130 research outputs found
A Compartmental Model for Traffic Networks and its Dynamical Behavior
We propose a macroscopic traffic network flow model suitable for analysis as
a dynamical system, and we qualitatively analyze equilibrium flows as well as
convergence. Flows at a junction are determined by downstream supply of
capacity as well as upstream demand of traffic wishing to flow through the
junction. This approach is rooted in the celebrated Cell Transmission Model for
freeway traffic flow. Unlike related results which rely on certain system
cooperativity properties, our model generally does not possess these
properties. We show that the lack of cooperativity is in fact a useful feature
that allows traffic control methods, such as ramp metering, to be effective.
Finally, we leverage the results of the paper to develop a linear program for
optimal ramp metering
An Adaptive Algorithm for Synchronization in Diffusively Coupled Systems
We present an adaptive algorithm that guarantees synchronization in
diffusively coupled systems. We first consider compartmental systems of ODEs,
where each compartment represents a spatial domain of components interconnected
through diffusion terms with like components in different compartments. Each
set of like components may have its own weighted undirected graph describing
the topology of the interconnection between compartments. The link weights are
updated adaptively according to the magnitude of the difference between
neighboring agents connected by the link. We next consider reaction-diffusion
PDEs with Neumann boundary conditions, and derive an analogous algorithm
guaranteeing spatial homogenization of solutions. We provide a numerical
example demonstrating the results
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