# Enhancing Route Guidance with Integrated V2X Communication and Transportation Systems: A Review
## 3 Route Guidance Models
### Static Routing Guidance  
Static routing guidance (SRG) directs vehicles from their origin to their destination without information on real-time traffic conditions [55; 56; 57]. It is based on historical data, which might show traffic patterns over a specific period of time, but does not represent the network's current state. The SRG recommends the optimal path based on the assignment concept, whether it is UE or SO. Researchers have proposed several models and tested them on real roadways to determine the best algorithm for the shortest path scenarios. Many studies have looked at static assignment from a user equilibrium perspective. This assignment is based on [PERSON]'s first principle: Travel times between a specified origin and destination on all used routes are equal and less than or equal to the travel times on any unused routes [58]. Some of the studies adopted an analytical-based methodology. For example, [PERSON] and [PERSON] [52] utilized a convex nonlinear optimization on a Reduced Gradient (RGR) algorithm as an improvement on the Frank-Wolfe methods. The study uses 2, 5, and 10 as the number of active paths for choosing the basic path for a path-based algorithm on a large-scale network. The results show that the RGR algorithm achieves a good convergence at relative gaps of the order of \(10^{-14}\), when compared against several reference traffic assignment algorithms. Some research adopted a mathematical programming formulation as an analytical-based approach. Much research has entailed the need for generating a meaningful path flow solution in practice. Therefore, a convex objective function was proposed as an alternate approach to determine a single path flow solution representing the entropy-weighted average of the UE path flow solution space [24]. The model generalizes the Bar-Gera and [PERSON] [59] proportionality condition and is simple to understand. Moreover, according to the outcomes of numerical studies, the path flow solutions under the entropy-weighted user equilibrium and the maximum entropy user equilibrium are essentially the same. Using a convex objective function, the problem of proportionality and uniqueness for UE route flow models has been addressed. Also, the relationship between bypass proportionality and entropy maximization has been considered [60]. In addition, the unique proportionality conditions to determine the route flow numerically have been illustrated using [PERSON]'s method [60]. However, the proposed approach still needs to address the applicability to large-scale networks and consider the computational cost. [PERSON] and [PERSON] used sensitivity analysis to describe a static road traffic assignment model with queuing applied on large-scale congested networks [49]. The model captures flow metering and spillback effects of bottlenecks. The results show high-precision user equilibria in terms of accuracy, robustness and accountability, with a relative gap \(<\)10\({}^{-4}\), on large scale networks. In addition, some studies considered UE assignment from an origin-based point of view. Most studies in this direction have applied the analytical approach as their methodology. For instance, convex optimization algorithms (optimal control formulations) have been adopted for the static traffic assignment problem. The end model is called \"Physarum\", which needed to be revised to apply to real traffic networks with double-way traffic criteria and multiple OD pairs. Therefore, the modified Physarum-inspired model for UE has been proposed by decomposing traffic flux based on origin nodes to find the shortest path. The results showed a better convergence performance, when compared to algorithms such as Floyd-Warshall (FW), Bi-directional Floyd-Warshall (BFW) and Contraction Hierarchies algorithm (CH); the relative error is greater than 10\({}^{-4}\)[5]. Nevertheless, computing time, the dynamic nature of the traffic network, and the elastic demand traffic network have not been considered as parameters in the study.