Detecting Dynamic Traffic Assignment Capacity Paradoxes: Analysis of Non-Saturated Networks

In Akamatsu and Heydecker (2003), we presented a necessary and sufficient condition for the occurrence of capacity paradoxes in general saturated networks, in which there is a queue on each link. The present paper extends that analysis to the more usual case of non-saturated networks, in which there are queues on some links but not on others. First we formulate dynamic user equilibrium (DUE) assignment in non-saturated networks. We then show how non-saturated networks can be reduced by direct network transformations to corresponding saturated ones in a way that will not affect occurrence of the capacity paradoxes: the reduced network, which is saturated, can then be tested for DUE assignment paradoxes to determine whether or not they will occur in the original one. This technique therefore yields a convenient method to examine whether or not the paradox occurs from information on the queuing patterns on the links of the network. Finally, as an application of the theory, we consider a range of example networks and associated applications, including investigation of a freeway ramp metering strategy. The analysis of these networks leads to an interesting finding: it is likely that in many situations metering or closing a freeway entrance ramp can play an effective role to reduce travel times not only on the freeway but also in the whole network including arterial streets.