Phase transition of traffic states with on-ramp

We study the phase transition on a highway in a modified anisotropic continuum model with an on-ramp, which is recently developed by Gupta and Katiyar (J. Phys. A: Math. Nucl. Gen. 38 (2005) 4069]. To investigate whether this model can describe several distinct traffic states that are identified from real-traffic data [Kerner and Rehborn, Phys. Rev. Lett. 79 (1997) 4030; Kerner, Phys. Rev. Lett. 81 (1998) 3797], we carry out numerical simulations with an open boundary condition. The observed transition between free flow and various types of congested flow such as localized clusters, stop-and-go traffic and different kinds of synchronized traffic flow is obtained by applying a triggering pulse through an on-ramp in our simulation.We present the phase diagram for three representative values of the upstream boundary flux and for the whole range of the on-ramp flux. Several states like pinned localized cluster, triggered stop-and-go, recurring hump state, the oscillatory congested traffic and the homogeneous congested traffic are observed in phase transition from free flow to traffic-jam state. The phase diagram for our model near on-ramp is consistent with the results obtained by Lee et al. [Phys. Rev. E 59(5) (1999) 5101]. The results suggest that the modified model is able to describe all the three phases of traffic-flow theory developed by Kerner [Physica A 333 (2004) 379].