• Journal of Korean Society of Transportation
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• v.26 no.3
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• pp.155-167
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• 2008

This paper studies a multiple user class variable demand user equilibrium and system optimal condition, and then establishes solution algorithms for them. The traffic network equilibrium is accomplished with basis on following assumptions. For considering heterogeneous road user, several user classes have discrete set of VOTs and the travel demand of each user classes varies according to generalized travel cost. this paper specifically investigates following question on multi-class variable demand: Are user equilibrium flows pattern dependent on the unit (time or money) perceived by road user classes? What is system optimal condition according to the unit used in measuring the travel cost or disutility? Finally, using this network equilibrium condition, The traffic assignment algorithm of each equilibrium condition are established.

• Journal of the Korean Operations Research and Management Science Society
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• v.34 no.4
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• pp.123-138
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• 2009

This study examined the first- and second-best pricing by stable dynamics in congested transportation networks. Stable dynamics, suggested by Nesterov and de Palma (2003), is a new model which describes and provides a stable state of congestion in urban transportation networks. The first-best pricing in user equilibrium models introduces user-equilibrium in the system-equilibrium by tolling the difference between the marginal social cost and the marginal private cost on each link. Nevertheless, the second-best pricing, which levies the toll on some, but not all, links, is relevant from the practical point of view. In comparison with the user equilibrium model, the stable dynamic model provides a solution equivalent to system-equilibrium if it is focused on link flows. Therefore the toll interval on each link, which keeps up the system-equilibrium, is more meaningful than the first-best pricing. In addition, the second-best pricing in stable dynamic models is the same as the first-best pricing since the toll interval is separately given by each link. As an effect of congestion pricing in stable dynamic models, we can remove the inefficiency of the network with inefficient Braess links by levying a toll on the Braess link. We present a numerical example applied to the network with 6 nodes and 9 links, including 2 Braess links.

• Journal of Korean Society of Transportation
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• v.23 no.4 s.82
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• pp.37-45
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• 2005

This paper presents a relationship between Nash bargaining game and Wardrop user equilibrium, which has been widely used in transportation modeling for route choice problem. Wardrop user equilibrium assumes that drivers in road network have perfect information on the traffic conditions and they choose their optimal paths without cooperation each other. In this regards, if the bargaining game process is introduced in route choice modeling, we may avoid the strong assumptions to some extent. For such purpose, this paper derives a theorem that Nash bargaining solution is equivalent to Wardrop user equilibrium as the barging process continues and prove it with some numerical examples. The model is formulated based on two-person bargaining game. and n-person game is remained for next work.

• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.4 no.1 s.6
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• pp.81-88
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• 2005

Cooperation among network users would be possible in a near future, as real time communication between them can be available by telematics. This implies that non-cooperative assumption like Wardrop's principle, which has been widely used so far in network modelling may not be appropriate for route choice problem. So a new principle requires for describing such cooperative case. This paper presents a criterion, which represents cooperative route choice behaviour among network users. With some examples, we compare the non-cooperative principle and the cooperative one presented in this paper. Numerical results from the examples show that the new principle would be better than the existing one.

• Journal of Korean Society of Transportation
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• v.8 no.1
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• pp.55-71
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• 1990

The behavioral mechanism underlying the traffic assignment model is a choice, or decision-making process of traveling paths between origins and destinations. The deterministic approach to traffic assignment assumes that travelers choose shortest path from their origin-destination pair. Although this assumption seems reasonable, it presumes that all travelers have perfect information regarding travel time, that they make consistently correct decision, and that they all behave in identical fashion. Stochastic user equilibrium assignment relaxes these presumptions by including a random component in traveler's perception of travel time. The objective of this study is to compare "A Model of Deterministic User Equilibrium Assignment" with "Models of Stochastic User Equilibrium Assignment" in the theoretical and practical aspects. Specifically, SUE models are developed to logit and probit based models according to discrete choice functions. The models were applied to sioux Falls net ork consisting of 24 zones, 24 nodes and 76 links. The distribution of perceived travel time was obtained by using the relationship between speed and traffic flow.

