The optimal velocity traffic flow models with open boundaries
Laboratoire de Magnétisme et de Physique des Hautes Énergies,
Département de Physique, Faculté des Sciences, BP 1014, Rabat, Morocco
Corresponding author: a firstname.lastname@example.org
Published online: 8 December 2003
The effects of the open boundaries on the dynamical behavior of the optimal velocity traffic flow models with a delay time τ allowing the car to reach its optimal velocity is studied using numerical simulations. The particles could enter the chain with a given injecting rate probability α, and could leave the system with a given extracting rate probability . 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 probabilities rates α and β. However, for a fixed value of α, there exist a critical value of the extraction rate above which the wave density disappears and the metastable state appears and a critical value above which the metastable state disappears while the stable state appears. and depend on the values of α and the variation of the delay time . Indeed and increase when increasing α and/or decreasing . The flow of vehicles is calculated as a function of α, β and for a fixed value of τ. Phase diagrams in the () plane exhibits four different phases namely, unstable, metastable, stable. The transition line between stable phase and the unstable one is curved and it is of first order type. 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 .
PACS: 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.) / 64.60.Cn – Order-disorder transformations; statistical mechanics of model systems / 75.30.Kz – Magnetic phase boundaries (including magnetic transitions, metamagnetism, etc.) / 82.20.Wt – Computational modeling; simulation
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2003