1 Introduction

Crowd Dynamics can be defined as the study of the how and where crowds form and move above the critical density of more than one person per square metre. At high density there is the potential for overcrowding and personal injury. It is therefore important to understand the dynamics of crowds, how crowds understand and interpret information systems, how management systems affect crowd behaviour. We call this the science of crowd dynamics.

2014 update - this has expanded into psychology and behaviour and the broader term "Crowd Science" is now more commonly used. I have been teaching the principles and applications of crowd science for 15 years now. Topic include modelling spaces, behaviour and events coupled with crowd monitoring. The broad definition is Crowd Modelling, Monitoring and Management. These topics are aimed towards the development of safer, more robust, standards in the development of a crowd management plans.

We examine different approaches used to define crowd safety, in particular the Green Guide [1, 2] which defines the criteria for sporting grounds, the Purple Guide [3, 4] which defines the criteria for pop concerts and similar events and the Primrose Guide [5] which defines the criteria for existing places of entertainment.

We examine the relationships between crowd flow and density, specifically the work of Fruin [6] who has been instrumental in setting the standards for pedestrian planning around the world. We also examine the work of Ando, Aoki and Togawa [7, 8, 9, 10], Henderson [11, 12], Helbing [13, 14, 15, 16, 17, 18, 19, 20], Galea [23, 24], Paulsen [25], Cohen [26, 27] and Penn [28].

In addition to the existing body of literature and guides we perform extensive field studies to examine the nature of crowd dynamics with respect to local geometry, for example, building entrances, turnstiles and corridors. Case studies, Balham Station, Wembley Stadium and the Hong Kong Jockey Club are presented.

2013 update - since the publication of this material I've modelled many major projects and client sites such as the ** Jamarat Bridge** and the holy mosque -

**, Saudi Arabia,**

*Al-Haram***,**

*London New Year Events***, and the**

*Canary Wharf Evacuation***, London. However the bulk of my work turned away from simulations and towards education, teaching and training techniques, safety standards and risk analysis techniques. Why? Simply because the people who would have most impact on crowd safety don't (and perhaps never will) use computer simulations. The objective of this research was to make a difference. Education has a far greater impact on the industry than expensive computer simulations. The workshop courses, on-line training and support materials all put crowd safety, risk analysis and crowd management techniques where they could have most impact, in the hands of the crowd managers.**

*Royal Wedding*1.1 Legion

Legion is the name used to describe the collection of programmes developed to analyse the dynamics of crowds. The heart of this suite there is an algorithm which models the dynamics of the crowd by using a least effort algorithm. It treats every person (entity) in the crowd as an individual, calculating their positions by scanning their local environment and choosing an appropriate, humanlike, action.

2013 update - I sold off the rights to Legion in 2000 and developed Myriad I then Myriad II. Legion was an agent based tool and, as such, limited to the modellers abilities as trails had to be defined for the crowd movements. Myriad, on the other hand, is a mutli-scalar modelling, using three different mathematical tools for the analysis of built and complex spaces and, as such, is far more flexible, covers a wider range of modelling environments and the three disciplines complementing each other for detailed analysis. Myriad does not require “ rails” for the entity movement is a very complex modelling environment, expert tools for expert users. My work is now focussed on developing operational tools for a much wider remit of crowd safety for non-experts.

1.1.1 The least effort algorithm

Suppose we have N entities, with an entity i at position (xi, yi) inside a region R of the plane R2, representing the accessible parts of a building. Each entity's path Pi through the building is constrained: first, by the entity's speed distribution, and secondly by the requirement that entity i visit certain places or subregions of the building in some order. Call the set of all these constraints on the entity i's path Ci.

