a static-dynamic network model for crowd flow simulation - CiteSeerX

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A STATIC-DYNAMIC NETWORK MODEL FOR CROWD FLOW SIMULATION

Shrikant B. Sharma Buro Happold Engineers Ltd.

101 Keywords: Network analysis Graph theory Origin-destination Crowd flow Dynamic simulation

Shrikant B. Sharma Buro Happold Engineers Ltd., Camden Mill, Lower Bristol Road, Bath BA2 3DQ, UK, Tel. +44-1225-320600, +44-870-7874148 Shrikant.Sharma@BuroHappold. com

Abstract The existing crowd flow simulation models fall into two major categories: those based on space syntax theories, and those based on the vehicular micro-simulation models incorporating origin-destination matrix. The space-syntax based models have a unique strength in their ability to analyse the spatial geometry quickly and generating valuable information about the configuration of space. However it suffers from the exclusion of dynamic effects of flow that are driven by the needs of people to go from A to B. The origin-destination based models are fundamentally micro-simulation models that provide for these dynamic effects. These models provide the valuable information on interaction of agents and densities as a function of time. However these models tend to be complex, both in pre-processing and execution, and reliable information on space effectiveness is only available at the end of a number of simulation runs. The present work brings these two techniques together by integrating graph-theory based network analysis with an origin-destination matrix model. The resulting model can be analysed in a static as well as dynamic state. In the static state, the model analyses space based on connectivity of nodes, superimposed with the origin-destination matrix of population to provide valuable information such as footfalls, density maps, as well as quasi-static parameters such as mean flow rates. In the dynamic state, the model allows time-dependent analysis of flow using a detailed agent based simulation that also incorporates dynamic route-choice modelling, agent behaviours and interaction, and stochastic variations. The paper presents the modelling technique and its implementation into simulation software SmartMove. The space is represented as a 3D network of nodes and links, with each link modelled as “1.5D” (width information is used for lateral positioning of people on the links). This enables rapid dynamic simulation of multiple scenarios without major computational overheads. The model is very effective in rapid design optimisation of spaces within and outside buildings. The static state model allows testing of various configurations quickly. The dynamic state model provides detailed investigation of such as maximum flow rates, queue lengths, and design parameters to attain a required level of service. The model is easily scalable and applicable to a range of scenarios. The paper illustrates this with reference to the circulation design of a 2,200+ capacity school, covering the pre-processing (population and origin-destination data), static analysis, dynamic simulation results, and (design and management) optimisation strategies.

