## 2 Related Work  
Traffic assignment deals with the distribution of a given traffic demand in a network following ideal driver's behaviors. Static traffic assignment is based on [PERSON]'s user equilibrium (UE) and system optimum (SO) principles [23]. There is a huge amount of literature on traffic assignment concepts and methods [5; 6; 24; 25]. User equilibrium entails a user-centric traffic assignment, where each individual selfishly selects the most convenient route. This principle ensures fairness among users, as all individuals sharing a common origin and destination encounter identical travel times upon reaching equilibrium. However, a significant drawback of user equilibrium is that it fails to minimize the overall system travel time, leading to the incurrence of the \"Price of Anarchy\" (PoA) [26]. [PERSON] [20] furnishes evidence establishing the user equilibrium's existence and uniqueness. [PERSON] et al. [27] extend this by proving that this equilibrium aligns with a Nash equilibrium within a game involving many players. The stochastic version of the user equilibrium introduced in [20] considers drivers with incomplete information and less than complete rationality. [PERSON] and [PERSON] [28] proposed a model based on the expected utility theory. In the same direction, the travel time budget model was proposed by [29], the late arrival penalty model presented in [30], and the prospect-based user equilibrium model introduced at [31]. The ambiguity of driver travel time perception was handled using fuzzy decision techniques [32; 33; 34]. In contrast, the system optimum represents an efficient network-wide traffic assignment. Here, drivers are directed through the network in a manner that minimizes the total travel time. Nonetheless, users might encounter travel durations surpassing those of fellow travelers journeying from the same origin and destination, impacting overall compliance. Consequently, the limitations of either of these two approaches can be surmounted by amalgamating them, striving to establish a connection between user fairness and system-wide efficiency. The calculation of the optimal solution involves solving the TAP. It is an NP-hard problem, so heuristic approximate methods are used, such as the cumulative assignment method (CAM), the successive averages method (MSA), or the Frank-Wolfe algorithm [5]. Second-order cone and linear programming (LP) approaches have recently been proposed [19] with a very efficient calculation. Constrained SO (CSO) was presented by [PERSON] [35], where length-bounded alternatives were offered to the drivers. The impact of choosing a CSO traffic assignment is described in [36], where a theoretical work on efficiency and fairness is proposed. [PERSON] et al. [37] recently created an efficient method based on interpolation between SO and UE considering the Constrained System Optimum (CSO) defined by [PERSON] [35] and bounding the route unfairness. Dynamic traffic assignment (DTA) deals with the time-varying traffic conditions, leading to dynamic user equilibrium (DUE). Additional stochastic models are used to model the user's perception and travel time uncertainty, leading to stochastic user equilibrium (SUE) [7]. Route diversification is a critical factor in reducing congestion in traffic assignment. [PERSON] and [PERSON] [38] demonstrated the effects of an intelligent vehicle routing strategy on the performance and utilization of the traffic network in relation to system optimum in terms of overall transit times and congestion. Guidance diverts traffic from the freeway using a freeway overlaid on city streets when its marginal cost exceeds streets. Managing street speeds was a key finding for this routing guidance, though practical general implementation was not suggested. Modifying edge costs through the design of tolls has also been one of the mechanisms employed for diversifying routes and leading to system optimality [39; 40]. Ref. [41] considers the origin and destination tuples for the tolling service. In all cases, a microscopic simulation is used.