# Enhancing Route Guidance with Integrated V2X Communication and Transportation Systems: A Review
## 3 Route Guidance Models
### Static Routing Guidance
Many investigations have been developed to compare and recommend methods, when highly accurate solutions are required. For example, algorithms belonging to link-, path-and bush-based methods, namely conjugate Frank-Wolfe (CFW), bi-conjugate Frank-Wolfe (BFW), algorithm B [61], linear user cost equilibrium (LUCE) [62] and traffic assignment by paired alternative segments (TAPAS) [63]. The findings indicate that advanced techniques like algorithm B and TAPAS are to be used to produce exact solutions. Furthermore, both algorithms demonstrate the capacity to attain high accuracy for instances of various sizes, ranging from small to large, in a reasonable amount of time [64]. Parallelization of the B algorithm, a bush-based approach for user equilibrium (UE) static traffic assignment (STA) has been presented in [25]. Three parallel variants were implemented to enhance computational efficiency, with the core idea allowing partially independent processing of bushes. The primary parallel variant achieved a significant speedup, reducing computation time by up to 77% with 12 threads, while maintaining good convergence, though slightly worse than the sequential version. The other two variants, employing parallel flow shifting, failed to achieve sufficient convergence for large networks, demonstrating that the sequential flow shift is critical for the algorithm's performance and is challenging to parallelize. The study also highlights optimization strategies, such as replacing the library power function with an iterative approach, which reduced computation time by 70%. On the other hand, some research has adopted mathematical programming formulation of the traffic assignment problem for origin-based UE. Most UE traffic assignment models are based on trips that use the cheapest path. Nevertheless, the path cost is the sum of the roads' (edges') costs, which concludes that these costs increase as the flow on these roads increases. [PERSON] and [PERSON] evaluated the convergence, usability, and speed by implementing three parallel variations and testing them on existing road traffic networks [25]. The results show that computation time was lowered by approximately 70%, when the power function from the library was replaced with an iteration-based solution. Another study used mathematical programming as an analytical-based methodology. The study discussed an origin-destination-based road pricing model with static and multiple period traffic assignment models. It used variational inequality formulation based on the Karush-Kuhn-Tucker (KKT) optimality conditions. The proposed model is compared to the no-toll UE scenario. The OD-based toll scenario was 10% better than the no-toll scenario, with a percentage cost reduction of 9.82%. A drawback to the study is that route splitting has not been considered in the optimization [65]. Many studies considered the System Optimum (SO) perspective as the assignment rule. The studies in this field are categorized as link-based, path-based and origin-based. For instance, the system optimum fuzzy traffic assignment problem model (SOFTAP) was introduced in previous research [48]. It adopted an analytical base for converting the conventional system optimal traffic assignment model to a fuzzy quadratic programming problem (QPP). Thus, the nonlinear objective function of the model is articulated in terms of fuzzy link flows and fuzzy link travel times. The link travel time is expressed with the Bureau of Public Roads (BPR) function to minimize the total system fuzzy travel time. However, the BPR method does not capture the driver behavior or the dynamic nature of traffic, such as speed and flow. Also, the technique only applies to highly continuous traffic [66]. [PERSON] et al. [67] introduced a micro-simulation model calibration using non-parametric statistical methods. The study evaluated the system optimum (SO) from a path-based perspective, using simulation-based methodology. The hypothesis is \"the travel time distribution of the simulated and observed travel times is statistically identical\".