• Proceedings of the KOR-KST Conference
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• 2002.02a
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• pp.97-139
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• 2002

The aim of the present study is to find a good quality user equilibrium assignments under time varying condition. For this purpose, this study introduces a dynamic network loading method that can maintain correct flow propagation as well as flow conservation, and it develops a novel solution algorithm that does not need evaluation of the objective function by modifying the Schittenhelm (1990)'s algorithm. This novel algorithm turns out to be efficient and convenient compared to the conventional Frank-Wolfe (1956) algorithm because the former finds solutions based on routes rather than links so that it can maintain correct flow propagation intrinsically in the time-varying network conditions. The application of dynamic user equilibrium (DUE) assignment model with this novel solution algorithm to test networks including medium-sized one shows that the present DUE assignment model gives rise to high quality discrete time solutions when we adopt the deterministic queuing model for a link performance function, and we associate flows and costs in a proper way.

• Journal of Korean Society of Transportation
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• v.25 no.4
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• pp.99-108
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• 2007

This paper presents an elastic demand stochastic user equilibrium traffic assignment that could not be easily tackled. The elastic demand coupled with a travel performance function is known to converge to a supply-demand equilibrium, where a stochastic user equilibrium (SUE) is obtained. SUE is the state in which all equivalent path costs are equal, and thus no user can reduce his perceived travel cost. The elastic demand SUE traffic assignment can be formulated based on a dynamic system, which is a means of describing how one state develops into another state over the course of time. Traditionally it has been used for control engineering, but it is also useful for transportation problems in that it can describe time-variant traffic movements. Through the Lyapunov Function Theorem, the author proves that the model has a stable solution and confirms it with a numerical example.

• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.7 no.5
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• pp.180-183
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• 2008

This research addresses the problem of estimating Origin-Destination (O-D) trip matrices from link volume counts, a set of unobserved link volumes and information of user equilibrium flows in transportation networks. A heuristic algorithm for estimating unobserved link flows is derived, which provides volume estimates that are approximately consistent with both observed flows and an assumption of user equilibrium conditions. These estimated link volumes improve the constraints associated with the synthetic OD estimation model, providing improved solution search procedure. Model performance is tracked in terms of the root mean square errors (RMSE) in predicted travel demands, and where appropriate, predicted linked volumes. These results indicate that the new model substantially outperforms existing approaches to estimating user-equilibrium based synthetic O-D matrices.

• Journal of the Korean Operations Research and Management Science Society
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• v.32 no.3
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• pp.63-80
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• 2007

This study is a generalization of 'stable dynamics' recently suggested by Nesterov and de Palma[29]. Stable dynamics is a new model which describes and provides a stable state of congestion in urban transportation networks. In comparison with user equilibrium model that is common in analyzing transportation networks, stable dynamics requires few parameters and is coincident with intuitions and observations on the congestion. Therefore it is expected to be an useful analysis tool for transportation planners. An equilibrium in stable dynamics needs only maximum flow in each arc and Wardrop[33] Principle. In this study, we generalize the stable dynamics into the model with multiple traffic classes. We classify the traffic into the types of vehicle such as cars, buses and trucks. Driving behaviors classified by age, sex and income-level can also be classes. We develop an equilibrium with multiple traffic classes. We can find the equilibrium by solving the well-known network problem, multicommodity minimum cost network flow problem.

• IE interfaces
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• v.15 no.4
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• pp.474-482
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• 2002

In this paper, we propose a parametric optimization approach to simultaneously determining trip distribution, mode choice, and user-equilibrium assignment. In our model, mode choice decisions are based on a binomial logit model and passenger and cargo demands are divided into appropriate mode according to the user equilibrium minimum travel time. Underlying network consists of road and rail networks combined and mode choice available is auto, bus, truck, passenger rail, and cargo rail. We provide an equivalent convex optimization problem formulation and efficient algorithm for solving this problem. The proposed algorithm was applied to a large scale network examples derived from the National Intermodal Transportation Plan (2000-2019).