Mathematics of traffic flow networks

Mathematics of traffic flow networks

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Traffic flow has been a continuous source of challenging mathematicalproblems. The following work is dedicated to recent questions inmodeling, simulation and optimization of traffic flow networks.Mathematics can help to solve traffic problems in differentways. Modelling provides fundamental understanding oftraffic dynamics and behaviour. Optimization yields solutions forcomplex situations and helps to organize traffic flow. During the lastdecade there has been intensive research in different fields of and relatedto traffic flow. One of the primary research activities focus on thedevelopment of new and more realistic models for traffic flow on asingle road. Our work's primaryfocus is on models for networks.We provide new ideas on modelling flow in networks and solve differentoptimization problems analytically and numerically.The main result is the derivation of a hierarchy ofmodels treating different situations with suitabletraffic flow models.To each level of modeling we consider the optimal controlproblems and present techniques to address those problems.Furthermore, wederive an adjoint calculus for scalar hyperbolic equations withnonlinear boundary controls.The derived concepts fit for general network problemsas well as they do for traffic flow issues. The principles ofmodeling and simplification can be applied to all kinds of networkflows, like fluid flow inopen channels or gas networks.... a5.1711 = 2, 3 and 71 = E71 (1-31) Maximize 71 w.r.t. (1.32) We obtain as before a#39;7, - E Q1 for j = 1, . . . , 3 is uniquely determined as the solution to problem ( 1.32). A reformulation yields 71 = 012, 1 min{c1, c2/012, 1} + a3, 1 min{c1, c3/013, 1 }.

Title:Mathematics of traffic flow networks
Author:Michael Matthias Herty
Publisher: - 2004


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