## 1 Introduction  
When a driver heads to his/her destination via intercity expressways, despite the fact that the destination is often deterministic, the multiplicity of available routes leads to randomness in exit selection. Concretely, a driver will pick the travel route from multiple candidates based on considerations of economy, timeliness, and traffic conditions [1]. Under such a scenario, the exit section is randomly induced by route selection, contrary to the conventional deterministic exit selection. We call the random exit selection phenomenon route-induced random exit selection. The aggregation of the random exit selection by individual drivers will affect the distributions of traffic flow in space-time along the expressway [2]. Besides, due to the dense traffic flow and the relatively fast speed of the expressway traffic, any vehicle that passes through the expressway exit will affect the speed of the following vehicles. The combined effect of a large number of individual random decisions at different destinations/exits along the expressway makes the overall traffic flow exhibit significant inhomogeneities, nonlinearities, and uncertainties in space-time [3]. Considering this random exit selection of drivers in traffic flow simulation might help to reduce model uncertainty and improve model accuracy. Current traffic volume simulation models can be divided into two major categories: deterministic and stochastic models [4]. Most of the current traffic volume simulation models consider the overall traffic volume and rarely consider the influence of random exit selection in the model. The deterministic models consider the overall traffic volume that can be accurately modeled and solved by numerical methods, and the output of the model is fully determined by the parameter values and the initial conditions. Deterministic models can be further classified into three subcategories: macroscopic models, microphysical models, and intelligent agent models [5]. Macroscopic models consider the overall effects of random exit selection. Such models commonly use endogenous or exogenous variables to summarize the effects for the traffic volumes at each exit, including the exit selections (e.g., origin-destination models [6] and logit analysis [7]). Therefore, it only reflects the total or average effects of traffic volume rather than the random exit selection of individual drivers [8]. Microphysical models (e.g., gravity models [9] and lagrangian traffic state models [10]) use physics laws to approximately describe the influences of random exit selection. Such models abstract each driver into indistinguishable particles, characterizing the influences of random exit selection by varying the attractiveness of the particles to approximate the spatial and temporal dynamics of each driver through different exits [11]. The intelligent agent models simulate the traffic volume from each exit through an agent with active sensing and decision-making ability [12]. Such models can support the random exit selection of drivers by giving the agent predefined evolution rules or targets to evolve the agent autonomously [13]. However, the predefined rules can only be used to model exits choices from the perspective of certainty rather than stochasticity [14]. Therefore, the intelligent agent models cannot reveal the impact of the dynamic nature of a driver's random exit selection in driving. These deterministic models have the advantages of having clear mechanisms and can be efficiently solved numerically, but they do not have the ability to model the dynamic effects of the random nature of drivers. The second category is the stochastic models. Such models assume that random exit selection is a complex stochastic system, formed randomly under the influence of many factors and cannot be accurately modeled with simple deterministic physics or evolutionary rules. Stochastic models formulate random exit selection within a complex network, which considers each choice the driver made as a node in the network.