Deployable stable traffic assignment models for control in dynamic traffic networks: A dynamical systems approach
Abstract
This study addresses stability issues in the context of operational dynamic traffic assignment (DTA) strategies for traffic networks equipped with advanced information and sensor systems. LaSalle's theorem, an extension of the Lyapunov approach from non-linear dynamical systems, is used to analyze the global behavior vis-à-vis the stability of the solutions prescribed by the control strategies for dynamic traffic networks with time-dependent demand. The stability analysis focuses on demonstrating that the proposed control strategies move the system towards the corresponding time-dependent stable desirable states rather than focusing on a single stable state. An important contribution of the study is that the Lyapunov functions for the system optimal (SO) and user equilibrium (UE) objectives are their corresponding objective functions under DTA. This overcomes the key difficulty of constructing a meaningful Lyapunov function for such systems, and provides a general framework for the stability analysis of operational dynamic traffic assignment problems. These different control structures are proposed based on the available traffic information. The feedback control structure is used only when current traffic information is available and there is a lack of predictive information. The internal model control (IMC) structure can be applied when reasonably accurate near-term future predictions are feasible. The external prediction control structure can be used when robust models are available to predict future traffic conditions. This flexibility provides the ability to make trade-offs between computational efficiency and solution accuracy facilitating the implementation of deployable solution algorithms. Simulations experiments are performed for a real traffic network to test the effectiveness, efficiency, and reliability of the proposed models. The results show that the proposed models provide orders of magnitude improvements in computational efficiency over benchmark deterministic DTA models while maintaining a sufficient level of solution accuracy.
Degree
Ph.D.
Advisors
Peeta, Purdue University.
Subject Area
Civil engineering
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