There are also non-collision constraints Kij which asserts that entities i and j cannot occupy the same position at the same time. There is a cost function u(Pi) for example, length, total time, effort. For a set P of paths Pi satisfying constraints Ci and Kij, there is a total cost U(P) = u(P1) + ... + u(Pn). The problem is to minimize U(P) subject to those constraints, thereby finding the set of paths (flow pattern of the crowd) that requires the least effort (in total). This optimization problem can be solved by a type of simulated annealing, iteratively starting from a set of paths P, randomly varying it, seeing if the cost goes down, and if so choosing the cheaper set of paths; then repeat. The algorithm stops when it fails to improve the solution.

It can be shown that the algorithm solves the problems of calculating the dynamics of a large population (>100,000) in the simulation in polynomial time.

2013 update - this turned out to be a bit of an understatement. Due to the speed of processing at the time we were running models of 100,000 in real-time, since then a typical large scale model of 250,000, ** Jamarat Bridge**, was developed which ran in real-time.

Further detail of the algorithm is subject to a commercial non disclosure agreement. However, we discuss its inputs, outputs and the validation process in this thesis. We also examine the emergent phenomena, unique to crowds, which can be examined using the simulation suite and the least effort algorithm.

2013 update - the least effort algorithm now features in a range of tools from around the world and over 70,000 copies of my thesis has been downloaded and referenced by modellers and researchers. Thank you all for the support over the last decade.

1.1.2 Introduction to the Legion tools

The Legion Crowd Dynamics tool kit consist of a prototype development suite, a C library, a model builder and simulator (the latter two were the first attempts to develop commercial products developed for client projects) and a replayer, which allows the clients to view, review and analyse their models.

With the Legion simulation it is possible to alter various parameters and study the effects of, for example, increasing the crowd density. The use of a simulation provides us with two important perspectives. Firstly, the simulation provides us with insights to the nature of crowd dynamics, often it is the insight to the problem that leads us to the solution. Secondly, the simulation can be used to prove or disprove a variety of relationships observed in the crowd, for example, it is presently assumed that doubling the width of an egress route will double the flow of people on that route, but this turns out to be wrong.

Applications include modelling multi-venue events, such as the Olympics Games. Figure 1 shows the screen display from the Legion simulation replayer and Figure 2 shows the plan of the same area of the Sydney Olympic Park.

The boulevard and rail station are a common domain for all venues. Loading and unloading crowds are simulated using the Legion system (Figure 1).

Figure 3 shows the validation tool displaying the entities (yellow dots) moving along two corridors (grey = walls). During the simulation run the entities move around the screen, avoiding each other and the local geometry.

1.2 Brief synopsis of chapters 2 - 9

In ** chapters 2** and

**we discuss the various problems relating to crowd movement and crowd safety. We discuss the problems of applying the present guidelines and review the various methodologies used to assess crowd safety. We also discuss the application of a variety of techniques presently used to model crowds and review the existing literature.**

*3*** Chapter 4** discusses the principles of computer simulation, the problems of developing a suitable model of crowd dynamics and the parameters required for accurate crowd modelling. We relate the psychological factors of human decisions to a mathematical framework, using the four rules which define the least effort algorithm: Objective, Motility, Constraint and Assimilation.

In ** chapter 5** we discuss the various inputs to the Legion simulation suite, why they were chosen and the relevance they have in determining the parameters for assessing crowd risk and crowd safety. The entity behaviour, and its significance to simulating crowd dynamics are also discussed in chapters 5 and 6.

** Chapter 6** discusses the validation of the algorithms and compares the results to field observations and historical studies. We examine the qualitative and quantitative data, the results of the Legion crowd simulation analysis and the emergent phenomena which are unique to crowds.

** Chapters 7** and

**discuss case studies using the tools we have developed.**

*8*** Chapter 9** draws the previous chapters to a conclusion and indicates the scope of the simulation, how and where it should be applied and the potential future developments of the Legion pedestrian simulation methodology.

It is important to understand the framework for the development of these tools and we need to outline the various guidelines which are used to define crowd safety in places of public assembly.

