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University of Warwick
Web Version - August 2000 updates - GKS
G. Keith Still BSc Physical Sciences (Robert Gordon's 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.
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. John Parkinson for researching materials on crowd disasters and Steve Hick of the Cabinet Office Emergency Planning College (Easingwold UK) 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 hereby declare that the dissertation, submitted in partial fulfilment 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
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.
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.
2013 update "I read your thesis and thought it was excellent, and a great contribution to the art. There should be many applications for your computer models....Wishing you great success with your endeavours. Sincerely, John Fruin" Dr. John J Fruin, Author of "Pedestrian planning and design" 8th May 2002
List of Tables and Illustrations
List of Tables
1 Gate C statistics - ingress counts over several football matches.
2 Fruin Level of Service categories (converted to metres)
3 Fruin Level of Service summary
4 Anthropomorphic sizes of the worlds population
5 Calculated speed v density relationship from the Green Guide
6 Data from field study at Liverpool Street Station (London Underground)
7 Speed and density from Liverpool Street Station
List of illustrations
1 Legion replayer model screen shot. Olympics Stadium and general layout.
2 Sydney Olympics Park. General plan and location of stadium
3 Screen shot of validation tool
4 Wembley stadium - gate C - gap in fence
5 Gate C Wembley Stadium. Gap in fence and people coming up stairs
6 Gate C pre-event use of grass embankment
7 Gate C using the gap as a short cut from the embankment.
8 Plan of Gate C showing the flow of people up the embankment.
9 View from players’ tunnel of bidirectional crowd flow.
10 Zoom of Figure 14 showing the bidirectional movement and fingering patterns
11 Aerial view of Wembley stadium showing the location of the gates
12 Histogram of the turnstile usage of gate C - averaged over several events.
13 14th April 1991 - Counts per minute - ingress at turnstiles
14 14th April 1991 - Cumulative entry count - ingress at turnstiles
15 18th May 1991 - Counts per minute - ingress at turnstiles
16 18th May 1991 - Cumulative entry count - ingress at turnstiles
17 31st March 1993 - Counts per minute - ingress at turnstiles
18 31st March 1993 - Cumulative entry count - ingress at turnstiles
19 14th May 1994 - Counts per minute - ingress at turnstiles
20 14th May 1994 - Cumulative entry count - ingress at turnstiles
21 Plan of G, H and J turnstiles at Wembley Stadium
22 View of dense crowd outside G, H and J turnstiles - showing no direction
23 Enlarged plan of Wembley complex station platforms and bridge.
24 Station platforms as seen from Wembley Hill Road.
25 The queue of 20,000 supporters waiting for the train on South Way.
26 View of unregulated queues spilling onto Wembley Hill Road
27 Plan of Leppings Lane end of the grounds at Hillsborough Stadium.
28 The Fruin Labourer compared to the Author 99 percentile
29 Fruin Level of service shown with metric scale and bodyspace
30 Anthropomorphic sizes shown by weight and area
31 Fruin Level of service D (at one person per square metre)
32 Fruin speed v density relationship (from Pedestrian Planning and design)
33 Comparison of speed v density. Green Guide, Togawa and Fruin.
34 Gate C packing density exceeding 4 people per square metre
35 Wembley Stadium approaches and local area.
36 Wembley plan showing the main routes taken by spectators
37 The Wembley turnstiles (A-M)
38 Plan of gate D and turnstiles at Wembley Stadium
39 Graph of turnstile usage at Gate D
40 Plan of gate F and turnstiles at Wembley Stadium
41 Graph of turnstile usage at Gate F
42 Plan of gate G and turnstiles at Wembley Stadium
43 Graph of turnstile usage at Gate G
44 Diagram from the Green Guide showing network analysis of egress system.
45 Photograph of crowds turning a corner (low density)
46 Photograph of crowds turning a corner (high density)
47 Network of four roads as a cost for travel
48 Network from Figure 47 showing additional road and increased cost.
