In this paper a new traffic flow model for congested arterial networks, named shockwave profile model (SPM), is presented. Taking advantage of the fact that traffic states within a congested link can be simplified as free-flow, saturated, and jammed conditions, SPM simulates traffic dynamics by...

For uninterrupted traffic flow, it is well-known that the fundamental diagram (FD) describes the relationship between traffic flow and density under steady state. For interrupted traffic flow on a signalized road, it has been recognized that the arterial fundamental diagram (AFD) is...

The Braess paradox and its variants have been studied under the perfectly rational behavior assumption. However, when the perfect rationality assumption is relaxed to bounded rationality, which assumes that travelers can take any route whose travel cost is within an ‘indifference band’ of...

Probabilistic models describing macroscopic traffic flow have proven useful both in practice and in theory. In theoretical investigations of wide-scatter in flow–density data, the statistical features of flow density relations have played a central role. In real-time estimation and traffic...

A Gaussian approximation of the stochastic traffic flow model of Jabari and Liu (2012) is proposed. The Gaussian approximation is characterized by deterministic mean and covariance dynamics; the mean dynamics are those of the Godunov scheme. By deriving the Gaussian model, as opposed to assuming...

Existing day-to-day traffic assignment models are all built upon path flow variables. This paper demonstrates two essential shortcomings of these path-based models. One is that their application requires a given initial path flow pattern, which is typically unidentifiable, i.e. mathematically...

A network change is said to be irreversible if the initial network equilibrium cannot be restored by revoking the change. The phenomenon of irreversible network change has been observed in reality. To model this phenomenon, we develop a day-to-day dynamic model whose fixed point is a boundedly...

This paper is the second of a two-part research wherein we undertake a mathematically rigorous investigation of the continuous-time dynamic user equilibrium (DUE) problem using the recently introduced mathematical paradigm of differential complementarity systems (DCSs). Based on the thorough...

How to optimally allocate limited freeway sensor resources is of great interest to transportation engineers. In this paper, we focus on the optimal allocation of point sensors, such as loop detectors, to minimize performance measurement errors. Although it has been shown that the minimization...

Boundedly rational user equilibria (BRUE) represent traffic flow distribution patterns where travellers can take any route whose travel cost is within an ‘indifference band’ of the shortest path cost. Those traffic flow patterns satisfying the above condition constitute a set, named the BRUE...