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Dynamic systems, variational inequalities and control theoretic models for predicting time-varying urban network flows. (English) Zbl 0849.90061
Summary: We set forth certain axioms for a positive theory of dynamic urban network flows. We then show that mathematical models which fulfill these axioms may be created by adapting and extending certain fundamental notions from microeconomics and nonlinear systems theory. We further show that models created in this fashion, using concepts of fast and slow dynamic processes, may be manipulated into a variety of mathematical forms, thereby providing a synthesis of dynamic systems, variational inequality and control theoretic perspectives for predicting dynamic urban network flows. We close with a discussion of the implications of this synthesis for route guidance and intelligent vehicle infrastructure. Throughout, our presentation is at a conceptual level; the mathematical arguments are purposely not rigorous to embrace the widest possible readership.

MSC:
90B20 Traffic problems in operations research
90B10 Deterministic network models in operations research
90B06 Transportation, logistics and supply chain management
93C95 Application models in control theory
49J40 Variational inequalities
93C10 Nonlinear systems in control theory
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