The optimality condition of the multiple-cycle smoothed curve signal timing model

In this paper, we study the global optimality of the multiple-cycle smoothed curve signal timing model that was proposed in Liu et al. (2008) for individual oversaturated intersections. First, we propose a counterexample to show that the recursively decomposing design method in Liu et al. (2008) cannot guarantee the global optimality of multiple-cycle signal timing plan for all traffic scenarios. Second, we give a simple sufficient global optimality condition and show that this condition will usually be satisfied in ordinary traffic scenarios. It indicates that the powerful smoothed curve signal timing model in Liu et al. (2008) is useful in practices. This finding also provides a good starting point to further analyze the performance of oversaturated intersections.

► We explain the greedy-search nature of a powerful control algorithm.
► We give a simple sufficient global optimality condition for this algorithm.
► We show that this algorithm can be decomposed sequentially under such a condition.