Proceedings, 6th International Space Syntax Symposium, İstanbul, 2007

Sharma; A Static-Dynamic Network Model for Crowd Flow Simulation

Introduction

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The study of movements of people within a building or city has had a long history. The majority of early work focused on the modelling of vehicular traffic, aimed at estimating the distribution of vehicular traffic in cities. Consequently, several traffic flow models have been derived in macroscopic and microscopic forms (Helbing et al. 2002). Macro models (e.g. Faieta and Huberman, 1993) use fluid flow analogies and follow a top-down approach, focusing on the observable behaviour of a system. They involve aggregate parameters such as traffic volume and average speed on links in a traffic network. Microscopic or agentbased traffic models (e.g. Chu et al. 2002) take a bottom-up approach, where a complex system is viewed as a large set of small, interacting components. The main focus is on identifying the components in a system, discovering their individual behaviors and the interactions among them. The global system behavior emerges from the local behaviors of the individual components, and their interactions. The resulting data is then used for the design and management of traffic network and junctions. Primarily because traffic simulation models deal with semi-intelligent entities (vehicles with drivers) and because the traffic rules are clearly laid out, these models are more deterministic than their people-flow counterparts and have therefore been well consolidated. These models are usually applied for highway design/planning, traffic management and urban planning projects. People flow modeling because of several fundamental differences from vehicle modeling has not yet reached the same level of sophistication. As noted by Kerridge et al (2001), pedestrian trips are less homogenous than vehicle trips in terms of journey purpose and their route choices are less well defined. The pedestrian network can also be much harder to define than vehicular networks and the rules for turning, pauses, and gaps are less certain. These limitations however have only helped accelerate the research in the people movement modelling over the last few years, especially as the design of spaces is becoming more relevant in terms of safety, comfort and quality of experience. The crowd flow simulation models fall into two major categories: • network analysis models that are based on space syntax theories (e.g. Penn et al. 1994) • agent based models that are based on the vehicular microsimulation models incorporating origin-destination matrix (e.g. Thompson, 1994). The space syntax approach uses a network modeling technique to estimate pedestrian movement potentials based on graph theories to measure normalized network parameters (Hillier, 1996; Teklenburg et al. 1993). It then uses pedestrian counts to calibrate these parameter values and convert them into estimates of pedestrian count per hour. Hillier et al and Penn et al. found that this approach estimated pedestrian volumes in central London with an r-squared value of 0.77 (Hillier, Penn et al. 1993; Penn, Hillier et al. 1998). The space syntax techniques have since been applied to the correlation of urban networks with pedestrian flow in several other cities too: Barnsbury, England (Penn and Dalton, 1994), New Jersey (Swords, Goldman et al. 2003), Oakland, California (Raford and Ragland, 1993), and Boston, Massachusetts (Raford and Ragland, 2005). The origin-destination based models are fundamentally agent based micro-simulation models that provide for the dynamic effects that are

Proceedings, 6th International Space Syntax Symposium, İstanbul, 2007

Sharma; A Static-Dynamic Network Model for Crowd Flow Simulation

missing from the space syntax models. These models offer highly realistic simulations of regions such as individual streets and enclosed spaces such as hotels, airports, and malls. Micro-simulation models use detailed virtual representations of thousands of individual agents in the region in question, with pre-determined or random origins and destinations, and specific rules for individual behaviour and movement pattern. Simulated pedestrians seek their destinations based on rules of movement such as avoiding collision with walls and other pedestrians and seeking the shortest or quickest routes to their destination. The output of these individual interactions can then be analyzed and visualized. Although the early work in agent based people movement models concentrated on building evacuation scenario under fire (Thompson, 1994; Owen et al. 1996; Klüpfel and Meyer-König, 2003), the current focus (Sharma et al. 2004) is on modeling normal circulation in airport/rail terminals, sports stadia, and shopping malls, and streets. There is also a growing interest in the use of virtual avatars (Thomas and Donikian, 2000; Tecchia et al. 2001), guided by emotions and information about the environment (e.g. visibility graphs).

Motivation for the Present Work The space-syntax based models have a unique strength in their ability to analyse the spatial geometry quickly and generating valuable information about the configuration of space. However it suffers from the exclusion of dynamic effects of flow that are driven by the needs of people to go from A to B. Agent based models provide a valuable information on interaction of agents and densities as a function of time. However these models tend to be complex, both in pre-processing and execution, and reliable information on space effectiveness is only available at the end of a number of simulation runs. In essence, the strength derived from the fundamental basis of the space-syntax work – that ‘spatial layout greatly influences the movement patterns’ – is also its limitation. It ignores the influence of the “needs” of people that creates a rather direct (or less layoutdependent) A to B journeys which then result into a different movement pattern. In addition, the dynamics of the movements – the time-element, need to be accounted for separately. Attempts to provide detailed agent based simulation deriving from the space syntax analysis made in recent years (Turner, 2000; Penn and Turner, 2002) are along the same lines. Also the needs of the people to make journeys has also been looked at in terms of what is known within the space syntax community as “choice” or “betweenness”, although the choices are really determined by the spatial connections and not by the real journey needs. The present work brings the two techniques together by integrating graph-theory based network analysis with a time-dependent origindestination matrix model. The resulting model can be analysed in a static as well as dynamic state. In the static state, the model analyses space based on connectivity of nodes, superimposed with the origindestination matrix of population to provide valuable information such as footfalls, density maps, as well as quasi-static parameters such as mean flow rates. In the dynamic state, the model allows timedependent analysis of flow using a detailed agent based simulation that also incorporates dynamic route-choice modelling, agent behaviours and interaction, and stochastic variations. The paper presents the modelling technique and its implementation into simulation software SmartMove. The space is represented as a 3D network of nodes and links. Static analysis is carried out to Proceedings, 6th International Space Syntax Symposium, İstanbul, 2007

