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Road traffic networks are chaotic and highly complex systems. In this paper, we introduce a dynamic gravity model that characterizes the behaviors of the O-D (origin-destination) traffic, such as equilibrium, period-doubling, chaos, and fractal in discrete time. In cases where the original cost function is used, the trip distribution model might degenerate into an all-or-nothing problem without the capacity constraints. To address this shortcoming, we propose substituting the original cost function with an improved conical volume-delay function. This new function retains some of the properties of the original cost function, and its parameters have the same meaning as those in the original function. Our analysis confirms that the double-constrained dynamic gravity model successfully characterizes complex traffic behavior because of the improved conical volume-delay function. Our analysis further shows that the three-parameter bifurcation diagram based on the period characteristics provides deep insight into the actual state of the road traffic networks. Investigating the properties of the model solutions, we further show that the new model is more effective in addressing the all-or-nothing problem.

The real-time dynamic coupling under the virtual-coupling technology guarantees running multi-group trains in different sections based on passenger flow's spatial and temporal distribution characteristics. It enables more flexible transport organization modes such as full-length and short-turn routing and the express/local stop mode. Utilizing the redundant capacity of the airport line to carry out coordinated transportation of passengers and goods is an essential means of relieving urban traffic pressure, saving energy, and protecting the environment. To promote urban rail transit to achieve the goal of "double-carbon," the optimization of passenger and freight cooperative transport schemes based on the virtual coupling technology for the airport line of the rail transit is investigated. Based on the train operation of full-length and short-turn routing under the virtual-coupling technology, according to the unbalanced distribution characteristics of passenger and freight flows in urban rail transit, this paper constructs an optimization model of urban rail transit capacity allocation to minimize passenger travel costs, enterprise operation costs, and carbon emission costs, and considering the constraints of the carbon emission policy, with the constraints such as the train operation safety, the constraints of the balance of the passenger flow and freight flow loading. The multi-objective model to solve the optimization problem has been designed. Given the complexity of the multi-objective model solution, an improved nondominated sorting genetic algorithm is designed, and the algorithm makes use of the screening function of the constraints during the initial population generation process, which effectively balances the relationship between the whole process of screening and time-consumption of the NSGA-II algorithm. Taking Wuxi Metro Line 3 as an example, the results show that: (i) Compared with the traditionally large and small crossing mode, full-length and short-turn routing of virtual coupling Trains proposed in this paper can reduce the average waiting time of passengers by about 2.01min, the cost of carbon emission by 15.7% and the cost of enterprise operation by 20.2%, and at the same time, improve the average total rate by about 50%, which verifies that the virtual formation technology is conducive to improving the efficiency of passenger travel and reducing the operating cost and the carbon cost. It is also beneficial for improving passenger traveling efficiency. (ii)The single-alignment fixed configuration mode, compared with the single-flow mode, can increase the average full-load rate by 26.6% while increasing the passenger travel cost by only 0.98% and reducing the carbon emission cost by a small margin; the virtual configuration technology based-on the large and smallalignment operation and transport scheme increases the passenger travel cost by about 0.3% and further reduces the carbon emission cost by 1.9%. They further reduced the carbon emission cost by 1.9% while increasing the average total occupancy rate by about 5.8%. The proposed models and algorithms provide some decision support for urban rail transit operators to optimize transport schemes under different carbon emission policies and the virtual coupling operation mode. [ABSTRACT FROM AUTHOR]

Regarding alleviating urban traffic pressure and conserving environmental energy, it is essential to utilize the redundant capacity of urban rail transit during non-peak hours for passenger-freight collaborative transportation. In order to achieve the "dual carbon" goals in urban rail transit, a study has been conducted on the coordinated transportation of passengers and goods, which can adapt to the evolving carbon emission policies. A method for calculating the waiting time that allows passengers to queue for a second time has been proposed by studying the queue of passengers. A multiobjective optimization model for urban rail transit passenger-freight collaborative transportation has been constructed, with the objectives of minimizing carbon emissions and passenger waiting time, considering constraints such as carbon emission policy, train operation safety, passenger and freight loading balance, and train formation scheme. An improved nondominated sorting genetic algorithm (NSGA-II) has been designed to deal with the complexity of solving the multiobjective model. The algorithm utilizes the filtering function of the constraint conditions during the initial population generation process, effectively balancing the relationship between the filtering and time consumption of the NSGA-II algorithm. Taking the Wuxi Metro Line 3 as an example for analysis, the results show that: ① Although the average passenger waiting time increases by about 0.53 minutes in this method, the carbon emissions of the trains decrease by approximately 21.3%. Meanwhile, the average seating rate of the optimized solution is 5%~15% higher than the traditional transportation scheme used by Wuxi Metro Line 3. The superiority of urban rail transportation for passenger-freight collaborative transportation has been verified. ② With the mandatory control of carbon emission control, the passengerfreight collaborative optimization scheme is not affected by different carbon emission limits. Under the carbon tax policy, transportation schemes are less affected by different carbon tax levels. Transportation schemes remain consistent under the different limits of carbon trading policies. The proposed model and algorithm provide decision-making support for urban rail transit operators to optimize transportation plans under different carbon emission policies. [ABSTRACT FROM AUTHOR]

Urban rail transit has the potential to utilize surplus capacity to carry out urban freight transportation during off-peak periods. Based on the characteristics of virtual coupling operation and organization mode, this paper comprehensively considers the competition between passenger flow and freight flow, takes the train stopping plan and train carriage allocation as the main decision variables, and takes the minimization of passenger waiting time and the maximization of average full load rate as dual objectives to construct a multi-objective optimization model of passengerfreight collaborative transport scheme of urban rail transit under virtual coupling conditions. The multi-objective optimization model is developed to obtain the system optimization of the train stopping plan, running plan, carriage allocation plan, and passenger-freight collaborative transport plan. Numerical experiments are designed to verify the model's validity, using Wuxi Metro Line 3 as an example, and the NSGA-II algorithm solves all experiments. The results of the algorithm show that, compared to the traditional single passenger transport with a fixed large coupling, the scheme in this paper can simultaneously improve the average full capacity of the whole line by about 38.5% during the study period with only 0.65 minutes increase in the average passenger waiting time for the same number of rolling stocks, which can effectively shorten passenger travel time and improve the quality of passenger service in urban rail transit while ensuring transport efficiency. [ABSTRACT FROM AUTHOR]