49 Virtual reality screen shot - showing people moving through a door gap.
50 Graph of flow rate v door width
51 Illustration from New Scientist article on door widths - without barrier
52 Illustration from New Scientist article on door widths - with barrier
53 Graph of enhanced flow using barrier.
54 Three ball collision on a billiard table.
55 Shortest route to pens 3 and 4 at Hillsborough.
56 Speed distribution graph of the crowds at the Hong Kong race meetings.
57 Normal distribution curve - showing frequency distribution of stature
58 Illustration of packing different body sizes 4 people per square metre
59 Illustration of body area as both area and smallest rectangle
60 Packing 8.4 people per square metre
61 Wembley stadium concourse Level B during ingress
62 Wembley stadium close packed bi-directional crowd flow
63 Orientation of a body space onto a 10 cm grid
64 Graphic of 30 cm grids packed to highest possible density.
65 Screen shot of a model of entities navigating with a random walk
66 Screen shot of entities using a course correction algorithm
67 Graph of a non polynomial time collision detection algorithm
68 Graph of the Legion algorithm showing polynomial time
69 Photograph of plan (Figure 123) showing location of concessions
70 Plan of area of outer concourse at Wembley stadium
71 Photograph of a platform illustrating that density is not evenly distributed
72 Queues are static (standing waves) in space, but the people are changing
73 A small group of people in a moving crowd creates a static cluster
74 Crowds have dynamic clusters which alter flow rate calculations (cluster in time)
75 Entity turning a corner by a series of straight lines
76 Screen shot of the validation tool, illustrating both the fluxed and on fluxed entities
77 Scale (Blue to Red) for the speed ergodic maps
78 Scale (Green to Red) for the density ergodic maps
79 Screen shot of the validation tool showing the bottleneck experiment
80 Screen shot of the validation tool showing the bottleneck after 1 second
81 Screen shot of the validation tool showing the bottleneck after 5 seconds
82 Screen shot of the validation tool showing the bottleneck after 240 second2
83 Screen shot of 240 Seconds after initialisation. Dynamic Density Map Bottleneck
84 Screen shot of 240 Seconds after initialisation. Speed Average Map Bottleneck
85 Speed distribution histogram for the edge effect experiment.
86 Graph of the edge effect speed profile
87 Graph of the edge effect density profile
88 Showing the wake of free space around corners in free flowing areas
89 Photograph of unused space on Olympic Way (Wembley Stadium)
90 Screen shot of validation tool illustrating the space utilisation map
91 Graph of cross sectional density from the edge effect experiment
92 Progression of entities in a bidirectional flow model (1)
93 Progression of entities in a bidirectional flow model (2)
94 Progression of entities in a bidirectional flow model (3)
95 Progression of entities in a bidirectional flow model (4)
96 Progression of entities in a bidirectional flow model (5)
97 Progression of entities in a bidirectional flow model (6)
98 Photograph illustrating the ease of following the natural flow of the crowd.
99 Screen shot of the QB45 tool for analysis of the evolution of trails
100 Screen shot of the QB45 tool for showing the first passes of the assimilation
101 Screen shot after 5 frames of assimilation as the circle erodes
102 Screen shot after 10 frames of assimilation showing the formation of islands
103 Screen shot after 15 frames of assimilation showing erosion in corners
104 Screen shot after 19 frames of assimilation with entities at origins
105 Screen shot after 20 frames of assimilation blanked during the erosion algorithm
106 Screen shot after 23 frames of assimilation with entities starting from origins
107 Screen shot after 23 frames of assimilation with entities running through model
108 Screen shot after 25 frames of assimilation symmetry being established
109 Screen shot after 27 frames of assimilation model nearing equilibrium
110 Screen shot after 30 frames of assimilation dynamic equilibrium
111 Screen shot after 20 frames of assimilation, same model with fewer entities
