Crowd Dynamics G. Keith Still PhD Thesis University of Warwick August 2000 Crowd Dynamics by G. Keith Still BSc Physical Sciences (Robert Gordons Institute of Technology, Aberdeen 1981) A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics University of Warwick, Department of Mathematics August 2000 Acknowledgments Although a few words do not do justice to their contribution I would like to thank the following people for making this work possible. Andy Ward (Aylesbury Fire Brigade) for his interest and assistance in reaching the right people. The staff and management at Wembley, especially George Wise (Operations Director, retired); to Eric Powell and Tom Williams (Cubic Transportation Systems) for their support in providing access to the initial calibration data. To Frank Wood for his endless references and pointers to research material. Bill Phillips, Nigel Smithy, Brian Piggot (who stuck his neck out for me more than once, it was very much appreciated) and Dr. David Wooley of the Fire Research Station. Dr. Kevin Towler (International Fire Consultants) for the discussions on the fire safety legislation. The ACO and staff at the Fire Services College (Morton-on-Marsh) for the encouragement, video footage and staff discussions during the initial research. Mark L. Briggs BEM for funding, long before a product became a reality. Stuart Tracy- Dunn, for believing enough to quit his job and assist in the initial development of the commercial software and futhre developments against the odds. Thanks for all the financial and moral support for everyone who helped us create Crowd Dynamics Ltd. and for turning the theory and algorithms into worldwide produ cts. T o Joh n Park inson for re searc hing m ater ials o n crow d disa sters and St eve Hicks of the Cabinet Office Emergency Planning College (Easingwold) for his kind invitation to lecture on crowds which expanded to a workshop on crowd dynamics. Special thanks to Ian Stewart for his guidance through all weathers. Without his tireless moral and academic support it would not have happened, or been as much fun. -i- Declaration I hereby declare that the dissertation, submitted in partial fulfillment of the requirements for the degree of Doctorate of Philosophy and entitled Crowd Dynamics , represents my own work and has not been previously submitted to this or any other institution for any degree, diploma or other qualification. G. Keith Still August 2000 -ii- Abstract of thesis entitled Crowd dynamics Crowd dynamics are complex. This thesis examines the nature of the crowd and its dynamics with specific reference to the issues of crowd safety. A model (Legion) was developed that simulates the crowd as an emergent phenomenon using simulated annealing and mobile cellular automata. We outline the elements of that model based on the interaction of four parameters: Objective, Motility, Constraint and Assimilation. The model treats every entity as an individual and it can simulate how people read and react to their environment in a variety of conditions, this allows the user to study a wide range of crowd dynamics in different geometries and highlights the interactions of the crowd with its environment. We demonstrate that the model runs in polynomial time and can be used to assess the limits of crowd safety during normal and emergency egress. Over the last 10 years there have been many incidents of crowd related disasters. We outline deficiencies in the existing guidelines relating to crowds and, by comparison and contrast with the model, we highlight specific areas where the guides may be improved. We demonstrate that the model is capable of reproducing crowd dynamics without additional parameters thus satisfying Occam s Razor. We propose an alternative approach to assessing the dynamics of the crowd through the use of the simulation and analysis of least effort behaviour. The model is tested against known crowd dynamics from field studies, including Wembley Stadium, Balham Station and the Hong Kong Jockey club. Finally we test the model in a variety of applications where crowd related incidents warrant structural alterations at client sites. We demonstrate that the model explains the variance in a variety of field measurements, that it is robust and that it can be applied to future designs where safety and crowd comfort are criteria for design and cost savings. -iii- To my beloved wife Valerie. None of this would be possible without your love and support To my children, Harry and Erin, who are the reason to try and make the world a safer place. -iv- Contents Acknowledgments ................................................... i Declaration ........................................................ ii Abstract .......................................................... iii Dedication ........................................................ iv Table of contents ................................................... v List of Tables and Illustrations ........................................ x Chapter 1 Introduction .............................. Page 1 1.1 Legion ................................... Page 1 1.1.1 The least effort algorithm ................ Page 2 1.1.2 Introduction to the Legion tools ........... Page 2 1.2 Brief synopsis of chapters 2 - 9 ................ Page 5 1.3 The Guides ................................ Page 6 1.4 Crowds and occupant capacity ................ Page 6 1.5 Nomenclature .............................. Page 7 Chapter 2 Crowd problems and crowd safety ............ Page 9 2 Introduction ................................Page 9 2.1 Keeping the crowd out of danger: an overview .....Page 9 2.2 A catalogue of catastrophes ....................Page 10 2.3 Gate C ....................................Page 11 2.4 Players tunnel ..............................Page 13 2.5 The fluid analogy ............................Page 15 2.5.1 Why is the fluid analogy untenable? .......Page 16 2.5.2 Definition of crowd density ..............Page 16 2.5.3 Crowds find their own levels. ............Page 16 2.6 Two key questions ...........................Page 17 2.7 Ingress safety at Wembley .....................Page 17 2.7.1 Wembley turnstile data .................Page 18 2.7.2 Wembley ingress capacity ...............Page 19 2.7.3 G and J turnstiles ......................Page 22 2.8 Wembley Complex Station ....................Page 23 2.9 Why we need something different ...............Page 26 2.10 Analysis of the Hillsborough disaster ............Page 27 2.11 Conclusion .................................Page 29 Chapter 3 Crowd dynamics ........................... Page 31 3 Introduction ................................Page 31 3.1 John J. Fruin - Pedestrian planning and design .....Page 31 3.1.1 Fruin Level of Service (LoS) .............Page 32 3.1.2 Anthropomorphic tables ................Page 34 3.1.3 Field observations contradict Fruin ........Page 36 -v- 3.1.4 Fruin. Density v speed ..................Page 37 3.1.5 Green Guide - density v speed ............Page 38 3.1.6 Fruin v the Green Guide .................Page 38 3.1.7 Is high density unsafe? ..................Page 40 3.1.8 How long can high density be sustained? ...Page 41 3.1.9 Is the Fruin Level of Service Wrong? Page 42 3.2 Effects of geometry ..........................Page 44 3.2.1 Approach routes to Wembley stadium .....Page 45 3.2.2 Problems with entry points ..............Page 45 3.2.3 The Wembley Turnstiles (A-M) ..........Page 48 3.3 Network analysis (Green Guide) ................Page 52 3.3.1 The dynamics of crowds in a network ......Page 54 3.3.2 Braess s paradox ......................Page 56 3.3.3 Braess s paradox and the Green Guide .....Page 61 3.4 Review of other simulation systems .............Page 61 3.4.1 Passenger flow evaluation system .........Page 62 3.4.2 Egress (SRD, AEA Technology) ..........Page 63 3.4.3 Pedroute .............................Page 64 3.4.4 Exodus ..............................Page 65 3.4.5 Rampage - Animation science ............Page 66 3.4.6 The social force models .................Page 67 3.5 VEgAS ....................................Page 70 3.5.1 The uses of virtual reality in egress analysis . Page 71 3.5.2 Intractable parameters ..................Page 73 3.5.3 Flow through a door ....................Page 74 3.6 Conclusions to chapter 3 ......................Page 78 3.6.1 Emergent solution .....................Page 79 Chapter 4 Principles of a simulation ................... Page 81 4 Introduction ................................Page 81 4.1 Key components of a computer simulation ........Page 81 4.1.1 Defining rules in a simulation ............Page 83 4.1.2 Modelling movement in a simulation ......Page 84 4.2 Computer simulation vs network analysis .........Page 87 4.2.1 Flock of Boids ........................Page 88 4.3 Programming people .........................Page 89 4.3.1 Objective and Constraint ................Page 90 4.3.2 Motility and Assimilation ...............Page 93 4.4 Crowd psychology ...........................Page 95 4.4.1 Psychology and the OMCA rules ..........Page 98 4.5 Conclusions to Chapter 4 ......................Page 99 Chapter 5 Legion ................................... Page 100 5 Introduction ................................Page 100 5.1 Choosing the simulation parameters .............Page 100 5.2 Modelling People ............................Page 101 5.2.1 Choosing the 95th percentile ..............Page 102 5.3 Modelling Space ............................Page 108 5.3.1 Logic conditions .......................Page