NETWORK EQUILIBRIUM MODELS OF URBAN LOCATION AND TRAVEL CHOICES: A RETROSPECTIVE SURVEY*

ABSTRACT The origins and development of the network equilibrium problem are traced and interrelated. Two principal formulations are considered the network equilibrium problem with variable travel demand, and the combined model of trip distribution and traffic assignment. The relation of these models to subsequent developments concerning mode choice, residential location, estimation of origin-destination tables from link flows and stochastic route choice are then reviewed.     

STATISTICAL PROPERTIES OF MATHEMATICAL PROGRAMMING MODELS OF STOCHASTIC NETWORK EQUILIBRIUM*

ABSTRACT. Boyce et al. (1981, 1983) have proposed and implementd the use of observed entropy levels to estimate the travel-cost coefficient in mathematical programming models of network equilibrium which involve logit route-choice probabilities. This so-called “dispersion-constrained” model is shown to give severely biased and statistically inefficient underestimates. A natural counterpart, the entropy-maximizing model, is proposed here and overestimates the travel-cost coefficient with much lower bias and much higher statistical efficiency. Even though the two models are mathematically homeomorphic in some respects, they have vastly different statistical properties. It follows that the use of observed entropy levels is undesirable and should be avoided, since maximizing entropy provides an unambiguously superior alternative.     

A REGIONAL ECONOMY,LAND USE,AND TRANSPORTATION MODEL (RELU‐TRAN©): FORMULATION,ALGORITHM DESIGN,AND TESTING*

ABSTRACT RELU is a dynamic general equilibrium model of a metropolitan economy and its land use, derived by unifying in a theoretically valid way, models developed by one of the authors [ Anas (1982) , Anas–Arnott (1991, 1997) , Anas–Kim (1996) , Anas–Xu (1999) ]. RELU equilibrates floor space, land and labor markets, and the market for the products of industries, treating development (construction and demolition), spatial interindustry linkages, commuting, and discretionary travel. Mode choices and equilibrium congestion on the highway network are treated by unifying RELU with the TRAN algorithm of stochastic user equilibrium [ Anas–Kim (1990) ]. The RELU‐TRAN algorithm's performance for a stationary state is demonstrated for a prototype consisting of 4‐building, 4‐industry, 4‐labor‐type, 15‐land‐use‐zone, 68‐link‐highway‐network version of the Chicago MSA. The algorithm solves 656 equations in a special block‐recursive convergent procedure by iterations nested within loops and loops within cycles. Runs show excellent and smooth convergence from different starting points, so that the number of loops within successive cycles continually decreases. The tests also imply a numerically ascertained unique stationary equilibrium solution of the unified model for the calibrated parameters.     

Maximizing Accessibility on Congested Networks

The problem of locating facilities to maximize their accessibility on networks where costs are functions of flow volume is considered. In particular, an accessibility model developed by Leonardi is extended to bipartite and tree networks whose arc costs are determined by a flow-dependent congestion function. The resultant nonseparable equilibrium problem is solved heuristically, and numerical simulations are used to explore the model's behavior under varying conditions.     

中国春运人口流动网络的富人俱乐部现象与不平衡性分析

基于“百度地图春节人口迁徙大数据”,利用加权网络的富人俱乐部系数和归一化不平衡系数方法,对2015年中国春运期间人口流动网络的富人俱乐部现象和不平衡性进行分析。研究结果表明：中国春运人口流动网络中存在明显的富人俱乐部现象,富人俱乐部城市包括北京、上海、广州、苏州、深圳和东莞,这些城市主导了超过77.66%中国城市的省际人口流动,且与这些城市之间的人口流动多属于不平衡关系,同时俱乐部城市之间、俱乐部城市与一小部分城市之间则属于平衡关系,这种流动格局很容易造成各城市在人口流动网络中的地位分化,严重影响了人口流动网络的公平性和安全性。     

Probing A Traffic Congestion Controversy: Density and Flow Scrutinized

Probing a die-hard traffic congestion controversy, this paper scrutinizes two key variables, density and flow, under equilibrium versus optimal states. Optimization requires equilibrium flow to decrease under mild congestion, but increase under hyper-congestion. However, both increasing flow needed under hypercongestion and decreasing flow needed under mild congestion should be accompanied by decreasing density. Thus, inflow of vehicles should always be discouraged to either increase or decrease flow of vehicles for economic efficiency. Moreover, even when optimal policy requires equilibrium flow to increase, the optimal flow itself must decrease eventually as demand increases beyond a critical level.     