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Sharma; A Static-Dynamic Network Model for Crowd Flow Simulation

determine the connectivity and flow density parameters for the network. This allows testing of various configurations quickly. The dynamic state model provides detailed investigation of such as maximum flow rates, queue lengths, and design parameters to attain a required level of service. The paper illustrates the methodology used in the model through the example of a modern academy in the UK.

Methodology The theoretical framework of the static-dynamic analysis is discussed in this section. The basic approach is to pre-process the network and behaviour data for static analysis, followed by a full dynamic analysis and post-processing, as illustrated in Figure 1.

101-04 Figure 1: Simplified flow-diagram of the static-dynamic model

Network Model The spatial model is based on a network of links representing paths connecting nodes that represent origins, destinations and junctions. • The layout is described in terms of a 3D network that has source, destination or intermediate nodes and links that are onedimensional. • Links represent streets, corridors, walkways, bridges and nodes represent junctions, doors, and stairs/escalators entry/exit points. They have attributes such as geometric dimensions, limiting flow rates, speeds, etc as applicable. • Special nodes such as queuing and service nodes are also included in the mode. Service nodes represent points in the network where people spend a certain time (e.g. at lockers, ticket

Proceedings, 6th International Space Syntax Symposium, İstanbul, 2007

Sharma; A Static-Dynamic Network Model for Crowd Flow Simulation

counters, etc.); they have an additional time parameter along with a statistical distribution associated to it. • Individuals are positioned laterally depending upon the interpersonal spacing and local geometric effects. This lateral positioning of people provides the link its “1.5D” characteristics. Figure 1 illustrates the schematic of the network model as it is applied to an airport arrivals terminal.

Figure 2: Network representation of walkable space. The 1D nature of the links makes calculations

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Behaviour Model and Origin-destination Matrix The model takes into account the interactions of people with the building, environment, and other people within the network. • Individual people are modelled, but they can be grouped and assigned specific profiles corresponding to their age, sex, final destination, etc. • Using nodal data the model works out the desired route taken by an individual, based on their behavioural characteristics: -

shortest/quickest routes with or without itinerary

-

preference for nearest exit/stairs vs. angle minimisation

-

visibility of a destination, and preference for those on the main/familiar routes

-

preferences for stairs vs escalators

-

behaviour under crowding at links, e.g. preferences for stairs vs escalators

• The individuals compete for resources and target a destination favourable to them. On their way, they re-route their path depending upon further congestion. • Other behavioural factors such as reaction times (to events such as school bell ringing, end-of-race, fire alarm, etc.), speeds, overtaking, etc. are modelled usually as a stochastic distribution from available data.

Proceedings, 6th International Space Syntax Symposium, İstanbul, 2007

Sharma; A Static-Dynamic Network Model for Crowd Flow Simulation

Data on the network parameters as well as behavioural characteristics is modelled as a statistical distribution obtained from such as video observations in similar scenarios. An important part of the input data is the time based origin-destination matrix. This usually depends on the problem and the scenario being studied, e.g. for a school it is the time-table data, in the case of an airport arrivals area it is the aircraft landing data and the terminal processing sequences and routes. The origin destination matrix is defined as an itinerary data, adding intermediate nodes as necessary for people to visit as they approach their main destinations. This allows modelling of a complex scenario such as an airport terminal (aircraft → immigration → baggage → customs → exit), school (classroom → lockers → exit → coaches), etc.

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There is also a time dimension to the origin-destination data, such that certain journeys only begin at later stages of the simulation.

