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Bibliography: leaf 37

Traffic signals can be synchronized so that a car, starting at one end of a main artery and traveling at preassigned speeds, can go to the other end without stopping for a red light. The portion of a signal cycle for which this is possible is called the bandwidth for that direction. Ordinarily the bandwidth in each direction is single. For this case we formulate the arterial problem as a mixed-integer linear program: Given (1) an arbitrary number of signals, (2) the fraction of the cycle that is red at each signal, (3) upper and lower limits on signal period, (4) upper and lower limits on speed each way between adjacent signals, (5) limits on change in speed, and (6) a constant of proportionality between the two bandwidths; find (1) a common signal period, (2) speeds between signals, and (3) the relative phasing of the signals so as to maximize the sum of the bandwidths. A branch and bound algorithm is developed for solving the given mixed-integer linear program by solving a sequence of ordinary linear programs. The problem of synchronizing a network of signals is also formulated. The resulting program consists of the arterial programs for the individual streets plus a set of further constraints that arise because the streets connect together to form closed loops.