# A Hybrid Control Path Planning Architecture Based on Traffic Equilibrium Assignment for Emergency
## 2 Related Work  
### Path Planning Based on Traffic Assignment  
The research community has proposed various techniques to improve path planning in emergencies using traffic assignment methods. Earlier, researchers used the static traffic as signment (STA) [6; 7; 8; 9] to estimate road impedance conditions and guide traveler assignment. For example, the Logit assignment model [5] is a typical probabilistic stochastic assignment method that assumes that the user's error in estimating the actual road impedance satisfies a Logit distribution. However, the period of traffic distribution is difficult to determine. If the interval is short, the traffic state will be affected by the previous period, and vice versa, it will change drastically. This is because static models do not reflect dynamic changes in traffic states. This has led to a shift in the study of traffic assignment to the more realistic dynamic traffic assignment (DTA) [16]. DTA focuses on discovering the natural evolution of the transportation system and thus depicts the continuous distribution of traffic flows [17]. DTA has been favored by various works for its typical application in congested networks such as frequent emergencies [18; 19; 20]. Several researchers have proposed different DTA-based techniques to estimate and depict the continuous distribution of traffic flows and in the process accomplish path planning. [PERSON] et al. presented a review of travel behavior modeling in dynamic traffic simulation models of evacuation from four aspects [10]: traveler behavior, travel demand, trip distribution, and traffic assignment representation. In addition, [21; 22] and others have also studied the DTA problem through real-time traffic simulation. [PERSON]. [11]  optimized the traffic distribution using the method of successive averaging (MSA) and solving the dynamic equilibrium problem for UEs and SOs using the time-varying shortest path algorithm. The MSA method is also used in [12]. The authors additionally utilized [PERSON]'s temporal queuing method [23] to solve the path runtime computation, which improves the computational efficiency. These two studies are based on simulated small-scale road network models, and it can be seen that MSA will be extremely inefficient in large-scale transportation networks due to its iterative computational approach. Subsequently, some researchers have started to consider the impact of real transportation network evolution on path planning. [PERSON] [13] proposed an extension to a mesoscopic dynamic traffic assignment (DTA) model which was developed to determine quantitative indicators for estimating the exposure component of the total risk incurred by the transport networks in an area. But the method's deterministic assessment using linear or constant metrics does not express the complex dynamics of transportation well. Ref. [24] proposed an equilibrium model considering dynamic background traffic flow in a problem targeting parking lot evacuation optimization, and experimentally demonstrated that the background traffic flow has a great influence on the selection of the optimal path. Then, [PERSON] [14] clearly defined the concept of background traffic, i.e., the traffic flow consisting of existing vehicles on a road network before emergency evacuation affects the assignment of evacuation vehicles, consequently affecting the formulation and implementation of emergency plans. In this work, they considered the presence of background traffic in dynamic evacuation traffic studies based on three constraints, including the state equation, propagation function, and conservation. Experimental validation by [14; 24] shows that background traffic is an important guide for the generation of traffic assignment strategies. However, while some of the above work also attempts to give real-time path planning decisions by determining the evolution of traffic flows, the evolution of network traffic predicted by the model is usually only applicable to deterministic scenarios. Emergencies have considerable uncertainty.