Static Analysis Using the available network model and the origin/destination data, a static analysis is performed to gain valuable parameters on the on the model. This is usually carried out in two stages, as shown in Figure 3. Figure 3: Simplified flow-diagram of the static analysis

Network analysis The 3D network is analysed for graph theory measures such as: • adjacency matrix • shortest/quickest routes • connectivity parameters The connectivity parameters may represent the number of links connected to each node or more sophisticated space syntax measures such as visibility. It provides a good snapshot of the spatial layout of the network on its own. Flow analysis The second half of static analysis is indeed a quasi-static analysis; it involves overlaying the dynamic elements of the movement, the origin-destination data, over the graph being studied. The effect of the shortest/quickest routes is superimposed over the network together Proceedings, 6th International Space Syntax Symposium, İstanbul, 2007

Sharma; A Static-Dynamic Network Model for Crowd Flow Simulation

with the origin-destination data to provide the hit-count and hit-rates (mean flow rates). The algorithm used for the overlay is as follows: Figure 4: Algorithm used for the hitcount analysis

101-07 The algorithm simply runs through the list of links and adds to it the number of people visiting them, and the approximate rate at which they hit them. The result is a weighted graph showing the count/rate/density of crowd movement over the network.

Dynamic Analysis The dynamic analysis starts off where the static analysis finishes. It uses the network analysis data coupled with the original route-choice models for the beginning of the simulation. As the simulation progresses, the route-choice as well as the speeds of the individuals is updated continuously to reflect the dynamics of the movement. The simulation combines the network, behavioural and movement models to provide a visual and interactive output on complex scenarios during normal circulation and evacuation. The model takes a local-global approach to the simulation and keeps track of people within and out of the system at anytime, introducing them when they come out of their rooms, or removing them when they arrive at their destinations (Figure 5). Figure 5: Simplified flow-diagram of the dynamic simulation

At the end of the simulation the following flow statistics are available, including: • dynamic simulation chart: time based profile of movement, queues, etc. Proceedings, 6th International Space Syntax Symposium, İstanbul, 2007

Sharma; A Static-Dynamic Network Model for Crowd Flow Simulation

• evacuation times and times to clear specific levels • flow summary (queues, congestion points, who-goes-where data) • stair/escalator utilisation (heavily/least used resources, flow-rate graphs, etc.) • design data (minimum necessary walkway widths, bridge widths near resources) It is also possible to trace the path taken by an individual through the network. The technique for network modelling, behavioural and origindestination data assignment, and static as well as dynamic analysis has been implemented into SmartMove: a 3D visual simulation tool.

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Case Study – Peterborough Academy The methodology presented in the previous section is best illustrated by application to Peterborough Academy, a modern 3-storey school in Peterborough, UK, with a capacity of over 2,200 students. Figure 6: Peterborough Academy (architects: Foster and Partners)

The school architecture comprises of six different “colleges” or faculties, served by circulation and evacuation stairs connecting the three floors. In the middle of the building sits a central resource centre comprising of library and study areas.

Network Model Figure 7 shows the network model for the school layout. Each classroom door is represented as a node (so also any turns in the walkways), which are connected using links. Individual networks on each levels are connected using stair links to form the full 3D network for the building as shown. Figure 7: 2D network model for one of the floors (Inset: 3D model for all floors)

This network is ready for static analysis, provided the population behaviour data and origin-destination data is available.

