On Driver Anticipation, Two-Regime Flow, Fundamental Diagrams, and Kinematic-Wave Theory

Abstract

The Cellular Automata (CA) Model CA-184a is introduced as a simplified traffic model that incorporates a rudimentary representation of driver anticipation. Simulations of single-loop and dual-loop acquisition of density-flow data upstream of a bottleneck are shown to display either a considerable similarity to density-flow data commonly so observed in vehicular traffic (i.e., two-regime flow, including an “inverted-lambda” shape), or a well-defined but clearly unrealistic density-flow relationship (fundamental diagram, FD), depending sensitively on the details of how the data are acquired. Simulation on a closed loop leads to stationary equilibria that provide a well-defined FD that is not manifestly unrealistic. The kinematic-wave model (KWM), employed with this closed-loop stationary equilibrium FD, provides results that agree arguably well, with some caveats, with the time-series data (upstream of the bottleneck) that generated the two-regime inverted-lambda FD. The source of the sensitivity of density-flow data to details of data acquisition is a strong correlation, in enqueued flow, between observed speeds and position relative to the bottleneck. This correlation, along with demand fluctuations near saturation, accounts for the departure from kinematic-wave predictions of simulated loop-based density-flow observations upstream of a bottleneck.