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In order to obtain an effective method for solving route travel time reliability, this paper proposes an effective new method to calculate travel time reliability using an independent link travel time function. Based on several months of historical data, the results show that the Edgeworth expansion can better reflect travel time distribution law. In addition, travel time reliability can be calculated more conveniently by combining an approximate discretization algorithm and an empirical distribution function.

In this paper, we propose an optimization model for planning a robust path against changes in traffic volume. Robustness is based on the form of the travel time function. The proposed model can be applied not only when traffic volume increases but also when it decreases. In addition, the proposed model can set the ratio of consideration by a parameter depending on whether the traffic volume is increasing or decreasing. The effectiveness of the proposed model is evaluated using actual traffic data from the Kanto region in Japan.

Rainfall always has a direct impact on the travel time reliability of the highway network. Taking into account the adverse driving conditions under rain environment, such as poor visibility and low friction coefficient, the improved model of free flow speed, capacity and demand is established based on the analysis of spatial distribution pattern of rainfall. Thus, the generalized road travel time function is proposed to elaborate these factors. With user optimal equilibrium assignment formula and the series-parallel theory, the model to evaluate the travel time reliability of the road unit, path, OD pairs and network system is proposed by analyzing the network supply and demand levels. Then, the distribution of the rainfall on the highway network is simulated by the Matlab toolbox, and the model is solved with the Monte Carlo methods. Finally, a simple example illustrates the methods in the application to evaluate the travel time reliability of highway network under rain environment. The results indicate that the methods enable effectively identify the critical road sections with high sensitivity about travel time in the network.

This study examined the detection of the Braess Paradox by stable dynamics in general 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. In comparison with the user equilibrium model, which is based on the arc travel time function in analyzing transportation networks, stable dynamics requires few parameters and is coincident with intuitions and observations on congestion. It is therefore expected to be a useful analysis tool for transportation planners. The phenomenon whereby increasing network capacity, for example creating new routes, known as arcs, may decrease its performance is called the Braess Paradox. It has been studied intensively under user equilibrium models with the arc travel time function since it was first demonstrated by Braess (1968). However, the development of a general model to detect the Braess Paradox under stable dynamics models remains an open problem. In this study, we suggest a model to detect the paradox in general networks under stable dynamics. In our model, we decide whether the Braess Paradox will occur in a given network, detect Braess arcs or Braess crosses if the network permits the paradox, and present a numerical example of the application of the model to a given network.

In this paper we develop a new theory of static equilibrium in congested transportation networks. We show that under some natural assumptions, the Wardrop principle leads to a very strong relation between the loading of the arc, arc flow and arc travel time. This relation allows us to simplify significantly the arc performance model. We show that instead of fixing a functional form of travel time function, we can obtain equilibrium solutions for static traffic assignment models using only some natural bounds for arc travel time and arc flow. We compare the results of our model with the results of standard Beckmann model.

Considering characteristics of Chinese urban mixed traffic, the author develops a combinatorial model involving the mixed deterministic traffic volume distribution and user’s equilibrium (UE) assignment on the basis of symmetrical link travel time function (or deterrence). Its uniqueness and equivalance to the Wardropian principle of UE are also proved. Finally, we give the algorithm of model.

This paper presents a survey of the mathematical methods used for modeling and solutions for the traffic assignment problem. It covers the static (steady-state) traffic assignment techniques as well as dynamic traffic assignment in lumped parameter and distributed parameter settings. Moreover, it also surveys simulation-based solutions. The paper shows the models for static assignment, variational inequality method, projection dynamics for dynamic travel routing, discrete time and continuous time dynamic traffic assignment, and macroscopic dynamic traffic assignment (DTA). The paper then presents the macroscopic DTA in terms of the Wardrop principle and derives a partial differential equation for experienced travel time function that can be integrated with the macroscopic DTA framework.

The network flow constraints construct the feasible region for dynamic travel choice models. Although the feasible region associated with each dynamic travel choice model may be different, the basic components of the network flow constraints are essentially the same. The complete requirements of dynamic travel choice models include the constraints of flow conservation, flow propagation, nonnegativity, definition, first-in-first-out (FIFO) and oversaturation.

Why does a consumer choose a variant of a product rather than another one? The commonly invoked reason is that of the consumer’s preferences: he prefers the variant which is best for him. If the price is the only attribute which distinguishes the variants from one another, the consumer chooses the cheapest variant and he can be described as a cost-minimizing (or utility maximizing) economic decision maker.

Dynamic route guidance systems are being developed to inform and guide drivers regarding their best departure times and routes so as to avoid congestion delay. However, some drivers may not rely on the information provided by the route guidance system to adjust their departure times and routes. Furthermore, drivers without navigation systems do not have perfect information on the network traffic and must use their own experience and perception of current traffic conditions to make travel decisions. Thus, there is a need to develop dynamic route choice models under imperfect as well as perfect information.

This work deals with the problem of traffic assignment with a nonlinear travel-time function. The nonlinear travel-time function makes it possible to simulate congestion on urban streets in a more realistic manner. The optimal traffic assignment pattern is obtained by using a variational technique for a multicopy network problem with nonlinear travel-time functions and turn penalties.

In this paper we address the methodology of the equilibrium traffic assignment on congested networks. The paper presents a unified approach to a class of iterative solution procedures within a general mathematical programming framework. A preliminary comparative analysis of three basic algorithms for the equilibrium traffic assignment is reported.