1.3 The Guides

There are a number of documents which have been produced to advise on crowd safety issues. The relevant documents are the Green, Purple and Primrose Guides. The guides are advisory documents for use by competent persons. They are the distillation of many years of research and experience of the safe management and design of places of public assembly. The guides have no statutory force but many of their recommendations are given force of law at individual sites by their inclusion in safety certificates issued under the Safety of Sports Grounds Act 1975 or the Fire Safety and Safety of Places of Sport Act 1987. The advice given in the Guides is without prejudice to the application of the appropriate building regulations, the Health and Safety at Work Act 1974, and any other relevant legislation.

2013 update - I'm still surprised at the number of people around the world who use older Guides - specifically referencing the 109 people per metre per minute. This value, in light of international research, was adjusted DOWN to 82 people per metre per minute to bring the Green Guide - 5th Edition - in line with the rest of the world - the table below illustrates that value can differ - indeed will differ - depending on the nature of the crowd, event and measurement criteria. However for sustainable, high density crowd flow, there needs to be a "competent" person utilising these value both in design and in operations.

1.4 Crowds and occupant capacity

The maximum size of the audience for a particular event is generally determined by the licensing authority (taking advice from the fire authority) and is known technically as the "occupant capacity". This will include all ticket holders, pass holders and guests. The method for establishing this capacity is calculated by finding the total area available to the public (in square metres) and multiplying by 2, where 2 = two people per square metre. For example: An outdoor site measuring 100 metres x 50 metres with all areas available to the public could accommodate a maximum of 10,000 people (100 x 50 = 5,000 sq. metres x 2 = 10,000 people). We will discuss the naivety of this type of calculation in later chapters.

1.5 Nomenclature

Crowds have certain interactions which are part fluid, part granular and part psychological reaction. The nomenclature we will use as follows.

**Unimpeded speed**. The individual, free space, walking speed

**Least effort. **The easiest path or route from A to B that individuals take as they progress through an environment. This can be reduced to two simple algorithmic rules.

1. Individuals will take the shortest available route to get from source to destination.

2013 update - "shortest" is defined by shortest time, which may not be the shortest distance

2. Individuals try to move at their normal speed.

**Focal routes.** A focal route is the shortest (least effort) path an individual would take to reach their destination.

**Multiple path interference**. When more than two focal routes cross

2013 update - this developed into a methodology that we use to define areas the may have problems in high density. There are three main elements to this - cross flow, counter flow and convergence.

**Crowd speed.** The emergent speed of a group of individuals. The speed/density relationship is not a constant value but is a function of the local geometry and the interactions within the group/crowd. 2013 update - furthermore this is a function of homogeneity in the crowd

**Space utilisation.** The use of space over time (that is the relative proportion of time in which a given region of space is occupied). An area of low space utilisation is rarely used and an area that is in constant use has a high space utilisation.

There are other effects which we introduce during the discussion on validation in ** Chapter 6** These relate to the emergent phenomena unique to crowds, such as the fingering effect seen in areas of high density bidirectional flows, crowd compression effects which alter the dynamics of crowd movement, and edge effects where speeds are distributed within the crowd.

The author has attended and worked alongside many crowd safety engineers, security staff, stadium managers, computer programmers and mathematicians for the last 10 years. The author is a regular visiting speaker at Easingwold, (the Cabinet Office Emergency Planning College) where he runs a three day crowd dynamics workshop to those people responsible for the safety of crowds at public venues. The inclusion of the photographs, illustrations and diagrams, are based on the experience of meeting, talking, lecturing and learning from that audience and extensive field experience.

2013 update - I have lectured and delivered workshop on the topic of crowd dynamics and crowd safety at the UK Cabinet Office Emergency Planning College for the past 14 years. Having worked on some of the worlds largest and most challenging ** crowded environments/projects** . Currently I'm focussing on educational materials - click

*here*for further information.

*Chapter 2 - Crowd problems and crowd safety*

*Chapter 4 - Principles of a simulation*

*Chapter 5 - Legion (agent based simulation)*

*Chapter 6 - Validation of a computer model*

*Chapter 7 - Case study 1: Balham Station*