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1 Introduction

Imagine yourself being stranded on your train journey for four hours! What would you do and how would you feel? A lot of times passengers get frustrated and angry and start to yell or intimidate other passengers or the personnel on the train. Sometimes, passengers break out the train while that is not allowed and could start walking on the train tracks or other dangerous areas. On November 24th 2015 for example, passengers on the train towards Utrecht Central Station, Netherlands, got stranded for four hours without any clear threat and repeated misinformation. Several passengers decided to break free and open the emergency exit without permission and despite warnings of the conductor. Luckily nobody got hurt.

The problem in these situations is that many stranded passengers need to be kept within a confined space, without electricity, working toilet, food and in very warm or cold conditions. How long will the stranded passengers follow the orders of the personnel? When does the frustration lead to a dangerous level, so that passengers start to perform misbehaviours such as verbal and psychical violence or opening emergency doors without permission? To investigate these questions, computer models can be used, since real world experiments with humans are difficult to perform for these situations. With computer simulations, many different scenarios can be investigated.

The research question is: what is the effect of (1) age, (2) gender, and (3) traveller type, on: (a) the group frustration level and (b) the number and (c) type of misbehaviours in a scenario with stranded passengers on a train. Factors important for the level of frustration and for answering the research question were modelled in an agent-based model. The rest of this paper is organized as follows. First, the proposed stranded passengers model and literature background is presented in Sect. 2. Then, in Sect. 3 the hypotheses and simulation results are shown, followed by a summary and discussion in Sect. 4.

2 Stranded Passengers Model

In this Section: (1) it is described which theories and concepts from the literature have been translated into modelling concepts for the agent-based model; (2) which scenario is modelled and (3) the conceptual model and formalisation are described briefly.

2.1 Socio Cultural Modelling Concepts

Different socio-cultural factors were chosen for modelling: age, gender, traveller type, emotional contagion and social identity. Here, it is explained how they are based upon the literature and how they are modelled. Social contagion of frustration takes place, based on social identity [4, 9]. Every passenger compares him/herself to other passengers. Passengers that are similar to him/herself (based on age, gender, traveller type) can infect their frustration level stronger than passengers not similar to him/herself. This influence is causing a strengthening or diminishing of the frustration experienced. This mechanism is based on social identification theory [10] and emotional contagion [2].

The agent’s age and gender affect the selection of actions. According to literature, young men are more prone to exert aggressive behaviour compared to any other age group or gender. [5]. Aggressive actions undertaken by other agents are attributed a negative valence, further increasing the passenger’s own frustration.

There are two traveller types: commuters versus tourists, representing different experiences of travelling. These travellers have different goals based on their travel experiences: arriving on time versus arriving in itself (not necessarily on time).

Based on the frustration level in combination with the characteristic of the passenger (age, gender, traveller type) an action is chosen (do nothing, ask questions, yell, intimidate or apply force). This is based on the literature: the higher the frustration level, the more aggressive the behaviour and men are more likely than women to express aggression. [1, 3]. This is modelled with different thresholds for behaviours for each passenger type.

Every passenger has a frustration level that will increase or decrease based on: 1. the events (public service announcements with information about the delay or speed of the train), 2. the frustration of others around the passenger, 3. the goal(s) of the passenger. The frustration level increases when the estimated arrival time (based on the delay) is later then the scheduled arrival time. The larger this difference, the higher the frustration level becomes. The public service announcements and speed of train can increase or decrease the frustration level. (increase: information about a delay or train standing still, decrease: train starts to move, new information on arrival time). This is combined with the goals of the passenger. A passenger that wants to arrive instead of arriving on time won’t increase its frustration level in case of a delay, but does increase its frustration level if a new estimated arrival time can’t be given (arrival is unsure). Finally, it’s combined with the social contagion of frustration levels of other passengers similar to the passenger in focus.

2.2 Scenario of Stranded Passengers in a Train

The model simulates passengers that are in a train that is stranded outside of a train station, whereby passengers are not allowed to exit the train without clear instructions. All agents in the model are either passengers or railway staff. Passengers can be either commuters (assumed to be in a rush to arrive at a location on time) or tourists (assumed to be more relaxed and less worried about arriving on time). Public service announcements (PSA’s) are made on the train and all agents can perceive them. At the initialisation of the model (before the first PSA is made), passengers have a belief on their arrival time and location of arrival. A passenger will update his/her beliefs based on the first public service announcement broadcasted through the entire train. After the broadcast, the agent will believe it will arrive at a new time X on location Y. After initialisation, a first announcement about the delay is made. Beliefs are also dependent on the movement of the train. At the start of the simulation, the train is moving and all passengers and staff are at a certain location in the moving train. All passengers notice the movement of the train and will be able to notice that the train moves, or is standing still. Should the train stand still, passengers start to update their beliefs and attribute negative valence to this event, since it is in conflict with prior held beliefs about their supposed arriving time. Commuters will keep getting frustrated at PSA’s indicating there is no movement yet and often check if the train has already started moving. Tourists on the other hand overcome the initial negative valence associated with the violation of their beliefs, because they are less in a rush than the commuters. Passengers are experiencing the increasing levels of frustration and are also expressing it towards other passengers. Passengers that are resembling each other closely (in gender, age and traveller type), can influence each other’s level of frustration more than people that do not resemble each other. This influence is causing a strengthening or diminishing of the frustration experienced. The level of frustration also indicates which intentions for subsequent behaviours each passenger has. When frustration reaches a certain threshold, then a passenger might get up and start asking questions to the conductor regarding the delay, it can start to yell or can perform physical violence. Otherwise the passenger does nothing (keeps enjoying the journey). The quality of information received might be positive and alleviate the frustration a little or it might also be ‘bad’ information leading to more frustration. In the case that frustration is reaching high levels, the passenger starts to become aggressive and has a higher chance of acting aggressively, by spitting, punching or vandalizing. Whether or not the passenger will partake in such drastic actions is based on the makeup of the agent. The agent’s age and gender are influencing the selection of actions, according to literature. Aggressive actions undertaken by other agents are attributed a negative valence further increasing the passenger’s own frustration.

