## 1 Introduction
### Motivations and Contributions  
(1) **Methodology**. Passenger gatherings, responding to and deciding upon information, varies according to different circumstances. Studies should be conducted based on the characteristics of scenarios to model passenger decision-making processes [26; 37]. As analyzed earlier, microscopic models adequately consider the individual choice behaviors based on the integration of environmental information into mental representations, leading to interpretable results. However, in a large-scale problem with numerous objects, accurately characterizing the behaviors of each individual and formulating their interplay are almost impossible, bringing exponential computational complexities [10; 16; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36]. On the other hand, adopting a macroscopic model [14; 15; 20; 22; 23; 24; 25] is beneficial for solving large-scale problems, while it heavily relies on repeated simulation experiments based on giving appropriate parameters. In order to meet the requirements of the application scenario and eliminate the shortcomings of the models mentioned above, we address the issue of passenger flow assignment by the micro-individual passenger choice model and calculate total passenger flow based on the macro-traffic flow model (Table 1).  
(2) **Problem Circumstance**. The above literature showed that the evacuation problem generally implies two assumptions: One is that the evacuation occurs in an enclosed place with complex internal structures, such as subway stations, buildings, etc., that obstruct pedestrians' vision. The other is that evacuation is an emergency scenario and pedestrians are in a hurry and panic, which causes pedestrians to leave or escape at an abnormal speed [5, 6, 7, 8, 10, 11, 12]. These situations force pedestrians to subconsciously make decisions and choose the nearest exit or the least crowded route within their vision. However, a typical high-speed railway platform is open without any obstruction, expanding passengers' visibility to collect information comprehensively, resulting in accurate and reasonable choices, such as selecting the shortest paths or the least crowded exits, and achieving the maximum utilities.  
Therefore, the contributions of this paper are threefold:  
* In order to quantify the risk of passengers falling off the platform, we propose a new concept of risk probability. We apply a normal distribution to fit the probability distribution of the number of disembarking passengers. The risk probability is defined using the gap of cumulative probability corresponding to the number of passengers completing the exit under the maximum allowable travel time.
* We propose a novel integrated approach that combines passenger flow assignment based on choices of individual passenger path utility with a dynamic calculation of passenger flow. This methodology determines a fully demonstrated range of exit widths that reduce the risk probability to 10%.
* We prove that the optimal solution of the passenger flow assignment model with minimum generalized cost is equivalent to the number of passengers based on path utility choices, thereby simplifying this problem.
* We identify the bottleneck areas on a typical platform of a Chinese high-speed railway. The bottlenecks have opposite effects on the exit width on different travel paths (links), which suggests that the exit cannot be expanded infinitely to reduce congestion.