Proceedings, 6th International Space Syntax Symposium, İstanbul, 2007

Sharma; A Static-Dynamic Network Model for Crowd Flow Simulation

Behaviour Model and Origin-destination Data The behaviour of pupils was analysed using extensive surveys on the existing Thomas Deacons school, which had the same population that was to move to the target school. Normal distribution was assumed for the majority of data and values for walking speeds, limiting flow-rates, etc were obtained as shown in the table below. Locations

Table 1: Values used for speeds and flows in the simulation

Units Attributes

1

Doors

2

Walkways

2

Walkways

3

Stairs - up

4

Stairs - up

3

Stairs - down

4

Stairs - down

flow-rate limiting flow-rate free speeds limiting flow-rate free speeds limiting flow-rate free speeds

Average # / min

42

-

# / min / m

100

-

m/s

1.25

0.1

# / min / m

57

-

m/s

0.53

0.15

# / min / m

61

-

m/s

0.75

0.15

The origin data came from the school time-table, an excerpt is shown in Table 2. The worst case scenario analysed was the tutor group changeover period, during which all the 2200+ students in the schools moved, each class being split into several parts, thereby creating a major cross-flow on the walkways and stairs. The destination data was created by randomly assigning each student to a tutor group in the school. CLASS

ROOM NO.

7A1 7A2 7A3 7A4 7B1 7B2 7B3 7B4 7C1 7C2 7C2 7CX 7CX 7B6

Comms 01 Comms 02 Comms 03 Comms 04 Comms 05 Comms 06 Comms 07 Comms 08 PE PE PE PE PE Lecture 1

PUPIL NUMBER 26 26 25 25 26 26 26 25 25 25 25 15 15 25

Values Std. deviation

MOVEMENT TO THESE AREAS Groups of 18 students in each location: approx. 3 in each year group Science ground floor Social Science ground floor Arts ground floor (music ensemble 2 spaces) Technology ground floor (engineering 2 spaces) Communications ground floor Achievement Support ground floor Maths ground floor Cyber Café Science first floor Social Science first floor Arts first floor (music 02/Art Gallery/Art 03 2)

TOTAL ROOMS 4 7 5 6 4 4 6 1 5 5 7

Table 2: Excerpt of the school timetable (occupancy) at 1200 hours NOTES

Study area counted as two spaces for tutor bases Study area counted as two spaces for tutor bases Study area counted as two spaces for tutor bases

The first part of static analysis comprised of analysing the spatial network for connectivity. As is clear from Figure 8 which shows a plot of the number of connections at each node, the central resource centre in the school provides the most integrated space that will normally attract the most students during the day-to-day operation of the school. However, this plot only represents a static picture of the level of crowding and does not account for the occupancy level nor the activities within the school. To get a better idea of the movement during the worst case (tutorgroup changeover) scenario, hit count plot (Figure 9), hit-rate plot, and hit-rate-density plots can be plotted for the network, using the methodology presented in section 3.3.2. The hit-count plot shown in Figure 9 is clearly different from the connectivity plot and shows the stairs and central bridges to be the main focus of crowding. The static analysis is quick to perform, and detailed sensitivity studies can be carried out before the full dynamic simulations to get a better understanding of the design parameters that will provide safe movements.

Proceedings, 6th International Space Syntax Symposium, İstanbul, 2007

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Sharma; A Static-Dynamic Network Model for Crowd Flow Simulation

Figure 8: Connectivity plot for the network

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Figure 9: Hit count plot for the network

Dynamic Simulation The static analysis on its own is unable to predict the detailed elements of flow that affects the safety and comfort of people. A dynamic simulation is essential to determine such parameters as the waiting times, queue lengths, and crowd densities. The model that was set-up during the static analysis is ‘run’ in incremental time-steps to investigate the detailed dynamic effects. As the simulation progresses, agents are introduced into the system at appropriate times and locations as per their source positions and discharge times. Once into the system, they move towards their goals while interacting with the geometry of routes, other people in the neighbourhood, and any environmental influences. Depending on the crowding levels they are able to update their route choices, while always attempting to minimise the time to their destinations. Anomalous behaviour such as a given percentage of pupils delaying their way to the tutor groups can also be modelled. Another important element that was modelled in this simulation was that if a bunch of students arrive at their tutor group that is not empty (the students in that class have not yet started to move), then the arriving students Proceedings, 6th International Space Syntax Symposium, İstanbul, 2007

Sharma; A Static-Dynamic Network Model for Crowd Flow Simulation

have to queue outside. This effectively reduces the width of the walkway outside the classroom as other students attempt to walk past, thereby creating a potential congestion spot. Figure 10 shows the SmartMove software snapshots at various stages of one of the dynamic simulation runs. It shows the agents modelled in 3D and the network model with link areas coloured according to density.

