# Enhancing Route Guidance with Integrated V2X Communication and Transportation Systems: A Review
## 3 Route Guidance Models
### Multi-Class Route Guidance
In 2019, [PERSON], [PERSON], and [PERSON] studied the intricacies of modern urban transportation systems, taking into account various factors such as diverse traffic, parking availability, and multiple travel modes [77]. They presented an extensive modeling framework for spatio-temporal passenger and vehicularflows within a multi-modal network, covering solo driving, carpooling, ride hailing, public transit, and park-and-ride. The proposed model combines dynamic network loading, focusing on cars, trucks, and buses, with a multi-layer nested logit model that encapsulates passenger travel behavior. The resulting multi-modal dynamic user equilibrium (MM-DUE) is formulated as a Variational Inequality problem, which can be efficiently solved for large-scale networks using a gradient projection method. The numerical experiments conducted in Pittsburgh and Fresno illustrate that various factors, such as total passenger demand, parking prices, transit fares, and ride-sharing impedance, significantly impact the system's performance and individual user costs. The paper concludes by highlighting the adaptability of the MMDUE framework for diverse scenarios and suggesting its application to smaller cities with limited travel modes. The proposed model can be adapted to scenarios like solo driving and carpooling, driving with parking choices, and driving with transit. Nevertheless, more suburban area with trips of greater distances may be affected differently. The authors also express their intentions to conduct further research to calibrate the model using real-world data and extend the framework to include shared travel modes and uncertainties in future studies [77]. In 2023, the multiclass bi-criteria traffic assignment (MBTA) problem was examined and an alternative formulation that eliminates the need for class-specific path flow variables by utilizing traveler order preferences was proposed. High-value-of-time (VOT) travelers prefer faster, costlier routes, while low-VOT travelers opt for slower, cheaper ones. The study proves the equivalence of this formulation to the conventional MBTA model, while maintaining similar solution properties [78]. To address the nondifferentiable convex objective function, a path-based subgradient projection (SGP) algorithm was developed. This algorithm leverages subgradient and quasi-Newton methods, demonstrating superior computational efficiency and reduced memory usage in numerical experiments, particularly for large networks and multiple user classes. Despite excluding class-specific variables, the alternative formulation delivers equivalent results and extracts class-specific flows with fewer variables, outperforming conventional MBTA models in speed and scalability [78]. In conclusion, a static routing system offers the most straightforward solution, whereas a dynamic system offers a more sophisticated one but is less vulnerable to congestion. Similarly to how a stochastic system provides a more reliable system at the expense of additional computational work, a deterministic system can only offer route direction as the shortest path. Although reactive and decentralized systems add far less complexity to the road infrastructure, they can also be considered part of this trend. In addition, predictive and centralized systems can offer a better approach to handling traffic congestion. The intricacy of route guidance systems makes it possible that several development trends may evolve. Implementing simple, localized, decentralized, deterministic, reactive procedures in congested urban areas is the most likely development course. These systems have already been partially implemented in cities with significant traffic congestion. These systems lay the foundation for route guidance control strategies. These systems would develop into more centralized, predictive systems as technology advanced. Because of this evolution, the technological constraints of the present can be gradually overcome, alleviating concerns about traffic congestion [4].