Modeling Dynamic Transportation Networks: An Intelligent by Dr. Bin Ran, Dr. David Boyce (auth.)

By Dr. Bin Ran, Dr. David Boyce (auth.)

This booklet seeks to summarize our fresh development in dynamic trans­ portation community modeling. It concentrates on excellent dynamic community types in keeping with genuine commute instances and their corresponding resolution algorithms. by contrast, our first ebook DynamIc city Transportation community versions - The­ ory and Implications for clever Vehicle-Hzghway platforms (Springer-Verlag, 1994) all in favour of prompt dynamic community versions. evaluating the 2 books, the most important changes will be summarized as follows: 1. This e-book makes use of the variational inequality challenge because the easy formula method and considers the optimum regulate challenge as a subproblem for resolution reasons. the previous booklet used optimum regulate conception because the uncomplicated formula procedure, which prompted serious difficulties in a few situations. 2. This ebook specializes in excellent dynamic community versions in response to real trip occasions. the previous publication fascinated by immediate dynamic community versions in response to presently winning shuttle occasions. three. This publication formulates a stochastic dynamic course selection version which may make the most of any attainable path selection distribution functionality rather than in basic terms the logit functionality. four. This booklet reformulates the bilevel challenge of mixed departure time/ direction selection as a one-level variational inequality. five. eventually, a suite of difficulties is equipped for school room use. moreover, this publication deals accomplished insights into the complexity and problem of making use of those dynamic community types to clever Trans­ portation structures (ITS). however, the types during this textual content will not be but totally evaluated and are topic to revision according to destiny research.

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Additional resources for Modeling Dynamic Transportation Networks: An Intelligent Transportation System Oriented Approach

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On the other hand, the statement, "To achieve equal minimal travel times over each used route for each O-D pair," does not directly suggest an objective function. In such a problem, the modeler may need to design an artificial objective function so that the resulting optimization conditions of the optimal control program represent desired physical properties. However, such an objective function may not have any direct physical interpretation. We shall discuss the definition of an objective function in more detail in the following chapters for various dynamic network problems.

In this chapter, we introduce the basic concepts of variational inequality theory which is capable of formulating and analyzing more general problems than the constrained optimization approach. 1, we first define variational inequality problems for both static and dynamic problems. We then introduce some fundamental definitions, along with qualitative results for variational inequality problems, such as conditions for existence and uniqueness of solutions. Subsequently, the relaxation method for solving a variational inequality is discussed.

State the resulting mathematical programming subproblem. 48 Chapter 2. t. x = -~x(t) + u(t), x(O) = xo. t. aT [au 2(t) + bu(t) + cx(t) + x 2(t)]dt x = u(t), x(O) = xo, a> O. t. aT f[u(t), x(t)]dt x = g[u(t), x(t)], x(O) = Xo has no explicit dependence on time t. Show that the Hamiltonian is a constant function of time along the optimal path. Hint: Using the chain rule, compute d1i dt a1i dx = ax dt a1i du + au Tt a1i d)" + f»:Tt and substitute from the necessary conditions for the partial derivatives of 1{.

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