In the present paper we are concerned with developing more realistic dynamic models of route choice and departure time decisions of transportation network users than have been proposed in the literature heretofore. We briefly review one class of models that is a dynamic generalization of the static Wardropian user equilibrium, the so-called Boston traffic equilibrium. In contrast, we then propose a new class of models that is also a dynamic generalization of the static Wardropian user equilibrium. In particular, we show for the first time that there is a variational inequality formulation of dynamic user equilibrium with simultaneous route choice and departure time decisions which, when appropriate regularity conditions hold, preserves the first in, first out queue discipline.

It could easily be argued that spatial interaction, the movement of people, objects and information over space resulting from a decision process, is one of the most important topics, if not the most important topic, within spatial analysis. The term "spatial interaction" encompasses such diverse subjects as retailing and locational analysis, migration, transportation, residential choice, information dissemination, international trade, the spread of diseases, the provision of hospital services, attendance at events, and telecommunications.Not surprisingly, therefore, the study of spatial interaction is found in several disciplines including geography, economics, regional science, civil engineering, planning, and marketing, and there is an extensive and diverse literature on the subject. Underpinning the topic are concepts such as spatial choice and spatial cognition, as well as various statistical, mathematical, and computational issues that are necessary to understand both the theoretical development of spatial interaction models and their empirical application. Several well-known texts on spatial interaction modelling already exist, such as those of Wilson (19741, Batty(19761, Fotheringham and O'Kelly (1989), Erlander and Stewart (19891, and Ortuzar and Williamson (1990).Viewed against this backcloth, one can appreciate the potential importance of this book by Ashish Sen and Tony Smith which, by any criterion, is a serious tome. With 572 densely packed pages containing 1547 equations and over 300 references, the authors clearly intend it to be a standard reference text in spatial interaction modeling. This is not the product of a ~~~ ~~~~~ brief sabbatical-it has taken the better part of a decade to prepare and write and, like a good whisky, it has benefited from its lengthy distillation. The book has two parts: Part 1, "Theoretical Development," and Part 2, "Methods." Part 1 consists of four chapters, the first two of which contain overviews of spatial interaction processes and gravity models, respectively. The well-written first chapter provides discussions on macro and micro approaches to spatial interaction modeling, statics versus dynamics, probabilistic versus deterministic modeling, the measurement of variables, and general spatial interaction processes. The second chapter provides the general probabilistic model form that is used throughout the book and in which each observed flow is seen as the mean of a Poisson process. The chapter also discusses deterrence functions and generalizations of gravity models. The third and fourth chapters extend those themes. The third presents a formal discussion of search processes and mathematical formulations of space and interaction, and the fourth describes, in a series of propositions and proofs, the behavioral axioms embedded in various spatial interaction models. There is no doubt that it takes a great deal of effort and stamina to maintain interest throughout some of these sections (for example pages 21 to 48, pages 50 to 88, and the whole of Chapter 3) which ar...

The downsizing and closing of state mental health institutions in Philadelphia in the 1990's led to the development of a continuum care network of residential-based services. Although the diversity of care settings increased, congestion in facilities caused many patients to unnecessarily spend extra days in intensive facilities. This study applies a queuing network system with blocking to analyze such congestion processes. "Blocking" denotes situations where patients are turned away from accommodations to which they are referred, and are thus forced to remain in their present facilities until space becomes available. Both mathematical and simulation results are presented and compared. Although queuing models have been used in numerous healthcare studies, the inclusion of blocking is still rare. We found that, in Philadelphia, the shortage of a particular type of facilities may have created "upstream blocking". Thus removal of such facility-specific bottlenecks may be the most efficient way to reduce congestion in the system as a whole.

A Bayesian probit model with individual effects that exhibit spatial dependencies is set forth. Since probit models are often used to explain variation in individual choices, these models may well exhibit spatial interaction effects due to the varying spatial location of the decision makers. That is, individuals located at similar points in space may tend to exhibit similar choice behavior. The model proposed here allows for a parameter vector of spatial interaction effects that takes the form of a spatial autoregression. This model extends the class of Bayesian spatial logit/probit models presented in LeSage (2000) and relies on a hierachical construct that we estimate via Markov Chain Monte Carlo methods. We illustrate the model by applying it to the 1996 presidential election results for 3,110 US counties.

The spatial intensities of both industries and population are highly uneven across space. Moreover, these intensities differ not only across industries, but also change through time. Nevertheless, we show using Japanese data for metropolitan areas in two time periods that the location intensities of both industries and population are linked by surprisingly simple and persistent patterns. In particular, we identify a strong negative log-linear relation between the number and the average (population) size of metro areas in which a given industry is found. This relation, which we designate as the Number-Average Size (NAS) Rule, is also shown to be intimately connected to both the Rank-Size Rule and Christaller's (1966) Hierarchy Principle applied to metropolitan areas. In particular, we show mathematically that in the presence of the Hierarchy Principle (which holds quite well in Japan) this NAS Rule is essentially equivalent to the Rank Size Rule.

In this paper, we propose a statistical index of industrial localization based on Kullback-Leibler divergence. This index is particularly well suited to cases where industrial data is only available at the regional level. Unlike existing regional-level indices, our index can be employed to test the significance of industrial localization relative to a hypothesized reference distribution of probable locations across regions. In addition, one can test relative degrees of localization among industries. Finally, as with all Kullback-Leibler divergence indices, our index can be decomposed into components representing localization at various levels of spatial aggregation.

This article shows that, for both spatial lag and spatial error models with strongly connected weight matrices, maximum likelihood estimates of the spatial dependence parameter are necessarily biased downward. In addition, this bias is shown to be present in general Moran tests of spatial dependency. Thus, positive dependencies may often fail to be detected when weight matrices are strongly connected. The analysis begins with a detailed examination of downward bias for the extreme case of maximally connected weight matrices. Results for this case are then extended by continuity to a broader range of (appropriately defined) strongly connected matrices. Finally, a simulated numerical example is presented to illustrate some of the practical consequences of these biases.

The aim of this paper is to provide a new mechanism for the spatial mismatch hypothesis. Spatial mismatch can here be the result of optimizing behavior on the part of the labor market participants. In particular, the unemployed can choose low amounts of search and long-term unemployment if they reside far away from jobs. They choose voluntary not to relocate close to jobs because the short-run gains (low land rent and large housing consumption) are big enough compared to the long-run gains of residing near jobs (higher probability of finding a job).