Exploring the roles of automated vehicles in system optimal for traffic assignment problems

Abstract

The rise of automated vehicles (AVs) presents significant opportunities to improve transportation efficiency, safety, and sustainability. By leveraging advanced sensing, computing, and communication technologies, AVs have the potential to reduce congestion and improve the network-wide performance. Besides, traffic assignment model plays a crucial role in routing AVs efficiently in a traffic network. System optimal (SO) is one of the important routing principles in traffic assignment problems, which quantifies the best possible performance of a traffic network and provides policy implications and operation strategies for decision-makers. The rapid development of automated technology reveals the possibility to control all AVs to achieve SO in a fully automated environment. Therefore, this research aims to explore the roles of AVs in SO for traffic assignment problems in different aspects: vehicles, platform and network. Besides, the traffic assignment problem can be classified into two categories: static traffic assignment (STA), which assumes constant travel demand and network conditions, and dynamic traffic assignment (DTA). It is suitable to explore the equilibrium when AV control rules and routing decisions are fixed over the analysis horizon. On the other hand, DTA models capture the relationship between dynamic route choice behaviors and transportation network states. Therefore, depending on the nature of the strategies of AVs to achieve SO, different types of traffic assignment models are employed to ensure optimal routing and system performance. Furthermore, the non-uniqueness of the solution of SO in traffic assignment problems implies that the SO could be achieved by multiple strategies in each aspect and it inspires us to develop the second criterion of optimal strategy except SO in each aspect. In the vehicles aspect, this study develops the headway control framework in a fully automated road network, as we believe headway of AVs is another influencing factor to traffic dynamics in addition to conventional traveler behaviors (e.g. route and departure time choices). Specifically, this study aim to search for the optimal time headway between AVs on each link that achieves the network-wide system optimal dynamic traffic assignment (SO-DTA). To this end, the headway-dependent fundamental diagram (HFD) and headway-dependent double queue model (HDQ) are developed to model the effect of dynamic headway on roads, and a dynamic network model is built. It is rigorously proven that the minimum headway could always achieve SO-DTA, yet the optimal headway is non-unique. Motivated by these two findings, this study defines a novel concept of maximin headway, which is the largest headway that still achieves SO-DTA in the network. Mathematical properties regarding maximin headway are analyzed and an efficient solution algorithm is developed. Numerical experiments on both a small and large network verify the effectiveness of the maximin headway control framework as well as the properties of maximin headway. This study sheds light on deriving the desired solution among the non-unique solutions in SO-DTA and provides implications regarding the safety margin of AVs under SO-DTA. In the platform aspect, this thesis proposes a publicly-owned centralized platform (POCP) for shared automated vehicles (SAVs) that connects travelers, traffic network companies (TNCs), and parking spaces. It provides a novel insight for the regulation of government to save social costs by adjusting travelers' behaviors with spatial-temporal trip subsidies. In the proposed POCP, (i) government operates this centralized platform with the objective of minimizing social cost, collecting and distributing necessary information (i.e., trip orders, trip fees, discounts, parking vacancies) to corresponding users; (ii) travelers request and pay the trip order in the centralized platform and their trip order choices may be associated with the trip fee and discount; (iii) TNCs receive trip orders from the platform and provide mobility services by routing SAVs to maximize the profit. This study formulate the operation of POCP as a bi-level programming, where the government aims at minimizing the social cost by providing travelers with spatial-temporal discounts in the upper-level problem, and TNC aims at maximizing the profit given travel demand from the upper level as a DTA in lower level problem. This study prove that the proposed bi-level programming could be equivalently decomposed into two sub-problems with linear programming to solve for the minimum social cost and minimum subsidy amount, respectively. To validate our proposed model and solution algorithms, this study conducted numerical experiments in both small and real-world large networks. The results reveal substantial savings in social costs, equivalent to 110.38% of the subsidies spent in the small network and 121.96% in the large network. These findings underscore the efficacy of the proposed POCP model, emphasizing the potential of spatial-temporal subsidies in reducing traffic congestion and improving social welfare. In the network aspect, considering the route choice for AVs referring to the routes selected for the vehicle (e.g., via app, voice command, or a central controller), this study propose the concept of mixed sub-network equilibrium (MSNE) that divides a traffic network into two sub-networks: the user equilibrium sub-network (UESN), where AVs are controlled by users to follow the user equilibrium (UE) principle for seeking the route with minimum travel cost, and the system optimal sub-network (SOSN), where AVs are centrally controlled to minimize total travel cost by following the SO principle. This hybrid network setting addresses the challenge of applying system-wide control across large-scale networks by focusing centralized control only on critical regions. A key contribution of this research is the introduction of the critical size of the system optimal sub-network (CS-SOSN), which quantifies the minimum size of the SOSN required to achieve system-wide optimal performance. To solve for the CS-SOSN, this study propose a novel method of adaptive variable neighborhoods search (AVNS) algorithm. Through theoretical analysis and numerical simulation in three networks, this study demonstrate that the proposed framework effectively reduces total travel cost while minimizing the need for extensive centralized control. This study further validate the proposed CS-SOSN model on the real Hong Kong network and the results show that, in real-world traffic operations, only 44.17% of the network needs to be controlled to bring the whole network to the state of SO, without requiring full control of the whole network. The CS-SOSN model provides an effective method for managing the traffic network, reducing congestion, and improving performance in fully AV environment. This research offers practical insights for managing AVs in traffic networks by optimizing the balance between decentralized and centralized control strategies.