Dial's stochastic assignment algorithm restricts the assignment path set to "efficient path." As a result, it sometimes produces the unrealistic flow pattern that no flow is loaded on some paths where many vehicles are running in reality. To remove the drawback of Dial's algorithm, this paper presents the LOGIT type assignment that does not restrict the assignment paths. We first show the theoretical relation between the proposed model and Sasaki's assignment model through Markov process. This analysis makes it clear that the proposed assignment model can be calculated by some matrix operations. Next, we propose an efficient algorithm that does not require the matrix operation nor path enumeration over a network. The algorithm solves an equivalent program based on the entropy decomposition derived from the Markov property of LOGIT model. Finally, it is shown that the proposed approach can be easily extended to the flow dependent case,(i.e. stochastic equilibrium assignment).

We provide an analytical approach that facilitates understanding the bifurcation mechanism of a wide class of economic models involving spatial agglomeration of economic activities. The proposed method overcomes the limitations of the Turing (1952) approach that has been used to analyze the emergence of agglomeration in the multi-regional core-periphery (CP) model of Krugman (1993Krugman ( , 1996. In other words, the proposed method allows us to examine whether agglomeration of mobile factors emerges from a uniform distribution and to analytically trace the evolution of spatial agglomeration patterns (i.e., bifurcations from various polycentric patterns as well as a uniform pattern) that these models exhibit when the values of some structural parameters change steadily. Applying the proposed method to the multi-regional CP model, we uncover a number of previously unknown properties of the CP model, and notably, the occurrence of "spatial period doubling bifurcation" in the CP model is proved.

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This paper shows that the LOGIT type stochastic assignment/stochastic user equilibrium assignment can be represented as an optimization problem with only link variables. The conventional entropy function defined by path flows in the objective can be decomposed into a function consisting only of link flows. The idea of the decomposed formulation is derived from a consideration of the most likely link flow patterns over a network. Then the equivalence of the decomposed formulation to LOGIT assignment is proved by using the Markov properties that underlie Dial's algorithm. Through the analyses, some useful properties of the entropy function and its conjugate dual function (expected minimum cost function) have been derived. Finally, it is discussed that the derived results have a potential impact on the development of efficient algorithms for the stochastic user equilibrium assignment.

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Akamatsu et al.(2006) proposed a new transportation demand management scheme called "tradable bottleneck permits" (TBP), and proved its efficiency properties for a single bottleneck model. This paper explores the properties of a TBP system for general networks. An equilibrium model is first constructed to describe the states under the TBP system. It is proved that equilibrium resource allocation is efficient in the sense that the total transportation cost in a network is minimized. Theoretical relationships between TBP and congestion pricing (CP) are also discussed. It is demonstrated that TBP has definite advantages over CP when demand information is not perfect, whereas both TBP and CP are equivalent for the perfect information case. Finally, it is shown that the "self-financing principle" also holds for the TBP system. Key Words : bottleneck congestion, dynamic traffic assignment, time-space network, tradable permit, ITSRecent advances in information and communication technology (ICT) have led to rapid changes in the "virtual" world represented by the Internet. The increasing capabilities and decreasing cost of ICT is now becoming the impetus for changing the "real" world. The effects of ICT on transportation systems are no exception. The broadly defined "Intelligent Transportation Systems (ITS)" that exploits ICT has a large potential for dramatically improving efficiency of road transportation systems if the systems are implemented together with appropriate transportation demand management (TDM) schemes.As an example of such futuristic TDM schemes making the most of ICT/ITS, Akamatsu, Sato andNguyen (2006), andAkamatsu (2007a) proposed the "tradable bottleneck permit system." Their proposed scheme is designed for resolving the problem of congestion during the morning rush hour at a single bottleneck, and consists of the following two parts: a) the road manager issues a right that allows a permit holder to pass through the bottleneck at a pre-specified time period ("bottleneck permits"), b) a new trading market is established for bottleneck permits differentiated by a pre-specified time Note here that both parts a) and b) of this scheme are feasible for implementation from a technical point of view, even at the present time. The system for handling part a) may be constructed as an application of the dedicated short range communication (DSRC) system that is used in the current electric toll collection (ETC) system; the trading markets in part b) also can be realized inexpensively by using Internet auction markets. It is, therefore, reasonable to assume that implementing this scheme will become technically easier when we take into account the future advances of ICT/ITS.

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 oneconcentration 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.