Mathematical Models

“…In order to treat the discontinuities of the density among neighboring sections (i.e. neighboring continuous places), the idea of 'shock wave' (12) is introduced as follows. We consider the case shown in Fig.3 where the traffic density of ith section is higher than that of jth section in which the boundary of density difference designated by the dotted line is moving forward.…”

Section: Traffic Flow Dynamicsmentioning

confidence: 99%

Large-Scale Traffic Network Control Based on Convex Programming Coupled with B&B Strategy

et al. 2006

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This paper presents a new framework for traffic flow control based on an integrated model description by means of a Hybrid Dynamical System (HDS). The geometrical information on the traffic network is characterized by a Hybrid Petri Net (HPN). Then, the algebraic behavior of traffic flow is transformed into a Mixed Logical Dynamical System (MLDS) form in order to introduce an optimization technique. These expressions involve both continuous evolution of traffic flow and event driven behavior of traffic light. HPN allows us to formulate the problem easily for complicated and large-scale traffic network due to its graphical understanding. MLDS enables us to optimize the control policy for traffic light by means of its algebraic manipulability and use of model predictive control framework. Since the behavior represented by HPN can be directly transformed into corresponding MLDS form, the seamless incorporation of two different modeling schemes provide a systematic design scenario for traffic flow control.

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“…(1) models are designed to meet specified needs, (2) there are no unique solutions to practical problems, (3) there are often limitations on the applicabilities of models (the linear solution above was fine for average sized men, but not for the heavier range), (4) if a model is found to be inadequate, then a better one must be developed.…”

Section: Models For Introduction To Mathematical Modellingmentioning

confidence: 99%

“…The change in the teaching of Applied Mathematics has not been well managed or highly orchestrated and, as can be seen by studying the recent crop of books on mathematical modelling, there is still considerable divergence of opinion over what mathematical modelling is all about and how it should be taught (see [1][2][3][4][5]). Some books concentrate exclusively on known models, with little or no emphasis and practice on setting up the models, while others (see [6]) are keen to emphasize all the stages of modelling.…”

Section: Introductionmentioning

confidence: 99%