Bandwidth maximization: Split and unsplit solutions

The mathematical formulation of the problem of maximizing the green band in a two-way street is performed. In so doing, in addition to problems for which the bandwidths are unsplit, we consider cases in which the bandwidths in a single cycle, in one or both directions, are split into two intervals separated by a red time. The expression of the bandwidth as a function of the offset and the distance between a pair of signals is not the same for every possible value of these variables. However, the system is periodic in space as well as in time. It is, moreover, symmetrical with respect to a half-period both in time and in space. These properties made it possible to find, without ambiguity, the different expressions of the bandwidth and the best solution for any given pair of signals. As a result, when the best solution is of the split type, it is, obviously, better than the one of the unsplit type; however, the differences, usually small for a pair of signals, are generally negligible or nil for a sequence of a sufficiently large number of signals.