A nonlinear heat equation arising from automated-vehicle traffic flow models

On a Functional-Differential Equation Arising from a Traffic Flow Model

We provide a derivation in the context of a traffic flow model, and both analytical and numerical studies of the functional-differential equation (z(s) + α)2z′(s) = β(z(s+ z(s)) − z(s)). Here, α and β are positive parameters, and we are in particular investigating the existence and properties of non-constant “traveling-wave” type solutions.

Traffic Flow Analysis Based on Queuing Models

One of the most important issues in the plant layout design especially in mass production organizations with high inter-plant logistics is‘material flow and inter-plant traffic analysis and its effects on the production capabilities or pauses in production lines. In this paper the inter-plant traffic analysis issue on the basis of single channel queue model (M/M/1) is analyzed in a carmaker c...

Integrated Traffic Flow Models and Analysis for Automated Vehicles

With the emergence of connected and automated vehicle (CAV) technologies, research on traffic flow modeling and analysis will play a very important role in improving our understanding of the fundamental characteristics of traffic flow. The frontier of studies on CAV systems have examined the impacts of CAVs on freeway bottleneck capacity, and macroscopic traffic flow, CAV B. van Arem Delft Univ...

Null Controllability of a Nonlinear Heat Equation

On a Nonlinear Matrix Equation Arising in Nano Research

The matrix equation X + AXA = Q arises in Green’s function calculations in nano research, where A is a real square matrix and Q is a real symmetric matrix dependent on a parameter and is usually indefinite. In practice one is mainly interested in those values of the parameter for which the matrix equation has no stabilizing solutions. The solution of interest in this case is a special weakly st...