112 Screen shot after 30 frames of assimilation, solution same but with narrower paths
113 Screen shot after 15 frames of assimilation, the tracks begin to form
114 Screen shot after 18 frames of assimilation, some of the tracks lose use
115 Screen shot after 19 frames of assimilation, under used track allow greater growth
116 Screen shot after 20 frames of assimilation, now the track has died
117 Screen shot after 23 frames of assimilation, the entities start to erode a new path
118 Screen shot after 25 frames of assimilation, the nodes form in equilibrium points
119 Screen shot after 30 frames of assimilation, nodes half way down the path
120 Screen shot after 39 frames of assimilation, erosion along the path
121 Screen shot after 40 frames of assimilation, as the new path forms by erosion
122 Screen shot after 45 frames of assimilation, we can see the least effort evolve
123 Screen shot after 48 frames of assimilation, the final solution is minimum effort
124 Screen shot after 60 frames of assimilation, shortest routes now fully evolved.
125 Path forming from hole in fence towards the camera position
126 Path formed over several months of field erosion.
127 Graph of the Fruin data showing density (square metre per person) against speed.
128 Graph of Fruin data showing density (people per square metre) against speed
129 Graph of Legion output against the Fruin data (along horizontal and all angles)
130 The Togawa graph of speed v density (in people per square metre)
131 Comparison of the Fruin, Togawa and Green Guide speed v density relationship
132 Graph of the Legion data against the Green Guide data for speed v density
133 Graph of Legion data against Fruin data showing the effect of adding noise.
134 Graph of the London Underground data showing deviation from the Fruin curve.
135 Graph of London Underground data against a modified Legion speed distribution
136 Graph of the measured speed distribution from the London Underground study.
137 Graph of the Legion, Green Guide and London Underground study
138 Graph of the results from the Paulsen evacuation model
139 Schematic of Balham station (CTS plan)
140 View from security camera showing the pillar and the congestion in the ticket hall
141 Spreadsheet model of queuing theory. Poisson arrivals, exponential service time.
142 Spreadsheet model of queuing theory for the manual gate (single server)
143 Split screen view of the ticket hall and the gates from cameras in the ticket hall
144 The average queue depth conforms to the model for a single server.
145 Split screen view of the ticket hall showing a single server queue
146 Split screen view showing two servers and not queue.
147 Schematic of the ticket hall - preparation for a Legion model.
148 Focal route analysis showing the intersections where conflicts occur
149 Virtual reality model of the ticket hall showing main flow paths
150 Using the Legion model in an “ant” searching mode - finding the focal routes.
151 Testing configuration 1 in the Legion model - using the space utilisation map
152 Testing configuration 2 in the Legion model - showing the effect of a small change
153 Graph of the attendance figures for the Hong Kong Jockey Club
154 Graph of the drop in attendance for the Sha-Tin race course over the years
155 Plan of the Happy Valley race course in Hong Kong. Indicating areas I and II
156 Schematic of the run-in area to the Public Entrance of Happy Valley race course
157 Photograph of the entrance to the public enclosure at Happy Valley
158 Photograph of the wall behind the turnstiles which inhibits ingress
159 Focal route analysis of the entrance area.
160 Public entrance statistic for turnstile usage (averaged over several events)
161 Public Entrance ingress statistics for Happy Valley (afternoon session)
162 Public Entrance ingress statistics for Happy Valley (evening session)
163 Routes and flow rates measured from the video tapes of the Public Entrance
164 The queue exceed the depth predicted by queuing theory - conflicts with focal route
165 Focal route analysis of scenario 1, kiosk upper right - queue discipline 1
166 Focal route analysis of scenario 2, kiosk upper right - queue discipline 2
167 Focal route analysis of scenario 3, kiosk on lower right
168 Focal route analysis of scenario 4, smart card operation
