The Dilemma-Zone Calculation

Yellow traffic lights posed and provided an opportunity for applied mathematicians. Witness this study, published more than a half century ago:

“The Problem of the Amber Signal Light in Traffic Flow,” Denos Gazis [pictured here, reportedly thrilling an audience],  Robert Herman,  and Alexei Maradudint, Operations Research, vol. 8, no. 1, 1960, pp. 112-132. The authors, at General Motors Corporation, Warren, Michigan, explain:

“A theoretical analysis and observations of the behavior of motorists confronted by an amber signal light are presented. A discussion is given of the following problem: when confronted with an improperly timed amber light phase a motorist may find himself, at the moment the amber phase commences, in the predicament of being too close to the intersection to stop safely or comfortably and yet too far from it to pass completely through the intersection before the red signal commences. The influence on this problem of the speed of approach to the intersection is analyzed. Criteria are presented for the design of amber signal light phases through whose use such ‘dilemma zones’ can be avoided, in the interest of over-all safety at intersections…

“Many  drivers take the  attitude  that  there is nothing sacred about the speed  limit!… From [simple calculations] we see that  even if the driver is willing to  accelerate to speeds greatly  in excess of the speed limit,  he still cannot eliminate the dilemma zone.”

BONUS: A modern use of that research