Continuity of the path delay operator for dynamic network loading with spillback |
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| Institution: | 1. Department of Civil and Environmental Engineering, Imperial College London, United Kingdom;2. Department of Mathematical Sciences and CCIB, Rutgers University, Camden, USA;3. Department of Industrial and Manufacturing Engineering, Pennsylvania State University, USA;1. KTH Royal Institute of Technology, Department of Transport Science, 11428 Stockholm, Sweden;2. Massachusetts Institute of Technology (MIT), Department of Civil & Environmental Engineering, Cambridge, MA 02139, USA;1. School of Business Administration, Southwestern University of Finance and Economics, PR China;2. Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China;3. Institute for Transport Studies, University of Leeds, United Kingdom;1. SBA School of Science and Engineering, Lahore University, Department of Computer Science, Lahore, Pakistan;2. Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA;1. Dipartimento di Ingegneria Industriale e dell’Informazione, University of Pavia, Via Ferrata 5, Pavia 27100, Italy;2. Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Piazza Leonardo da Vinci 32, Milan 20133, Italy |
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| Abstract: | This paper establishes the continuity of the path delay operators for dynamic network loading (DNL) problems based on the Lighthill–Whitham–Richards model, which explicitly capture vehicle spillback. The DNL describes and predicts the spatial-temporal evolution of traffic flow and congestion on a network that is consistent with established route and departure time choices of travelers. The LWR-based DNL model is first formulated as a system of partial differential algebraic equations. We then investigate the continuous dependence of merge and diverge junction models with respect to their initial/boundary conditions, which leads to the continuity of the path delay operator through the wave-front tracking methodology and the generalized tangent vector technique. As part of our analysis leading up to the main continuity result, we also provide an estimation of the minimum network supply without resort to any numerical computation. In particular, it is shown that gridlock can never occur in a finite time horizon in the DNL model. |
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