On the basis of assumptions about the behavior of driver-vehicle units concerning acceleration, deceleration, overtaking, and lane-changing maneuvers, a gas-kinetic traffic model for unidirectional multi-lane freeways is constructed. Queuing effects are explicitly taken into account in an...

A coupled forward–backward stochastic differential system (FBSDS) is formulated in spaces of fields for the incompressible Navier–Stokes equation in the whole space. It is shown to have a unique local solution, and further if either the Reynolds number is small or the dimension of the...

There are three methods for analysing the flow and pressure distribution in looped water supply networks (the loop method, the node method, the pipe method), accounting for the chosen unknown hydraulic parameters. For all of these methods, the nonlinear system of equations can be solved using...

The analysis and numerical solution of non-equilibrium traffic flow models in current literature are almost exclusively carried out in the hyperbolic conservation law framework, which requires a good understanding of the delicate and non-trivial Riemann problems for conservation laws. In this...

This paper shows that traffic hysteresis arises due to variable driver characteristics within each driver and has a profound reproducible impact on the periodicity and development of traffic oscillations and the bottleneck discharge rate. Following an oscillation, traffic initially exhibits...

The Newell–Daganzo merge model is not only very simple but also accurately reproduces experimental findings. However, the capacity downstream of the merge is an exogenous variable in the model. This is a serious limitation for merges that behave as active bottlenecks because their downstream...