Extensions to the Hub Location Problem: Formulations and Numerical Examples

Although a tremendous amount of analytical research is being conducted on the hub location problem, few models exist that extend the number of characteristics found in actual hub-and-spoke networks. Four extensions are presented in this paper: (1) a capacitated network model; (2) a minimum threshold model; (3) a model that endogenously determines the number of open hubs for the network; and (4) a model that incorporates a flow-dependent cost function for the spokes as well as the interhub links. Both the capacitated and the minimum threshold models drop the assumption of a completely interconnected network commonly found in hub location models. Numerical results show that total network costs are often minimized by closing a few interhub links. The third extension is the first known hub location model to determine the optimal number of hubs based on the needs of the network. In this model, the number of open hubs depends on the distribution of flows in the network and how cost effectively the flows can be moved across the network. Previous models that endogenously determined the number of open hubs utilized a fixed cost for establishing each hub in order to limit the number of hubs in the network. The final extension recognizes the potential of all links to amalgamate flows and includes a separate flow-dependent cost function for the spokes in addition to the one for the interhub links. Numerical results are shown for all four models.     

Duopoly prices under congested access*

Abstract. Consider two firms, at different locations, supplying a homogenous good at constant marginal production cost. Consumers incur travel costs to the firm for each unit purchased, and the travel costs increase with the amount of travel to each firm (congestion). When all traffic and all congestion are generated by travel to a duopolist, both the Nash–Bertrand equilibrium prices and the Nash–Cournot equilibrium prices exceed the sum of the marginal production cost and the marginal external travel cost. However, when the road is shared by travelers to the duopolists' facilities and travelers in competitive markets, the Nash–Bertrand duopoly price equals the competitive price and the Nash–Cournot price contains a markup.     

LOCATION‐SPECIFIC HUMAN CAPITAL,LOCATION CHOICE AND AMENITY DEMAND*

ABSTRACT The role of amenities in the flow of migrants has long been a subject of debate. This paper advances an original model of amenities that work through household production instead of directly through utility. Area characteristics (amenities) affect household production, causing certain kinds of human capital investments to be rewarded more than others. Area heterogeneity thus makes such investments location‐specific. This specificity—along with a period of exogenous location—increases the opportunity costs of moving, diminishes migration flows between dissimilar locations and increases valuation of amenities that were present in the originating area. These theoretical results emphasize people's sorting across areas and thus differ from the results of the standard model of compensating differentials. Empirical tests of the model's predictions using NLSY79 data show that childhood investments affect migration flows in the way proposed by the model.     

Gravity-Type Interactive Markov Models—Part I: A Programming Formulation of Steady States

An important class of interactive Markov migration models is characterized by gravity-type transition kernels, in which migration flows in each time period are postulated to vary inversely with some symmetric measure of migration costs and directly with some population-dependent measure of attractiveness. This two-part study analyzes the uniqueness and stability properties of steady states for such processes. In this first part, it is shown that a flow version of the steady-state problem can be given a programming formulation which permits global analysis of steady-state behavior. Within this programming framework, it is shown that when attractiveness is diminished by increased population congestion, the steady states for such processes are unique. The second part of the study will employ these results to analyze the stability properties of such steady states.     

基于SNA的中国入境欧洲旅游流网络性质和结构特征研究

欧洲是世界最重要的出境旅游市场之一,研究入境中国的欧洲旅游流对于国家开拓欧洲市场具有重要的现实意义。通过构建入境中国的欧洲旅游流网络,应用社会网络分析法研究该网络的度分布、聚集系数、平均路径长度等统计特征,和网络的个体结构位置、整体形态结构特征。结果显示:①入境欧洲旅游流网络是具有小世界效应和无标度特性的网络。②北京和西安是入境欧洲旅游流的发散中心,上海和香港是旅游流的集聚中心。③入境欧洲旅游流网络的密度低,中心势高,网络结构紧密程度低,旅游城市之间的欧洲旅游流联系不密切,并呈现围绕核心城市集散的特点。④入境欧洲旅游流网络是核心-边缘网络,网络中核心节点突出,边缘节点明显。结合旅游流流向关系和节点位势指标分析,网络核心区节点可划分为核心节点和重要节点两大类型,边缘区节点均为边缘节点。     

RETAIL AMENITIES AND URBAN SPRAWL

This paper examines the interaction between local retail markets and population density in cities. We demonstrate that welfare costs of urban sprawl need not come only from road congestion or environmental externalities, as often suggested in the literature. A city also forgoes potential agglomeration economies in retail when it settles into a spatially sprawling equilibrium. Our theory predicts an additional spatial equilibrium where the city is inefficiently dense, characterized by strong retail agglomeration economies within the core.     

