Disorder Effect On The Traffic Flow Behavior
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
Traffic flow has attracted interest of physicists for a long time. A large number of approach and models have been proposed and studied using different methods, microscopic, macroscopic and mesoscopic. These models are based on empirical results.
Starting from a homogeneous traffic flow, the behavior may change by the introduction of disorder of different types; mixture of vehicles lengths and/or vehicles velocity, works on the road, weather, reduction of lanes in the free way.
The effects of some of these disorders, on the traffic flow behavior, are given. Especially, the effect of mixture of vehicles of different velocities and/or lengths, the effects of different drivers reactions, the position and the extraction rate of off-ramp in the free way,
.
Using a generalized optimal velocity model, for a mixture of fast and slow vehicles, we have investigated the effect of delay times and on the fundamental diagram. It is
Found that the small delay times have almost no effect, while, for sufficiently large delay time , the current profile displays qualitatively five different forms, depending on , and the fractions and of the fast and slow cars, respectively. The velocity (current) exhibits first-order transitions at low and/or high densities, from freely moving phase to the congested state, and from congested state to a jamming one, respectively. The minimal current appears in intermediate values of. Furthermore there exist, a critical value of above which the metastability and hysteresis appear.
The effects of disorder due to drivers behaviors have been introduced through a random delay time allowing the car to reach its optimal velocity traffic flow models with open boundaries. In the absence of the variation of the delay time , it is found that the transition from unstable to metastable and from metastable to stable state occur under the effect of the injecting and the extracting rate probabilities and respectively. For a fixed value of , there exist a critical value of the extraction rate , above which the metastable state disappears, while the stable state appears.
and depend on the values of and the variation of delay time . Indeed and increase when increasing and/or decreasing . The phase diagrams in the plane exhibits a first order transitions between stable phase and the unstable one. While the transition between stable (unstable) phase and the metastable phase are of second order type. The region of the metastable phase shrinks with increasing the variation of the delay time and disappears completely above a critical value .
The perturbation of the traffic flow behavior due to the off-ramp has been studied using numerical simulations in the one dimensional cellular automaton traffic flow model with open boundaries. When the off-ramp is located between two critical positions and the current increases with the extracting rate , for , and exhibits a plateau (constant current) for and decreases with for . However, the density undergoes two successive first order transitions: from high density to plateau current phase at ; and from average density to the low one at . In the case of two off-ramps located respectively at and , these transitions occur only when the distance between ramps, is smaller than a critical value. Phase diagrams in the , and phases exhibit first order transition between free traffic, congested traffic and plateau current phases. Furthermore, the competition between the off-ramp and on-ramp rate probabilities leads to the appearance of a sequence of first order transition between the free flow, plateau current and jamming phases. However, phase diagrams in the (on-ramp position , on-ramp injecting probability) plane exhibits critical, tricritical and multicritical behavior for special values of the off-ramp extracting probability.