The Optimal Velocity Traffic Flow Models With Open Boundary

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 β. In the absence of the variation of the delay time ∆τ, 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 βc1 above which the wave density disappears and the metastable state appears and a critical value βc2 above which the metastable state disappears while the stable state appears. βc1 and βc2 depend on the values of α and the variation of the delay time ∆τ. Indeed βc1 and βc2 increase when increasing α and/or decreasing ∆τ. The flow of vehicles is calculated as a function of α, β and ∆τ for a fixed value of τ. Phase diagrams in the (α,β) 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 ∆τ and disappears completely above a critical value ∆τc .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 β. In the absence of the variation of the delay time ∆τ, 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 βc1 above which the wave density disappears and the metastable state appears and a critical value βc2 above which the metastable state disappears while the stable state appears. βc1 and βc2 depend on the values of α and the variation of the delay time ∆τ. Indeed βc1 and βc2 increase when increasing α and/or decreasing ∆τ. The flow of vehicles is calculated as a function of α, β and ∆τ for a fixed value of τ. Phase diagrams in the (α,β) 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 ∆τ and disappears completely above a critical value ∆τc

The Effect Of Delay Times On The Optimal Velocity Traffic Flow Behavior

We have numerically investigated the effect of the delay times $\tau_f$ and $\tau_s$ of a mixture of fast and slow vehicles on the fundamental diagram of the optimal velocity model. The optimal velocity function of the fast cars depends not only on the headway of each car but also on the headway of the immediately preceding one. It is found that the small delay times have almost no effects, while, for sufficiently large delay time $\tau_s$ the current profile displays qualitatively five different forms depending on $\tau_f$, $\tau_s$ and the fractions $d_f$ and $d_s$ 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 the jamming one respectively accompanied by the existence of a local minimal current. Furthermore, there exist a critical value of $\tau_f$ above which the metastability and hysteresis appear. The spatial-temporal traffic patterns present more complex structur

The optimal velocity traffic flow models with open boundaries

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 $\beta$. In the absence of the variation of the delay time $\Delta\tau$, 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 $\beta_{c_1}$ above which the wave density disappears and the metastable state appears and a critical value $\beta_{c_2}$ above which the metastable state disappears while the stable state appears. $\beta_{c_1}$ and $\beta_{c_2}$ depend on the values of α and the variation of the delay time $\Delta\tau$. Indeed $\beta_{c_1}$ and $\beta_{c_2}$ increase when increasing α and/or decreasing $\Delta\tau$. The flow of vehicles is calculated as a function of α, β and $\Delta\tau$ for a fixed value of τ. Phase diagrams in the ($\alpha,\beta$) 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 $\Delta\tau$ and disappears completely above a critical value $\Delta\tau_{c}$