Dynamic States of a Continuum Traffic Equation with On-Ramp

Abstract

We study the phase diagram of the continuum traffic flow model of a highway with an on-ramp. Using an open boundary condition, traffic states and metastabilities are investigated numerically for several representative values of the upstream boundary flux $f_{up}$ and for the whole range of the on-ramp flux $f_{rmp}$. An inhomogeneous but time-independent traffic state (standing localized cluster state) is found and related to a recently measured traffic state. Due to the density gradient near the on-ramp, a novel traffic jam can occur even when the downstream density is below the critical density of the usual traffic jam formation in homogeneous highways, and its structure varies qualitatively with $f_{rmp}$. The free flow, the recurring hump (RH) state, and the traffic jam can all coexist in a certain metastable region where the free flow can undergo phase transitions either to the RH state or to the traffic jam state. We also find two nontrivial analytic solutions. These solutions correspond to the standing localized cluster state and the homogeneous congested traffic state (one form of the novel traffic jam),which are observed in numerical simulations.

13 pages, 8 figures (to appear in Physical Review E)

References in corpus (4)

• Gas-Kinetic-Based Traffic Model Explaining Observed Hysteretic Phase Transition
• Gas-kinetic derivation of Navier-Stokes-like traffic equations
• Origin of synchronized traffic flow on highways and its dynamic phase transitions
• Fundamentals of Traffic Flow

Cited by in corpus (19)

• Congested Traffic States in Empirical Observations and Microscopic Simulations
• Traffic and Related Self-Driven Many-Particle Systems
• Cellular automata approach to three-phase traffic theory
• Micro- and Macrosimulation of Freeway Traffic
• Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts
• Control of Spatial-Temporal Congested Traffic Patterns at Highway Bottlenecks
• Theoretical vs. Empirical Classification and Prediction of Congested Traffic States
• Failure of classical traffic flow theories: Stochastic highway capacity and automatic driving
• Macroscopic traffic models from microscopic car-following models
• Statistical Physics of Traffic Flow
• Microscopic features of moving traffic jams
• Spatio-temporal structure of traffic flow in a system with an open boundary
• Phase diagram of congested traffic flow: an empirical study
• The Physics of Traffic and Regional Development
• Steady state solutions of hydrodynamic traffic models
• Localized defects in a cellular automaton model for traffic flow with phase separation
• Spectrum of the totally asymmetric simple exclusion process on a periodic lattice -- first excited states
• Traffic Flow Theory
• Common feature of concave growth pattern of oscillations in terms of speed, acceleration, fuel consumption and emission in car following: experiment and modeling