One-dimensional Particle Processes with Acceleration/Braking Asymmetry

TL;DR

This paper investigates how asymmetry in acceleration and braking affects traffic flow models, revealing phenomena like spatial condensation, metastability, and providing a large deviation framework for the fundamental diagram.

Contribution

It introduces a novel asymmetry in exclusion and queueing processes, analyzing their steady states and fluctuation properties in the context of traffic flow modeling.

Findings

Observation of spatial condensation phenomena

Identification of metastability depending on asymmetry level

Development of a large deviation formulation for the fundamental diagram

Abstract

The slow-to-start mechanism is known to play an important role in the particular shape of the Fundamental diagram of traffic and to be associated to hysteresis effects of traffic flow.We study this question in the context of exclusion and queueing processes,by including an asymmetry between deceleration and acceleration in the formulation of these processes. For exclusions processes, this corresponds to a multi-class process with transition asymmetry between different speed levels, while for queueing processes we consider non-reversible stochastic dependency of the service rate w.r.t the number of clients. The relationship between these 2 families of models is analyzed on the ring geometry, along with their steady state properties. Spatial condensation phenomena and metastability is observed, depending on the level of the aforementioned asymmetry. In addition we provide a large deviation formulation of the fundamental diagram (FD) which includes the level of fluctuations, in the canonical ensemble when the stationary state is expressed as a product form of such generalized queues.