Study on dynamic system optimum assignment to establish marginal time equilibrium

Several analytical methods for Dynamic System Optimum (DSO) assignment have been proposed but they are basically classified into two kinds. This chapter attempts to establish DSO by equilbrating the path dynamic marginal time (DMT). The authors analyze the path DMT for a single path with tandem bottlenecks and showed that the path DMT is not the simple summation of DMT associated with each bottleneck along the path. Next, the authors examined the DMT of several paths passing through a common bottleneck. It is shown that the externality at the bottleneck is shared by the paths in proportion to their demand from the current time until the queue vanishes. This share of the externality is caused by the departure rate shift under first in first out (FIFO) and the externality propagates to the downstream bottlenecks. However, the externalities propagates to the downstream are calculated out if downstream bottlenecks exist. Therefore, the authors concluded that the path DMT can be evaluated without considering the propagation of the externalities, but just as in the evaluation of the path DMT for a single path passing through a series of bottlenecks between the origin and destination. Based on the DMT analysis, the authors finally proposed a heuristic solution algorithm and verified it by comparing the numerical solution with the analytical one.