## 1 Introduction  
In recent years, there has been a global increase in the demand for rail transport, and rail usage is expected to continue to increase worldwide [1]. Passenger streams in railway systems are growing dramatically in many cities over the world with the rapid development of rail transit. This reflects on stations that face enormous pressure from passenger congestion and the high level of overcrowding in peak times. The metro systems in Beijing and Shanghai provide a daily transport service for more than nine million passengers, and statistics indicate that the annual usage has almost doubled from 2011 to 2015 [2; 3]. In the UK, the number of rail passenger journeys has more than doubled over the last 20 years [4]. Moreover, by 2050, over 75% of the world's population is expected to be living in cities. It is a priority for municipalities worldwide to support citizens' mobility within the urban environment. The British rail network is likely to boost passenger-km by 50%, in accordance with the government targets set out in the Ten-Year Plan for Transport [5]. Moreover, in some parts of the world, railway infrastructure has been used extensively for carrying large volumes of goods and is now ageing; for example, in Europe, the network infrastructure was built 150 years ago [6]. Thus, the highly demanding and intensive use of old systems increases the risk factor and holds the industry under pressure from both society and government. Moreover, accommodating an increasing number of people on public transportation is a challenge, especially during peak commuting hours when overcrowding creates incredibly high levels of discomfort and unsafe train stations for passengers. It has been noted that crowding increases risks to the health and/or safety of those affected [7]. The industry offers some solutions, such as discouraging peak-time travel by means of fare differentiation. However, this has had no observable effect on passengers' travel patterns [8]. Railway stations are an essential part of railway systems; they are the point where passengers start and end their journey. Moreover, some stations now offer commercial facilities to travellers. This highlights the complexity of the entire system, whereby stations are dynamic systems that have to accommodate thousands or millions of people arriving and departing every second, whilst relying on infrastructure design, operational processes, and other factors. Managing the passenger flow in stations is vital because stations are a major component of the public transportation system and attract a large number of passengers. Increasing congestion in stations generates many risks to be managed [9] and remains a major source of complaints by travellers. Overcrowding affects railway operations, traveller satisfaction, dwell time, service reliability, passenger wellbeing, safety, and security. It has been shown that the optimization of passenger flow is essential for operation, traffic management and planning, improving terminal space, and increasing public safety and security [10; 11]. Hence, railway station operators can remove restrictions and allay fears, thus attracting passengers, improving passenger experience and satisfaction, and ensuring the long-term sustainability of stations [12]. Nevertheless, managing passenger flows and the risks of overcrowding are challenging owing to the complexity of station designs and unexpected passenger behaviour. Several operational processes need to be managed in real-time, creating a dynamic environment. Operators must monitor, scan, manage, investigate factors, and update plans based on the level of expected hazard. This enables them to select appropriate plans and strategies for reducing risks to an acceptable level [13]. In many situations, however, probable risk management methods may not provide satisfactory results because risk data are inadequate or introduce high levels of uncertainty [14].