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Control theory -- Mathematical models, Multiagent systems, Feedback control systems, Laplacian operators


We investigate in detail what one might call the canonical (automated) traffic problem: A long string of N+1 cars (numbered from 0 to N) moves along a one-lane road “in formation” at a constant velocity and with a unit distance between successive cars. Each car monitors the relative velocity and position of only its neighboring cars. This information is then fed back to its own engine which decelerates (brakes) or accelerates according to the information it receives. The question is: What happens when due to an external influence—a traffic light turning green—the ‘zero’th’ car (the “leader”) accelerates?

As a first approximation, we analyze linear(ized) equations and show that in this scenario the traffic flow has a tendency to be stop-and-go. We give approximate solutions for the global traffic as function of all the relevant parameters (the feed back parameters as well as cruise velocity and so on). We discuss general design principles for these algorithms, that is: how does the choice of parameters influence the performance.


This is the author’s version of a work that was accepted for publication in Journal of Statistical Physics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication.

A definitive version was subsequently published in Journal of Statistical Physics and can be found online at:



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