# Enhancing Route Guidance with Integrated V2X Communication and Transportation Systems: A Review
## 3 Route Guidance Models
### Dynamic Routing Guidance  
Dynamic routing guidance (DRG) models are proposed to overcome the weaknesses of static routing guidance (SRG) algorithms by utilizing real-time traffic information. It creates guidance based on current network conditions that the drivers are expected to experience. DRG models, as opposed to SRG models, reflect a more profound representation of traveler behavior decisions. Traffic processes are described with time-varying characteristics, including a detailed illustration of network components and intersection controls [68; 69; 70]. It has been proven that dynamic user equilibrium can be expressed as a differential variational inequality, which suggests a fixed-point approach for determining solutions. Also, it was demonstrated that fixed-point algorithms are highly effective on small and medium-sized networks [52]. However, these studies do not explain the applicability of the method to large traffic networks. A link-based semi-dynamic user equilibrium traffic assignment model considering signal effects has been introduced [54]. The study used optimal control formulation as the methodology. The model was examined on the Kanazawa urban area network in Japan. The simulation results demonstrate that a slight variation in signal cycle length within rush hours helps minimize total network trip time. Other studies have looked at dynamic user equilibrium from a trip-basedperspective [40; 41]. A study has investigated departure time choice in an isotropic urban network with identical travelers. The result shows that the width of the intended arrival time frame can result in a unimodal growth of accumulation and two peaks in the departure trajectory depending on the demand level [40; 41]. Another study combined UE and shared autonomous vehicle chain formation (DUESCF) as a bi-level model based on game theory. The study concluded that there are no empty trips and that each of the 100 vehicles used serves two trips, resulting in an ideal solution [41]. It is worth noting that the limitation of optimal control formulation is that the flow of existing links is treated as a set of control variables, where all travelers have equal trip length, rather than a variable function [66]. Variation inequality-based analysis has been applied to a path-based algorithm to solve the well-known logit-based stochastic UE using multiple-path gradient projection (MGP); the model achieved an RGP of \(10.0^{-4}\). The result of the model may differ when solving other traffic problems with a large number of paths existing for each OD pair [71]. Some studies examined dynamic traffic assignment (DTA) from a system equilibrium perspective considering link-based concepts. These studies have used optimal control formulation and variational inequality consecutively [41; 42]. A distributed assignment mechanism for DTA is proposed by utilizing heterogeneous-adviser-based multi-agent reinforcement learning (HAB-MARL) [42]. In terms of network throughput and network individual average trip time, the results reveal that HAB-MARL surpasses the other contrast techniques. However, variational inequality (VI) approaches are more computationally intensive than optimization models, raising issues of computational tractability for real-time deployment. Other studies have investigated SO-DTA using path-based assignment. For instance, different studies have examined the topic using optimal control formulation methodology [17; 19; 43; 44; 45]. The studies used trial and error, non-linear convex programming, sensitivity analysis, non-convex non-linear programming, and optimal control methods. Nevertheless, the optimal control theory approach optimizes the function using control variables that are subject to the optimizer's choice and the state of the interest variable. For instance, a path marginal cost estimate technique for SO quasi-DTA was investigated [17]. The derived SO solution improved the total system travel time by 4.8% compared to the UE solution. Also, the relative gap reached 0.01 at convergence.