Behaviour of traffic on a link with traffic light boundaries

TL;DR

This paper models traffic flow on a single link with traffic lights at both ends using hydrodynamic and stochastic domain wall theories, comparing results with NaSch simulations and analyzing parameter impacts.

Contribution

It introduces a combined hydrodynamic and stochastic domain wall approach to analyze traffic evolution with traffic lights, providing analytical expressions and insights into boundary effects.

Findings

Hydrodynamic model approximates short-term traffic behavior.

Domain wall model accurately reproduces local density evolution.

Signal offset significantly influences traffic flow.

Abstract

This paper considers a single link with traffic light boundary conditions at both ends, and investigates the traffic evolution over time with various signal and system configurations. A hydrodynamic model and a modified stochastic domain wall theory are proposed to describe the local density variation. The Nagel-Schreckenberg model (NaSch), an agent based stochastic model, is used as a benchmark. The hydrodynamic model provides good approximations over short time scales. The domain wall model is found to reproduce the time evolution of local densities, in good agreement with the NaSch simulations for both short and long time scales. A systematic investigation of the impact of network parameters, including system sizes, cycle lengths, phase splits and signal offsets, on traffic flows suggests that the stationary flow is dominated by the boundary with the smaller split. Nevertheless, the signal offset plays an important role in determining the flow. Analytical expressions of the flow in relation to those parameters are obtained for the deterministic domain wall model and match the deterministic NaSch simulations. The analytic results agree qualitatively with the general stochastic models. When the cycle is sufficiently short, the stationary state is governed by effective inflow and outflow rates, and the density profile is approximately linear and independent of time.