Traffic states of a model highway with on-ramp

Several distinct traffic states are identified from real highway traffic data (Kerner and Rehborn, Phys. Rev. Lett. 79 (1997) 4030. Kerner and Rehborn, Phys. Rev. E 53 (1996) R4275; Kerner, Phys. Rev. Lett. 81 (1998) 3797, Kerner and Rehborn, Phy's. Rev. E 53 (1996) R1297). Influence of on-ramp flux is Important In generating the stop-and-go traffic flow near the ramps (Lee ct at.. Phys. Rev. Lett. 81 (1998) 1130; Lee et al., Phys. Rev. E 59 (1999) 5101). In this work, we study the phase diagram of the continuum traffic flow model equation in the presence of an on-lamp. Using an open boundary condition, traffic stales and metastabilities are investigated for several representative values of the upstream boundary flux and for a range of the on-ramp Bur. We rind several traffic states such as the pinned localized cluster (PLC) slate, the oscillating pinned localized cluster (OPLC) or the recurring hump (RH) state, the oscillating congested traffic (OCT) stare and the homogeneous congested traffic (HCT) state. The latter two are traffic jam states. The free flow, the OPLC stare and the jam can coexist in a certain metastable region : here the free Row can undergo phase transitions to tither of the two states under fluctuations. Some of these stares are related to observed traffic states. (C) 2000 Elsevier Science B.V. All rights reserved.