Detecting Dynamic Traffic Assignment Capacity Paradoxes in Saturated Networks

Akamatsu, Takashi; Heydecker, Benjamin · 2003 · Crossref

DOI: 10.1287/trsc.37.2.123.15245

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Summary

This paper extends the theory of dynamic traffic assignment capacity paradoxes from saturated networks, where every link experiences queuing, to non-saturated networks, where queues exist on only some links. The capacity paradox is defined as a counterintuitive situation where increasing the capacity of a specific link leads to an increase in total network travel time, or decreasing capacity reduces travel time. While previous work established necessary and sufficient conditions for this paradox in fully saturated networks, this study addresses the more common scenario of mixed queuing patterns. The research is motivated by the need to apply these theoretical insights to general transportation networks and to evaluate traffic management strategies, such as freeway ramp metering, in realistic conditions. The authors formulate dynamic user equilibrium (DUE) in non-saturated networks using a First-in-First-Out (FIFO) principle and deterministic queuing. They partition the network links into saturated sets ($L_Q$) and unsaturated sets ($L_F$). The core methodological contribution is a network reduction technique that transforms a non-saturated network into an equivalent saturated "reduced network." This is achieved by unifying the initial and terminal nodes of each unsaturated link into a single node, effectively removing unsaturated links from the analysis. The authors prove that this transformation preserves the occurrence of capacity paradoxes. Consequently, the established conditions for paradoxes in saturated networks can be applied to the reduced network to determine if paradoxes will occur in the original non-saturated system. The analysis distinguishes between cases where the system matrix is invertible and non-invertible, showing that the reduced network approach yields unique equilibrium solutions for arrival times even when flow distributions on unsaturated links are indeterminate. The study derives specific mathematical conditions for the occurrence of capacity paradoxes in both invertible and non-invertible cases. For invertible matrices, the condition involves projecting the sensitivity of the equilibrium solution onto the null space of the unsaturated link incidence matrix. For non-invertible cases, the condition is applied directly to the reduced network. The authors validate these findings through example networks and applications. A significant practical finding emerges from the analysis of freeway ramp metering: closing or metering a freeway entrance ramp can effectively reduce travel times not only on the freeway itself but also across the entire network, including arterial streets. This suggests that restricting capacity at specific points can resolve capacity paradoxes and improve overall system performance, providing a theoretical basis for active traffic management strategies.

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• traffic density