Interaction of dynamic user optimal route choice and signal timing on a signalized transportation network

In this paper, the interaction of traffic signal timing and dynamic user optimal (DUO) route choice is studied. The problem is modeled as a Stackelberg game, with the leader minimizing total queuing delay by setting signal timing under the DUO flow status determined by the follower, and the follower finding the DUO flow given a fixed signal timing determined by the leader. The model and algorithm are applied to a simulation network in six cases with different cycle lengths and the interaction of traffic timing and the DUO are analyzed. The result indicates that different signal timing results in different DUO statuses, and different DUO flow pattern leads to different optimal signal timing, and the interaction of traffic signal timing and the DUO will reach equilibrium in which traffic signal timing reaches optimal and traffic reaches the DUO status. In all six cases, both the total travel time and the total queued vehicles under optimal signal timing are less than under initial signal timing. The percentage of travel time drop is 3.82%, 5.18%, 6.83%, 7.49%, 8.11%, and 9.26%, respectively, in each case. The percentage of queued vehicles drop is 42.11%, 42.11%, 37.21%, 37.21%, 37.21%, and 37.21%, respectively, in each case. In addition, the total travel time of all the demand increases with the increase of the cycle length under optimal or under initial signal timing. This is because a more considerable cycle length may cause more delay under under-saturation conditions.