# Review of Traffic Assignment and Future Challenges
###### Abstract  
The problem of traffic assignment consists of determining the routes taken by the users of transportation infrastructure. This problem has been the subject of numerous studies, particularly in analyzing scenarios for developing road infrastructure and pricing strategies. This paper reviews the major progress in the field. Accordingly, it shows that the evolution of intelligent transportation systems and the emergence of connected and autonomous vehicles present new challenges to classical approaches for solving the traffic assignment problem. It addresses two major perspectives: digital twins coupled with artificial intelligence to help decision-makers, and rule-based policy to offer users fair and efficient itineraries while respecting infrastructure capacity.  
traffic assignment; user equilibrium; intelligent transportation systems; smart cities +
Footnote †: journal: Applied  
0000-0002-414-407X/0000-0000-0000-0000-0000-0000-0000-0000-0000-00000  
projects. The results of traffic assignment enable the assessment of various planning scenarios, such as the construction of a bridge, the renovation of a railway line, tolling on a highway, or simply a change in traffic direction. The evaluation of the results assesses the impact on transportation network users, traffic conditions, and the environment.  
Numerous literature reviews on traffic assignment abound in academic literature. Special emphasis has been placed on traffic assignment from various perspectives, including traffic control [1], the convergence of simulation-based assignment [2], and the used models of traffic flow [3]. More recently, other notable areas include the application of traffic assignment for sustainable road traffic [4; 5], evolutionary game theory applied to traffic [6], and bridging user equilibrium and optimal solutions in static traffic assignment [7], among others.  
In contrast to the aforementioned papers, this review adopts a more generalist approach. Its primary purpose is to offer a broad introduction to the field of traffic assignment, catering to readers of all expertise levels. The review highlights significant contributions that constitute the domain's foundational pillars of theory and methodology, drawing on well-established and widely recognized fundamental contributions in the field. Importantly, this literature review avoids being application-specific. It refrains from delving into detailed discussions of traffic models, particular frameworks of transportation forecasting, or specific applications in reality. Instead, it focuses on introducing key contributions in the field and outlines future directions based on technological advancements in transportation. More precisely, it revisits the fundamental concepts of traffic assignment and juxtaposes them with the advancements in intelligent transportation systems in order to address promising directions.  
The rest of the paper is organized as follows. Section 2 presents the problem statement, gives the scope of Section 3, and ends with an illustrative example. This section aims to introduce the reader to the most important direction of the research in the domain. Section 3 presents the concept of traffic assignment and how the problem could be solved in a decentralized manner. Section 4 focuses on extending the model to handle public transportation and policies for improving traffic conditions. A discussion on emerging techniques and the challenge regarding traffic assignments in the upcoming years is presented in Section 5, which focuses mainly on the impact of the progression of intelligent transportation systems. Finally, the paper is concluded in Section 6.