# Congestion Evaluation of Pedestrians in Metro Stations Based on Normal-Cloud Theory
## 1 Introduction  
Metro stations are important infrastructure in the urban rail transit system because they are the distribution hubs for transferring passengers on/off board [1]. The contradiction in demand and capacity of the rail transit facility has become increasingly prominent with the rapid growth of passenger flow, highly concentrated in space and time. In China, by 2018, the total rail transit passenger reached 21.07 billion, which was 2.59 billion more than that in 2017, a 14% increase from last year [2]. The total RPK (revenue passenger kilometers) of rail transit is 176.08 billion-person kilometers, the average passenger intensity in 2018 was 8000 person/(km-day) [2]. The rail transit corporations, such as Beijing, Shanghai, and Guangzhou, have put forward restrictive measures on the rapid expansion of the passenger flow [3]. Traditionally, the metro stations are featured with closed space, complex facilities, short-term clustering, and uneven distribution of passenger flow. As such, controlling the large passenger flow has become a great challenge. A better understanding of the pedestrian congestion level would be beneficial to pedestrian flow management and control in metro stations.  
Most stations in metro networks are irreplaceable due to daily operations. If any of them were disrupted, it would impact not only the individual metro line but also the whole urban rail transit networks [4]. For example, recent years have evidenced several natural or man-made disasters that have prompted the evacuation of passengers in major metro/train/bus stations, resulting in fatalities and injuries [5; 6]. Moreover, metro networks are not incident free since heavy crowds may cause discomfort to passengers and even accidents [7]. [PERSON] et al. [8] divided the incidents into six categories, including passengers, technical failures, human performance, fires, malicious or illegal action, and management action, which represent the accident precursors as well. [PERSON] et al. [4] indicated that common incidents in metro networks included collapses, leaks, fires, and terrorist attacks. Therefore, assessing the pedestrian congestion level was critical for the urban rail transit systems. It is beneficial not only to understand passenger satisfaction [9; 10; 11] but also to assess the causes and develop corresponding strategies to manage or relieve congestion and improve safety [12; 13; 14; 15; 16; 17].  
The primary objective of this paper was to evaluate the passenger congestion level in metro stations. An indicator, the grade of pedestrian crowd, short for GPC, was defined to quantify the passenger congestion level from I to IV, ranges from 0 to 10, the interval value for each level is 2.5, which corresponds to excellent, good, ok, and bad. The status description of Level I to IV is completely unimpeded, relatively unimpeded, slightly impeded, and heavily impeded, correspondingly. The higher the value of the GPC, the more serious the pedestrian flow crowd is. Three facilities including the channel, stairway, and platform, were consideration for the evaluation. A normal-cloud (NC) model was used for the evaluation. The analysis was demonstrated using a case study from the city of Ningbo, Zhejiang province, China.