Synchronization of traffic lights for high flow

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Abstract
It is assumed here that the flow of traffic is so heavy that it can be described qualitatively by existing theories wherein each car follows another with no passing and that platoons formed by traffic lights spread so much between lights that the time between the arrival of the first and last cars of a platoon at a light exceeds the green period. Under such conditions it is shown that the best pairwise synchronization of lights gives the best overall synchronization for one-directional traffic. The synchronization which minimizes the total delay for all cars is one for which the tail car of a platoon suffers no delay but the lead car is stopped. For two-directional traffic, heavy in both directions, the best synchronization is very likely to be that which is optimal for the direction of traffic with the lower flow.

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