Critical damping in a kinetic interaction network

In a kinetic interaction network, signals are emitted through motion. Natural examples include bird flocks, fish schools, and robot teams. A kinetic interaction network transmits information about external cues quickly and accurately. Analysis of a one-dimensional interaction network reveals a bound on the algebraic connectivity above which the transient response is overdamped. A critically damped response, the fastest and most accurate, is achieved by maximizing the algebraic connectivity subject to this bound. For example, in an n-neighbor interaction network, output rise time is minimized for intermediate values of n. This analytical result yields insight into natural networks and a design method for synthetic networks. We apply this result to automobile congestion by extending the Intelligent Driver Model to include interactions with multiple vehicles. Simulations indicate that, in certain portions of parameter space, traffic flow is improved by including directed interactions with an intermediate number of vehicles.