Investigating Braess' Paradox with Time-Dependent Queues

In the 1960s, Braess showed that the overall system performance of a transportation network can be degraded when a new link is added to the network, given that travelers choose their routes based on the user equilibrium (UE) principle. This phenomenon is often referred to as Braess' paradox (BP). The original five-link BP network has been studied extensively with static link performance functions. In this paper, we revisit the original BP network with a dynamic point-queue model and examine whether the results from the static model would hold for the case with time-dependent queues. For this purpose, we solve the BP problem with the consideration of dynamic queuing that leads the system to a steady state while satisfying the dynamic user equilibrium (DUE) condition at every instant. Our results indicate that the locations of congestion, or “hot spots,” of the system are sensitive to the capacity of each link in an intricate manner. The “surprising result” reported in previous studies with link performance functions, that a system can spontaneously grow out of Braess' paradox if the demand is sufficiently high, does not occur with time-dependent queues. Instead, we show that queues in different stages have different impacts on the system performance. The implication of this result is discussed in the context of developing proactive dynamic traffic control strategies that can eliminate the negative impact of BP while keeping the system operating at the DUE condition. Even though this study focuses on the original five-link network, the results illustrate the potential pitfalls of extending insights developed from a static framework for dynamic traffic and the importance of studying the problem with a dynamic framework for real-time traffic control.