A Simplified Approach to Analyzing Multi-regional Core-Periphery Models

This paper shows that the evolutionary process of spatial agglomeration in multi-regional core-periphery models can be explained analytically by a much simpler method than the continuous space approach of Krugman (1996). The proposed method overcomes the limitations of Turing's approach which has been applied to continuous space models. In particular, it allows us not only to examine whether or not agglomeration of mobile factors emerges from a uniform distribution, but also to trace the evolution of spatial agglomeration patterns (i.e., bifurcations from various polycentric patterns as well as from a uniform pattern) with decreases in transportation cost.agglomeration; core-periphery model; multi-regional; stability; bifurcation

Spatial Period-Doubling Agglomeration of a Core-Periphery Model with a System of Cities

The orientation and progress of spatial agglomeration for Krugman's core--periphery model are investigated in this paper. Possible agglomeration patterns for a system of cities spread uniformly on a circle are set forth theoretically. For example, a possible and most likely course predicted for eight cities is a gradual and successive one---concentration into four cities and then into two cities en route to a single city. The existence of this course is ensured by numerical simulation for the model. Such gradual and successive agglomeration, which is called spatial-period doubling, presents a sharp contrast with the agglomeration of two cities, for which spontaneous concentration to a single city is observed in models of various kinds. It exercises caution about the adequacy of the two cities as a platform of the spatial agglomerations and demonstrates the need of the study on a system of cities

Spatial Period-Doubling Agglomeration of a Core-Periphery Model with a System of Cities

The orientation and progress of spatial agglomeration for Krugman's core--periphery model are investigated in this paper. Possible agglomeration patterns for a system of cities spread uniformly on a circle are set forth theoretically. For example, a possible and most likely course predicted for eight cities is a gradual and successive one---concentration into four cities and then into two cities en route to a single city. The existence of this course is ensured by numerical simulation for the model. Such gradual and successive agglomeration, which is called spatial-period doubling, presents a sharp contrast with the agglomeration of two cities, for which spontaneous concentration to a single city is observed in models of various kinds. It exercises caution about the adequacy of the two cities as a platform of the spatial agglomerations and demonstrates the need of the study on a system of cities.Agglomeration of population; Bifurcation; Core-periphery model; Group theory; Spatial period doubling

Queue replacement principle for corridor problems with heterogeneous commuters

This study investigates the theoretical properties of a departure time choice problem considering commuters' heterogeneity with respect to the value of schedule delay in corridor networks. Specifically, we develop an analytical method to solve the dynamic system optimal (DSO) and dynamic user equilibrium (DUE) problems. To derive the DSO solution, we first demonstrate the bottleneck-based decomposition property, i.e., the DSO problem can be decomposed into multiple single bottleneck problems. Subsequently, we obtain the analytical solution by applying the theory of optimal transport to each decomposed problem and derive optimal congestion prices to achieve the DSO state. To derive the DUE solution, we prove the queue replacement principle (QRP) that the time-varying optimal congestion prices are equal to the queueing delay in the DUE state at every bottleneck. This principle enables us to derive a closed-form DUE solution based on the DSO solution. Moreover, as an application of the QRP, we prove that the equilibrium solution under various policies (e.g., on-ramp metering, on-ramp pricing, and its partial implementation) can be obtained analytically. Finally, we compare these equilibria with the DSO state.Comment: 36 pages, 15 figure

The Shock Tube as a Short Duration Wind Tunnel

Descriptions of the shock tube recently constructed at Aerodynamic Laboratory and of some experimental results obtained thereby are given in this paper. The shock tube has a cross section of 156mm high and 50mm wide and is 3370mm long. By this shock tube a uniform flow field, free from turbulence, is obtained and its Mach number may freely be adjusted from zero to the supersonic range. Instantaneous photographs of the flow patterns have been taken by using the Mach-Zehnder interferometer or the schlieren method and are shown in this paper

Global stability of day-to-day dynamics for schedule-based Markovian transit assignment with boarding queues

Schedule-based transit assignment describes congestion in public transport services by modeling the interactions of passenger behavior in a time-space network built directly on a transit schedule. This study investigates the theoretical properties of scheduled-based Markovian transit assignment with boarding queues. When queues exist at a station, passenger boarding flows are loaded according to the residual vehicle capacity, which depends on the flows of passengers already on board with priority. An equilibrium problem is formulated under this nonseparable link cost structure as well as explicit capacity constraints. The network generalized extreme value (NGEV) model, a general class of additive random utility models with closed-form expression, is used to describe the path choice behavior of passengers. A set of formulations for the equilibrium problem is presented, including variational inequality and fixed-point problems, from which the day-to-day dynamics of passenger flows and costs are derived. It is shown that Lyapunov functions associated with the dynamics can be obtained and guarantee the desirable solution properties of existence, uniqueness, and global stability of the equilibria. In terms of dealing with stochastic equilibrium with explicit capacity constraints and non-separable link cost functions, the present theoretical analysis is a generalization of the existing day-to-day dynamics in the context of general traffic assignment.Comment: 26 pages, 3 figure

Origin of power laws and their spatial fractal structure for city-size distributions

City-size distributions follow an approximate power law in various countries despite high volatility in relative city sizes over time. Our empirical evidence for the United States indicates that the scaling law stems from a spatial fractal structure owing to the coordination of industrial locations. While the locations of individual industries change considerably over time, there is a persistent pattern in that the localized industries at a given time are found only in larger cities. The spatial organization of cities exhibits a stable hierarchical structure in which larger cities are spaced apart to serve as centers for surrounding smaller cities, generating a recursive pattern across different spatial scales. In our theoretical replication of the observed regularities, diversity in scale economy among industries induces diversity in their location pattern, which translates into diversity in city size via spatial coordination of industries and population. The city-size power law is a generic feature of Monte-Carlo samples of stationary states resulting from the spontaneous spatial fractal structure in the hypothetical economy. The identified regularities reveal constraints on feasible urban planning at each regional scale. The success or failure of place-based policies designed to take advantage of individual cities' characteristics should depend on their spatial relationships with other cities, subject to the nationwide spatial fractal structure