Abstract
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.
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Some beautiful photographs of these phenomenona can be found in http://epod.usra.edu/archive/images/sortsolsum-05042006-hw.jpg
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We thank Arturo Olvera and the referee for several useful remarks. JJPV gratefully acknowledges grants through the Dip. Ing. Inf. & Mat. App., Univ. di Salerno, Salerno, Italy, and the Ist. ‘Mauro Piccone’ per le Applicazioni del Calcolo, Rome, Italy, that made an extended stay at these institutions possible, as well as the generous hospitality offered by these institutions.
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Veerman, J.J.P., Stošić, B.D. & Tangerman, F.M. Automated Traffic and the Finite Size Resonance. J Stat Phys 137, 189–203 (2009). https://doi.org/10.1007/s10955-009-9816-z
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DOI: https://doi.org/10.1007/s10955-009-9816-z