The assumption of equilibrium in models of migration

In recent articles Evans (1990) and Harrigan and McGregor (1993) (hereafter HM) scrutinized the equilibrium model of migration presented in a 1989 paper by Schachter and Althaus. This model used standard microeconomics to analyze gross interregional migration flows based on the assumption that gross flows are in approximate equilibrium. HM criticized the model as theoretically untenable, while Evans summoned empirical as well as theoretical objections. HM claimed that equilibrium of gross migration flows could be ruled out on theoretical grounds. They argued that the absence of net migration requires that either all regions have equal populations or that unsustainable regional migration propensities must obtain. In fact some moves are inter- and other are intraregional. It does not follow, however, that the number of interregional migrants will be larger for the more populous region. Alternatively, a country could be divided into a large number of small regions that have equal populations. With uniform propensities to move, each of these analytical regions would experience in equilibrium zero net migration. Hence, the condition that net migration equal zero is entirely consistent with unequal distributions of population across regions. The criticisms of Evans were based both on flawed reasoning and on misinterpretation of the results of a number of econometric studies. His reasoning assumed that the existence of demand shifts as found by Goldfarb and Yezer (1987) and Topel (1986) invalidated the equilibrium model. The equilibrium never really obtains exactly, but economic modeling of migration properly begins with a simple equilibrium model of the system. A careful reading of the papers Evans cited in support of his position showed that in fact they affirmed rather than denied the appropriateness of equilibrium modeling. Zero net migration together with nonzero gross migration are not theoretically incompatible with regional heterogeneity of population, wages, or amenities.     

AN ALGORITHM FOR THE SPATIAL PRICE EQUILIBRIUM PROBLEM ON A GENERAL NETWORK IN THE SPACE OF THE PATH FLOWS*

ABSTRACT. The spatial price equilibrium on a general network may be formulated as a nonlinear-cost mathematical programming problem with simple constraints, when the decision variables are the path flows. The solution of this problem is difficult due to the very large number of variables (paths) and the impracticality of generating all the paths from all the origins to all the destinations. In this paper, we develop a Gauss-Seidel-Newton Projection algorithm and combine it with a restriction strategy. That makes it unnecessary to generate a priori all the paths. This algorithm may be further improved by exploiting the equivalence between the spatial price equilibrium on a general network and the network equilibrium. Computational results that we present in this paper demonstrate the efficiency of the proposed solution algorithms.     

Mineral precipitation associated with vertical fault zones: the interaction of solute advection,diffusion and chemical kinetics

This article is concerned with chemical reactions that occur between two interacting parallel fluid flows using mixing in vertical faults as an example. Mineral precipitation associated with fluid flow in permeable fault zones results in mineralization and chemical reaction (alteration) patterns, which in turn are strongly dependent on interactions between solute advection (controlled by fluid flow rates), solute diffusion/dispersion and chemical kinetics. These interactions can be understood by simultaneously considering two dimensionless numbers, the Damköhler number and the Z‐number. The Damköhler number expresses the interaction between solute advection (flow rate) and chemical kinetics, while the Z‐number expresses the interaction between solute diffusion/dispersion and chemical kinetics. Based on the Damköhler and Z‐numbers, two chemical equilibrium length‐scales are defined, dominated by either solute advection or by solute diffusion/dispersion. For a permeable vertical fault zone and for a given solute diffusion/dispersion coefficient, there exist three possible types of chemical reaction patterns, depending on both the flow rate and the chemical reaction rate. These three types are: (i) those dominated by solute diffusion and dispersion resulting in precipitation at the lower tip of a vertical fault and as a thin sliver within the fault, (ii) those dominated by solute advection resulting in precipitation at or above the upper tip of the fault, and (iii) those in which advection and diffusion/dispersion play similar roles resulting in wide mineralization within the fault. Theoretical analysis indicates that there exists both an optimal flow rate and an optimal chemical reaction rate, such that chemical equilibrium following focusing and mixing of two fluids may be attained within the fault zone (i.e. type 3). However, for rapid and parallel flows, such as those resulting from a lithostatic pressure gradient, it is difficult for a chemical reaction to reach equilibrium within the fault zone, if the two fluids are not well mixed before entering the fault zone. Numerical examples are given to illustrate the three possible types of chemical reaction patterns.     