2.3 Conceptual Model

The agent-based model was created with a belief-desire-intention (BDI) modelling approach. [8] The modelling concepts with their dynamical relations between them are shown in Fig. 1. Concepts on the left of the box are input states: environmental factors (events) and observations (group emotion, perception). The internal agent concepts inside the box are: beliefs, frustration, goals, intentions and the agents’ make-up. The output concepts at the right of the box are action and expression. The arrows depict which concept(s) influence another concept. In Table 1 these concepts are explained in more detail.

Fig. 1.
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Conceptual model.

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Table 1. Description of agent concepts.
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The model combines contagion mechanisms from the ASCRIBE model [2] (social contagion of emotion) with appraisal mechanisms (individual emotion) from the OCC model [7]. This fits the goal of modelling frustration dynamics in stranded passengers best. The current Stranded Passengers model differs from the ASCRIBE model in that it includes new agent mental states and agent characteristics to model the effects of culture on the processes during emergency situations and it includes appraisal mechanisms. The model was implemented in the Netlogo language [6]. For lack of space only an example rule for of the agent’s behaviour (a decision rule for a female traveller to start yelling) and the pseudo-code are shown below.

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3 Simulation Results

To determine the effect of (1) Age, (2) Gender, (3) Traveller Type on: (a) the level of frustration of the passengers and (b) the type of (mis)behaviours, multiple simulations were performed whereby these factors were systematically varied.

Hypotheses. (1) Adolescents and adults are expected to be most frustrated compared to children and elderly, because adults and adolescents have travel goals to arrive on time, while children and the elderly do not; (2) when there are more male passengers, there will be more misbehaviours than when there are less male passengers. It is assumed that men are more assertive and take more risk, together with emotional contagion this will lead to a faster increase in the group frustration level; (3) when most passengers are commuters, there will be more misbehaviours when there are an equal number of commuters as tourists. It is assumed commuters become more frustrated and faster than tourists. There were no a priori hypotheses on the effect of emotional contagion on the frustration level, because this is an emergent effect.

Simulation Results: Scenario. When comparing the actions performed by frustrated passengers in two scenarios (indefinite delay and long delay), passengers choose to yell or ask questions above intimidation or physical violence. See Fig. 2.

Fig. 2.
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Passenger actions during an indefinite delay (left) or long delay (right).

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Simulation Results: Emotional Contagion. In Table 2 it is shown that emotional contagion has an effect on the choice of action. When social contagion is off, asking questions is the most performed action. When social contagion is on, yelling is the main chosen action and applying intimidation or force are relatively chosen more frequently than when social contagion is off. An explanation could be that the spreading of emotions through social contagion speeds up the group frustration level, which in turn leads to more intense misbehaviours. The other way around, decrease in group frustration is also spread through emotional contagion when the train starts riding in the long delay scenario, which in turns leads to no aggressive actions quickly.

Table 2. Number of passenger actions in simulation experiment.
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Simulation Results: Gender, Age, Traveller Type. When most passengers are male, group frustration level is larger than when are more or an equal number of female passengers. This supports hypothesis 2. See Fig. 3. Mainly the adolescents and adults have a larger amplifying effect on the group frustration level compared to the children and elderly. This supports hypothesis 1. Traveller type does not seem to influence the group frustration level. Surprisingly, this is different than expected in hypothesis 3.

Fig. 3.
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Level of frustration by gender, traveller type and emotional contagion

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4 Conclusion and Discussion

An agent-based model of group frustration level and number and type of misbehaviours of stranded passengers on a train was created. The main research question was: what is the effect of (1) age, (2) gender, and (3) traveller type on: (a) the group frustration level and (b) the number and (c) type of misbehaviours in stranded passengers train scenario. Structured simulations supported two out of three a-priori hypotheses. Furthermore, social contagion showed an interesting emergent effect: an amplifying effect on the group frustration level. These results are of interest to emergency prevention and management stakeholders. This model will be further developed and used by transport operators and other emergency prevention and management professionals to run multiple stranded passenger’s scenarios and prepare for these scenarios.

A strong point of this work is that it is innovative. It models social contagion mechanisms and cultural factors. These are both still quite rare in crowd models. Next planned steps are (1) extending the model with more behaviours of the passengers and the presence of facilities; (2) changing the environment and scenario to stranded passengers at an airport (3) validating this model with real world data.