Response functions as a new concept to study local dynamics in traffic networks

TL;DR

This paper introduces response functions to analyze local traffic dynamics, revealing transient and long-term response phases influenced by congestion correlations, and models these effects using an epidemiology-inspired approach.

Contribution

It applies the concept of response functions to traffic networks and identifies distinct dynamic response phases, providing new insights into congestion propagation and recovery.

Findings

Transient response is prominent in backward congestion propagation.

Long-term response shows linear relation with congestion correlator.

Heavy congestion propagates forward and backward at similar rates, with forward sections recovering faster.

Abstract

Vehicle velocities in neighbouring road sections are correlated with memory effects. We explore the response of the velocities in the sequence of sections to a congestion in a given section and its dynamic characteristics. To this end, we transfer the concept of response functions from previous applications in finance to traffic systems. The dynamical characteristics are of particular interest. We identify two phases, a phase of transient response and a phase of long-term response. The transient response is pronounced when considering the backward propagation of heavy congestions but almost vanishes for forward propagation. For each response phase, we find a linear relation between the velocity response and the congestion correlator, implying that the correlation of congestion is most likely the cause for the velocity response. We also construct a susceptible-decelerated-withdrawing model mathematically inspired by the susceptible-infectious-recovered (SIR) model in epidemiology to describe the transient response. We find that the heavy congestion on a section propagates forward and backward at a similar rate, but the forward sections are more likely to recover from the effect of heavy congestion than the backward sections.