An Introduction to the Network Weight Matrix

This study introduces the network weight matrix as a replacement for the spatial weight matrix to measure the spatial dependence between links of a network. This matrix stems from the concepts of betweenness centrality and vulnerability in network science. The elements of the matrix are a function not simply of proximity, but of network topology, network structure, and demand configuration. The network weight matrix has distinctive characteristics, which are capable of reflecting spatial dependence between traffic links: (1) elements are allowed to have negative and positive values capturing the competitive and complementary nature of links, (2) diagonal elements are not fixed to zero, which takes the self‐dependence of a link upon itself into consideration, and (3) elements not only reflect the spatial dependence based on the network structure, but they acknowledge the demand configuration as well. We verify the network weight matrix by modeling traffic flows in a 3 × 3 grid test network with 9 nodes and 24 directed links connecting 72 origin‐destination (OD) pairs. Models encompassing the network weight matrix outperform both models without spatial components and models with the spatial weight matrix. The network weight matrix represents a more accurate and defensible spatial dependency between traffic links, and offers the potential to augment traffic flow prediction.     

Political institutions,punctuated equilibrium theory,and policy disasters

This paper develops a theory of the relationship between policy disasters and political institutions. Policy disasters, defined as avoidable, unintended extreme negative policy outcomes, are important political, and historical events above that receive relatively little attention from political scientists and scholars of public policy. Using the predictions of punctuated equilibrium theory, I argue that systems with higher error accumulation will experience more policy disasters. Systems with more veto players and weaker information flows will experience more policy disasters, but information flows will have a stronger impact than veto players. I test this theory using data on financial crises and natural and technological disasters across 70 countries over 60 years. I find strong evidence that systems with weaker information flows and more veto players tend to have greater policy disaster risk.     

The general equilibrium effects of high-occupancy vehicle lanes on congestion,sprawl, energy use,and carbon emissions

High-occupancy vehicle (HOV) lanes have been promoted to encourage carpools, reduce traffic congestion, and improve air quality. At the partial equilibrium level, commuting with three workers per automobile clearly reduces highway congestion, lowers carbon emissions, and saves energy compared with three single drivers. This paper develops a numerical urban simulation model to generate the general equilibrium effects of HOV lanes on urban spatial structure, energy use, and greenhouse gas emissions. The major findings are that while HOV lanes reduce traffic congestion and improve welfare, the fall in transportation cost leads to urban sprawl, which results in higher dwelling energy use and a larger carbon footprint. Overall, the HOV lane policy has little effect on total energy consumption and carbon emissions. This is another classic case of general equilibrium effects reversing the partial equilibrium effects of an urban policy. In contrast, a gasoline tax policy leads to less urban sprawl but is less effective at lowering energy consumption and carbon emissions. Imposing congestion tolls is a more effective tool at reducing traffic congestion, saving energy, and lowering carbon emissions.     

A Spatial Economic Analysis of Urban Land Use and Obesity*

Abstract. We analyze an urban spatial model to examine the possible link between urban land use and obesity. Households maximize utility defined over housing, weight, and food subject to a fixed time budget allocated to commuting, calorie expenditure, and work. Our model explains the observed correspondence between high obesity rates and low development densities, but implies that these are determined endogenously in a spatial market equilibrium. We study the sorting of residents by attributes such as income, initial weight, and weight preferences, and examine the impacts on weight and density of urban design modifications that lower the costs of calorie expenditure.     

An Integrated Network Equilibrium Model of Urban Location and Travel Choices

This paper develops a mixed, combined, and stochastic user-equilibrium model for urban location and travel choices with variable origin and destination costs. Different types of travelers will be considered explicitly, including: workers with fixed residences seeking jobs, workers with fixed job locations seeking residences, and workers with both fixed residences and jobs. The costs or benefits of residing or working in a zone are described by appropriate location functions. In order to reflect effects of activity congestion the location function includes variables such as the total number of persons residing in a zone and of persons working in a zone. We prove that the proposed model is equivalent to a convex optimization problem that can be solved by a convergent method of successive averages. A numerical example is presented to demonstrate the application of the model and algorithm.