with open boundaries. The bulk dynamics of such systems is governed by the rates at which particles enter or leave the system at the boundaries @cite_4 @cite_21 @cite_9 @cite_33 . The resulting phase diagram reveals distinct phases separated by first and second order phase transitions, respectively. Depending on the inflow and outflow rates of the system, a local perturbation may move either along the flow of particles or in the opposite direction. When compared with vehicular traffic, the latter case may be interpreted as a traffic jam propagating upstream. Similarly, the shock, which marks a discontinuity in the density profile, can be seen as the jam's upstream front. Hence, a traffic breakdown is a spatiotemporal phenomenon, whose observation requires a relatively broad spatial and temporal horizon.
@cite_9 @cite_21 @cite_4 @cite_33
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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. We investigate the stationary states of one-dimensional driven diffusive systems, coupled to boundary reservoirs with fixed particle densities. We argue that the generic phase diagram is governed by an extremal principle for the macroscopic current irrespective of the local dynamics. In particular, we predict a minimal current phase for systems with local minimum in the current density relation. This phase is explained by a dynamical phenomenon, the branching and coalescence of shocks; Monte Carlo simulations confirm the theoretical scenario. We consider the asymmetric simple exclusion process (ASEP) with open boundaries and other driven stochastic lattice gases of particles entering, hopping and leaving a one- dimensional lattice. The long-term system dynamics, stationary states, and the nature of phase transitions between steady states can be understood in terms of the interplay of two characteristic velocities, the collective velocity and the shock (domain wall) velocity. This interplay results in two distinct types of domain walls whose dynamics is computed. We conclude that the phase diagram of the ASEP is generic for one-component driven lattice gases with a single maximum in the current-density relation.