A mesoscopic approach on stability and phase transition between different traffic flow states

Abstract

It is understood that congestion in traffic can be interpreted in terms of the instability of the equation of dynamic motion. The evolution of a traffic system from an unstable or metastable state to a globally stable state bears a strong resemblance to the phase transition in thermodynamics. In this work, we explore the underlying physics of the traffic system, by examining closely the physical properties and mathematical constraints of the phase transitions therein. By using a mesoscopic approach, one entitles the catastrophe model the same physical content as in the Landau's theory, and uncovers its close connections to the instability of the equation of motion and to the transition between different traffic states. In addition to the one-dimensional configuration space, we generalize our discussions to the higher-dimensional case, where the observed temporal oscillation in traffic flow data is attributed to the curl of a vector field. We exhibit that our model can reproduce the main features of the observed fundamental diagram including the inverse-λ shape and the wide scattering of congested traffic data. When properly parameterized, the main feature of the data can be reproduced reasonably well either in terms of the oscillating congested traffic or in terms of the synchronized flow.

Dynamical capacity drop in a nonlinear stochastic traffic model

“…However, it is worth noting that the scatter around the transition region may also be caused by other mechanisms besides stochastic noises. For instance, the limit cycle solution forms a closed trajectory in phase space; it may also lead to the scatter in the data even in a purely deterministic system (Qian et al, 2017b). In practice, in order to differentiate a deterministic temporal evolution from stochastic noises, we have to pay specific attention to the different time scales of the two phenomena.…”

“…The mathematical simplicity of the model provides the facility to acquire all the solutions of the EoM analytical, and subsequently, to carry out the analysis of the stability of the system as well as its relationship to traffic congestion (c.f. (Qian et al, 2017b)).…”

“…One may study the stability of the stationary solution by investigating the temporal evolution via the linearized equation of small pertubations. These solutions are stable against small deviations if the stability criterion (Qian et al, 2017b)…”

“…If one assumes that a solution is stable, one may calculate the variance of expected value following the standard procedure of Itô calculus. It is not difficult to show that the variances of the flow reads (Qian et al, 2017b)…”

Coordination Optimization of VSL Strategy on Urban Expressway and Main Road Intersection Signal

“…In relieving traffic congestion and ensuring traffic safety, traffic flow model is the key part of simulating vehicle dynamics on the network. Generally speaking, traffic flow models can be divided into macroscopic [27,28], mesoscopic [29,30] and microscopic models [31~32]. Mesoscopic traffic flow model can achieve the balance between simulation accuracy and efficiency.…”