## 1 Introduction
Stochastic models commonly use a classical random walk to generate random paths that transit from one node to others to simulate the dynamic statistical characteristics of the drivers' random exit selection [15]. The classical random walk assumes that the transition probability between different nodes follows a particular probability distribution, thus the dynamics of all the traffic can be evaluated according to the statistical characteristics of the walk paths on the network [16; 17; 18]. Recently, with the continuous accumulation and refinement of traffic observation data [19; 20; 21], growing evidence shows that the classical random walk can well capture some nonlinear and nonstationary characteristics, e.g., power-law distribution [22], dynamic rerouting behavior [23], and percolation patterns [24] of urban traffics. However, rare study reports good results on applying the classical random walk on expressway traffic. This is because in the classical random walk, each driver leaving the expressway is independent. However, in expressway traffic flow, a driver's departure from the traffic flow during the exit selection process causes the state of the traffic flow to change, thereby affecting the random exit selection of the drivers in the subsequent traffic flow [25; 26]. There are several key challenges for the current models to integrate the effects of stochastic fluctuation caused by the random exit selection. Firstly, in a single random exit selection, the driver at a given time may consider exiting the expressway at multiple exits, which can occur at different times [22]. With this simultaneous decision making, the process of random exit selection for multiple alternatives should be modeled by a process of simultaneous searching and traversing of multiple alternative paths rather than a single path in the entire decision network. These will form a dynamically changing probability distribution that will then affect the spatial-temporal locations of the individual drivers and then lead to the fluctuations of the overall traffic volumes. The modeling of such chain interaction is difficult. Secondly, the dynamic decisions of drivers during the driving process can hardly be observed. Even if the trajectory of a driver can be logged with video or other methods, the detailed mechanisms of how a driver makes random exit selection is unknown [27]. With this unobservable nature of random exit selection, the deterministic model can hardly be used. Lastly, there are bidirectional interactions between the random exit selection and traffic volumes. The aggregation of random exit selection by many drivers will change the traffic condition, yet, the change of traffic condition will also affect the random exit selection of each driver. Because a continuous dynamic observation of a driver's choices of exits is not possible, the mechanisms of this bidirectional driver-to-traffic interactions are not clear. From the above discussion, it is clear that modeling the effects of the dynamic nature of random exit selection by drivers on traffic conditions is still a challenge yet to be addressed adequately. Quantum walk, is the quantum extension of the classical random walk, which is an ideal tool to solve dynamic and parallel stochastic path searching on complex networks [28; 29]. In the quantum walk, when the system is not observed, the driver can choose any of the feasible nodes (exits) at the same time with different probabilities. The transition between the nodes on the network is not \"either here or there\" but \"both here and there\", thus the path generation in the quantum walk is \"all possible paths\" rather than \"a single path\" as in the classical random walk [30]. All possible paths then will collapse to a single determined path when the observation is applied. With efficient matrix algorithms [31], a quantum walk can converge much faster than the classical random walk [32].