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, Phys. Rev. E 53 (1996) R1297). Influence of on-ramp flux is important in generating the stop-and-go traffic flow near the ramps (Lee et al., 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-ramp. Using an open boundary condition, traffic states and metastabilities are investigated for several representative values of the upstream boundary flux and for a range of the on-ramp flux. We find several traffic states such as the pinned localized cluster (PLC) state, the oscillating pinned localized cluster (OPLC) or the recurring hump (RH) state, the oscillating congested traffic (OCT) state and the homogeneous congested traffic (HCT) state. The latter two are traffic jam states. The free flow, the OPLC state and the jam can coexist in a certain metastable region where the free flow can undergo phase transitions to either of the two states under fluctuations. Some of these states are related to observed traffic states.