Analysis of dynamic system optimal assignment with departure time choice

Most analyses on dynamic system optimal (DSO) assignment are done by using the control theory with an outflow traffic model. On the one hand, this control theoretical formulation provides some attractive mathematical properties for analysis. On the other hand, however, this kind of formulation often ignores the importance of ensuring proper flow propagation. Moreover, the outflow models have also been extensively criticized for their implausible traffic behaviour. This paper aims to provide another framework for analysing a DSO assignment problem based upon sound traffic models. The assignment problem we considered aims to minimize the total system cost in a network by seeking an optimal inflow profile within a fixed planning horizon. This paper first summarizes the requirements on a plausible traffic model and reviews three common traffic models. The necessary conditions for the optimization problem are then derived using a calculus of variations technique. Finally, a simple working example and some concluding remarks are given

Analysis of dynamic traffic models and assignments

This paper develops a comprehensive framework for analysing and solving traffic models and assignments in dynamic setting. Traffic models capture the time-varying travel times and flows on a road network and traffic assignments represent the corresponding responses of travellers. There are two different kinds of traffic assignments: dynamic user equilibrium and dynamic system optimum. Under dynamic user equilibrium, traffic is assigned such that for each origin-destination pair in the network, the individual travel costs experienced by each traveller, no matter which combination of travel route and departure time he/she chooses, are equal and minimal. The system optimum assigns traffic such that the total system cost of the network system is minimized. The system optimal traffic pattern provides a useful benchmark for evaluating various transport policy measures such as implementing dynamic road tolls. This system optimal assignment is formulated as a state-dependent optimal control problem. The analysis developed in this paper is novel and it can work with general travel cost functions. Numerical examples are provided for illustration and discussion. Finally, some concluding remarks are given

Analysis of dynamic system optimum and externalities with departure time choice

This paper aims to analyse the dynamic system optimal assignment with departure time choice, which is an important, yet underdeveloped area. The main contribution of this paper is the necessary conditions and the sensitivity analysis for dynamic system optimizing flow. Following this, we revisit the issue of dynamic externality in a more plausible way. We showed that how the externality can be derived and interpreted from the control theoretic formulation and the sensitivity analysis of traffic flow. To solve the system optimal assignment, we propose a dynamic programming solution approach. We present numerical calculations and discuss the characteristics of the results. In particular, we contrast the system optimal assignment with its equilibrium counterpart in terms of the amount of travel generated, flow profiles, and travel costs

User equilibrium, system optimum, and externalities in time-dependent road networks

This paper develops a comprehensive framework for analysing and calculating user equilibrium, system optimum, and externalities in time-dependent road networks. Under dynamic user equilibrium, traffic is assigned such that for each origin-destination pair in the network, the individual travel costs experienced by each traveller, no matter which combination of travel route and departure time he/she chooses, are equal and minimal. The system optimal flow is determined by solving a state-dependent optimal control problem, which assigns traffic such that the total system cost of the network system is minimized. The externalities are derived by using a novel sensitivity analysis. The analyses developed in this paper can work with general travel cost functions. Numerical examples are provided for illustration and discussion. Finally, some concluding remarks are given

System optimizing flow and externalities in time-dependent road networks

This paper develops a framework for analysing and calculating system optimizing flow and externalities in time-dependent road networks. The externalities are derived by using a novel sensitivity analysis of traffic models. The optimal network flow is determined by solving a state-dependent optimal control problem, which assigns traffic such that the total system cost of the network system is minimized. This control theoretic formulation can work with general travel time models and cost functions. Deterministic queue is predominantly used in dynamic network models. The analysis in this paper is more general and is applied to calculate the system optimizing flow for Friesz’s whole link traffic model. Numerical examples are provided for illustration and discussion. Finally, some concluding remarks are given

System optimal traffic assignment with departure time choice

This thesis investigates analytical dynamic system optimal assignment with departure time choice in a rigorous and original way. Dynamic system optimal assignment is formulated here as a state-dependent optimal control problem. A fixed volume of traffic is assigned to departure times and routes such that the total system travel cost is minimized. Although the system optimal assignment is not a realistic representation of traffic, it provides a bound on performance and shows how the transport planner or engineer can make the best use of the road system, and as such it is a useful benchmark for evaluating various transport policy measures. The analysis shows that to operate the transport system optimally, each traveller in the system should consider the dynamic externality that he or she imposes on the system from the time of his or her entry. To capture this dynamic externality, we develop a novel sensitivity analysis of travel cost. Solution algorithms are developed to calculate the dynamic externality and traffic assignments based on the analyses. We also investigate alternative solution strategies and the effect of time discretization on the quality of calculated assignments. Numerical examples are given and the characteristics of the results are discussed. Calculating dynamic system optimal assignment and the associated optimal toll could be too difficult for practical implementation. We therefore consider some practical tolling strategies for dynamic management of network traffic. The tolling strategies considered in this thesis include both uniform and congestion-based tolling strategies, which are compared with the dynamic system optimal toll so that their performance can be evaluated. In deriving the tolling strategies, it is assumed that we have an exact model for the underlying traffic behaviour. In reality, we do not have such information so that the robustness of a toll calculation method is an important issue to be investigated in practice. It is found that the tolls calculated by using divided linear traffic models can perform well over a wide range of scenarios. The divided linear travel time models thus should receive more attention in the future research on robust dynamic traffic control strategies design. In conclusion, this thesis contributes to the literature on dynamic traffic modelling and management, and to support further analysis and model development in this area

System optimal traffic assignment with departure time choice.

This thesis investigates analytical dynamic system optimal assignment with departure time choice in a rigorous and original way. Dynamic system optimal assignment is formulated here as a state-dependent optimal control problem. A fixed volume of traffic is assigned to departure times and routes such that the total system travel cost is minimized. Although the system optimal assignment is not a realistic representation of traffic, it provides a bound on performance and shows how the transport planner or engineer can make the best use of the road system, and as such it is a useful benchmark for evaluating various transport policy measures. The analysis shows that to operate the transport system optimally, each traveller in the system should consider the dynamic externality that he or she imposes on the system from the time of his or her entry. To capture this dynamic externality, we develop a novel sensitivity analysis of travel cost. Solution algorithms are developed to calculate the dynamic externality and traffic assignments based on the analyses. We also investigate alternative solution strategies and the effect of time discretization on the quality of calculated assignments. Numerical examples are given and the characteristics of the results are discussed. Calculating dynamic system optimal assignment and the associated optimal toll could be too difficult for practical implementation. We therefore consider some practical tolling strategies for dynamic management of network traffic. The tolling strategies considered in this thesis include both uniform and congestion-based tolling strategies, which are compared with the dynamic system optimal toll so that their performance can be evaluated. In deriving the tolling strategies, it is assumed that we have an exact model for the underlying traffic behaviour. In reality, we do not have such information so that the robustness of a toll calculation method is an important issue to be investigated in practice. It is found that the tolls calculated by using divided linear traffic models can perform well over a wide range of scenarios. The divided linear travel time models thus should receive more attention in the future research on robust dynamic traffic control strategies design. In conclusion, this thesis contributes to the literature on dynamic traffic modelling and management, and to support further analysis and model development in this area.

Transportation modeling and management

EditorialTransport & PlanningCivil Engineering and Geoscience