In this paper, a generalized equilibrium problem is investigated based on fixed point methods. Strong convergence theorems of solutions are established in the framework of Hilbert spaces.

This paper examines the travelers’ day-to-day route-choice behavior with Advanced Traveler Information Systems (ATIS) through laboratory-like experimental method. Five groups of route-choice behavior experiments are designed to simulate actual daily behavior of travelers. In the experiment, subjects are provided with different levels of the complete road network information to simulate the proportion of subjects equipped with ATIS equipment (i.e., ATIS market penetration) and choose the routes repeatedly. The subject’s route-choice behavior under different proportions of complete road network information is analyzed, and the strategy of releasing such complete information is determined when the performance of road network system is the best. The Braess network which consists of three routes was used in the experiment and analysis. The results show that the fluctuation of traffic flow runs through the entire experiments, but it tends to converge to user equilibrium. When the market penetration is 75%, both the fluctuation of traffic flow and the tendency of subjects to change routes are the smallest, so the road network system is the most stable. This interesting result indicates that releasing traffic information to all travelers is not the best. Other results show that the travel times of the three routes in the five groups of experiments tend to converge to and finally fluctuate around user-equilibrium travel time. With the increase in ATIS market penetration, the average travel time of subjects in each round tends to increase. The overall trend of the five groups of experiments is that as the number of route switches increases, the average travel time increases. The results also indicate that releasing traffic information to all travelers cannot weaken the Braess Paradox. On the contrary, the more travelers are provided with traffic information, the less likely it will weaken the Braess Paradox.

In this study, the influence of traveler's departure time choice in day-to-day dynamic evolution of traffic flow in a transportation network is investigated. Combining historical information and real-time information, a dynamic evolution model of traffic flow with a study period divided into two intervals is proposed for a simple two-link network. Then, the evolution of network traffic flow is investigated using numerical experiments. Three types of information are considered: (1) only historical information, (2) only real-time information, and (3) both historical and real-time information. The results show that the dynamic evolution of network traffic flow under the three types of information is similar. However, the possibility of chaos occurrence under both historical and real-time information is smaller than that under two individual types of information. When chaos occurs, the chaotic behavior in traffic-flow evolution under only real-time information is relatively less complex than that under the other two types of information.

This paper proposes a traffic-flow evolutionary model under a dual updating mechanism that describes the day-to-day (DTD) dynamics of traffic flow and travel cost. To illustrate the concept, a simple two-route network is considered. Based on the nonlinear dynamic theory, the equilibrium stability condition of the system is derived and the condition for the division between the bifurcation and chaotic states of the system is determined. The characteristics of the DTD dynamic evolution of network traffic flow are investigated using numerical experiments. The results show that the system is absolutely stable when the sensitivity of travelers toward the route cost parameter (θ) is equal to or less than 0.923. The bifurcation appears in the system when θ is larger than 0.923. For values of θ equal to or larger than 4.402, the chaos appears in the evolution of the system. The results also show that with the appearance of chaos, the boundary and interior crises begin to appear in the system when θ is larger than 6.773 and 10.403, respectively. The evolution of network traffic flow is always stable when the proportion of travelers who do not change the route is 84% or greater.

When extracting flight data from airport terminal area, there are matters such as large volume, unclear features, and similar trend in time series. In order to deal with the related issues and to optimize the description, by combining with the TBO (Trajectory-Based Operation), an application proposed by the ICAO (International Civil Aviation Organization) in ASBU (Aviation System Block Upgrade), using multisource dynamic model to establish 4DDW (4D dynamic warping) algorithm, the multisource modeling integrated with evaluation system is proposed to realize the flight path optimization with time series characteristics and accord with the interval concept. The calculation results show that 4DDW can obtain the optimal solution for multiprofile calculation of TBO by comparing the composite trajectory deviation values and time dimension planning using the buffer and threshold values recommended by ICAO in airspace planning and flight procedure design. The results meet the requirements of high accuracy and convergence features of spatial waypoints and can improve the airport operation standards and terminal area capacity.