169 Schematic of the Public Entrance indicating area where people arrive and wait
170 Schematic of the Public Entrance indicating changes
171 Space utilisation map of the present configuration of the Public Entrance
172 Results from the Legion mode showing the simulation v reality.
173 Space utilisation map of scenario 1
174 Space utilisation map of scenario 2
175 Space utilisation map of scenario 3
176 Space utilisation map of scenario 4
177 Space utilisation map comparison of the two different queuing regimes
178 Plan of the Infield tunnel at Happy Valley racecourse in Hong Kong
179 Entrance area of the Infield Tunnel.
180 Entrance stairs to the Infield Tunnel - looking down
181 Entrance stairs to the Infield Tunnel - looking up from the bottom.
182 Photograph of the infield tunnel from the bottom of the stairs
183 Photograph of the stairs at the far end of the infield tunnel
184 Graph of the simulation results against the turnstile count.
185 Infield Tunnel ingress statistics afternoon session
186 Infield Tunnel ingress statistics afternoon session
187 Schematic of the Infield Tunnel - showing waiting points and turnstiles
188 Simulation model run of the Infield Tunnel
189 Schematic of the proposed changes for the Infield Tunnel
190 Space utilisation map of the Infield Tunnel after the safety features are added
191 Space to the right of the entrance allow the safety feature installation.
192 Plan of the two areas modelled at the Sha-Tin racecourse Hong Kong.
193 Photograph of the approach to the Gate 1 kiosks and turnstiles at Sha-Tin
194 Photograph of attendant shouting at patrons to use the appropriate turnstiles
195 Gate 1 distribution statistics - cumulative data averaged over several events
196 Gate 1 ingress statistics for 30th January 1998 showing the timed counts
197 Ingress rates at Sha-Tin racecourse. Peak time flow rates.
198 Sha-Tin moving average of the count from the ramp to the straight walkway.
199 Sha-Tin ratio of people walking down the ramp to those walking along the straight
200 Photograph of the queuing at the Gate 1 kiosks in line of sight.
201 Focal route analysis of the turnstile at Gate 1
202 Simulation of Gate 1 present design.
203 Space utilisation map of the present design of Gate 1
204 Simulation of the scenario 1 proposed for Gate 1
205 Scenario 1 space utilisation map
206 Scenario 2 space utilisation map
207 Graph of the comparisons of the two scenario space utilisation maps.
208 Left hand segment of the egress system at Sha-Tin main concourse
209 Middle segment of the egress system at Sha-Tin main concourse
210 Right hand segment of the egress system at Sha-Tin main concourse
211 Left hand segment of the egress system showing both ingress and egress routes
212 Photograph of the egress system (empty)
213 Photograph of the egress system (full)
214 Photograph inside the pen of the egress system during egress
215 Photograph of the view from the control gate of the bridge and platform
216 Simulation of the egress system during an egress analysis
217 15 second entity position of the egress system during reverse flow
218 15 second density map of the egress system during reverse flow
219 30 second entity position of the egress system during reverse flow
220 30 second density map of the egress system during reverse flow
221 45 second entity position of the egress system during reverse flow
222 45 second density map of the egress system during reverse flow
223 60 second entity position of the egress system during reverse flow
224 60 second density map of the egress system during reverse flow
225 Scenario 1 entity position map during egress (15 seconds)
226 Scenario 2 entity position map during egress (15 seconds)
227 Scenario 1 entity position map during egress (30 seconds)
228 Scenario 2 entity position map during egress (30 seconds)
229 Scenario 1 entity position map during egress (45 seconds)
230 Scenario 2 entity position map during egress (45 seconds)
231 Scenario 1 entity position map during egress (60 seconds)
232 Scenario 2 entity position map during egress (60 seconds)
233 Comparison of the egress rates for scenario 1, 2 against the original design
234 Egress route from Wembley Stadium - showing exit gates
235 Egress route from Wembley Stadium - showing focal routes