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The Dynamics and Equilibria of Day-to-Day Assignment Models   总被引:2,自引:0,他引:2  
Traffic network modelling is a field that has developed over a number of decades, largely from the economics of predicting equilibria across route travel choices, in consideration of the congestion levels on those routes. More recently, there has been a growing influence from the psychological and social science fields, leading to a greater interest in understanding behavioural mechanisms that underlie such travel choice decisions. The purpose of the present paper is to describe mathematical models which aim to reflect day-to-day dynamic adjustments in route choice behaviour in response to previous travel experiences. Particularly, the aim is to set these approaches in a common framework with the conventional economic equilibrium models. Starting from the analysis of economic equilibria under perturbations, the presentation moves onto deterministic dynamical system models and stochastic processes. Simple illustrative examples are used to introduce the modelling approaches. It is argued that while such dynamical approaches have appeal, in terms of the range of adaptive behavioural processes that can be incorporated, their estimation may not be trivial. In particular, the obvious solution technique (namely, explicit simulation of the dynamics) can lead to a rather complex problem of interpretation for the model-user, and that more analytical approximation techniques may be a better way forward.  相似文献
2.
Standard kernel density estimation is subject to bias that can mask structure by flattening peaks and filling in troughs in the density. A number of methods of bias reduction have been proposed including approaches based on reweighting the contributions from the individual data points. We explore the potential of bias reduction by reweighting, and propose a new type of reweighted kernel density estimator in which the weights are defined by a cubic spline on the logit scale. The free parameters of this spline are optimized with respect to a leave-one-out performance criterion. Technical aspects of the implementation of our estimator are discussed and its finite sample performance is analysed through experiments with simulated and real data. The results are very encouraging, and suggest that our new methodology is capable of significantly greater bias reduction than existing reweighted density estimators.  相似文献
3.
We consider Nadaraya-Watson type estimators for binary regression functions. We propose a method for improving the performance of such estimators by employing bias reduction techniques when estimating the constituent probability densities. Direct substitution of separately optimized density estimates into the regression function formula generates disappointing results in practice. However, adjusting the global smoothing parameter to optimize a performance criterion for the binary regression function itself is more promising. We focus on an implementation of this approach which uses a variable kernel technique to provide reduced bias density estimates, and where the global bandwidth is selected by an appropriately tailored leave-one-out (cross-validation) method. Theory and numerical experiments show that this form of bias reduction improves performance substantially when the underlying regression function is highly non-linear but is not beneficial when the underlying regression function is almost linear in form.  相似文献
4.
Deterministic assignment models are sometimes used to approximate properties of more complex stochastic models. One property that is of particular interest from a system optimization viewpoint is total travel cost. This paper looks at the approximation of mean total travel cost. It is shown that deterministic models will underestimate this quantity in many common situations. Furthermore, discrepancies between total travel cost under the different modelling frameworks can lead to situations in which network modifications which are detrimental according to a stochastic model appear beneficial when using the natural deterministic approximation. We conclude that estimation of mean travel cost in stochastic assignment is often best done using simulation. Some suggestions are made regarding the implementation of traffic assignment simulation.  相似文献
5.
In semiparametric regression models, penalized splines can be used to describe complex, non-linear relationships between the mean response and covariates. In some applications it is desirable to restrict the shape of the splines so as to enforce properties such as monotonicity or convexity on regression functions. We describe a method for imposing such shape constraints on penalized splines within a linear mixed model framework. We employ Markov chain Monte Carlo (MCMC) methods for model fitting, using a truncated prior distribution to impose the requisite shape restrictions. We develop a computationally efficient MCMC sampler by using a correspondingly truncated multivariate normal proposal distribution, which is a restricted version of the approximate sampling distribution of the model parameters in an unconstrained version of the model. We also describe a cheap approximation to this methodology that can be applied for shape-constrained scatterplot smoothing. Our methods are illustrated through two applications, the first involving the length of dugongs and the second concerned with growth curves for sitka spruce trees.  相似文献
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