Figure 10: Snapshots of the dynamic simulation

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The details of the simulation work and design iterations is not discussed here. However to highlight the specific elements of dynamic simulations some of the results in the form of graphs are presented below. Dynamic simulation provides a time-based profile of flow at any given link. Figure 11 shows the flow-rate (per minute) graph for a particular stair in the network. As can be clearly seen, the values are way over the stair capacity, which indicates the likelyhood of major queues and unsafe conditions at the stairs. The plot is compared for different conditions of class discharge, i.e. the time before or after the notional Proceedings, 6th International Space Syntax Symposium, İstanbul, 2007

Sharma; A Static-Dynamic Network Model for Crowd Flow Simulation

time (1200 hours in this scenario) when a particular class starts discharging. An interesting validation exercise performed during the course of this study showed that an absence of central bell in the school created a major dispersion in the discharge times (upto +/-6 minutes) which helped reduce congestion at the stairs. As the graph below shows, the maximum flow rate on the stair reduces as the class discharge interval is increased. Figure 11:

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Stair flow-rate as a function of time (for various class discharge options

Figure 12 shows the sensitivity of queue lengths on various stairs as a function of class discharge interval. Figure 12: Queue length at stairs for various class discharge intervals

As the queue lengths at stairs was to be kept below the safe limit (7 pupils at any time), a rigorous optimisation on the design and spatial layout of the stairs within the school was carried out (details omitted). Figure 13 shows the flow rate graph during two typical runs with the optimised design and management strategy. Based on the analyses it was decided not to have a central bell operating within the school. Figure 13: Modified layout & stair design limits the flowrate and hence queues on stairs

The same network model can be easily adapted for a different scenarios, by updating the origin-destination matrix and appropriate behaviour for the population. Proceedings, 6th International Space Syntax Symposium, İstanbul, 2007

Sharma; A Static-Dynamic Network Model for Crowd Flow Simulation

Figure 14 represents the evacuation simulation with all but one of the core stairs used for exit in the building because of fire. The plot brings out the essense of dynamic simulation as it plots the number of pupils moving (in corridors), queuing (due to crowding at stairs/corridors), and exiting the building, as a function of time since the fire alarm. Figure 14: Simulation progress for the evacuation scenario

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Conclusions and Further Work This paper presented a methodology to bring together the spacesyntax and agent based simulation techniques to provide an integrated static-dynamic model for people movement. In the static state, the model analyses space based on connectivity of nodes, superimposed with the origin-destination matrix of population to provide valuable information such as footfalls, density maps, as well as quasi-static parameters such as mean flow rates. In the dynamic state, the model allows time-dependent analysis of flow using a detailed agent based simulation that also incorporates dynamic routechoice modelling, agent behaviours and interaction, and their stochastic variations. The methodology has been illustrated through the use the example of a modern school in the UK. The flexibility offered by the static and dynamic stages of analysis, as well as the speed of simulations, enabled the optimisation of the design and management strategies for the school which had tight demands on pupil movements and safety. The paper has purposely limited its focus to the introduction of the integrated static-dynamic analysis model for people movement and illustrating the same through a real example. Validation work carried as part of the study has not been discussed in detail for the sake of clarity and because of the limitation on space. A rigorous validation work of the approach discussed here against a published dataset such as Barnsbury data (Penn and Dalton, 1994)0 is desirable and will be carried out in the near future. The discussion in this paper however clearly highlights the differences in the approach to the space-syntax techniques; the inclusion of time-based origindestination data into the static analysis model provides a comprehensive and realistic understanding of the spatial layout. Work is also underway to link in the static analysis work with origindestination matrix estimation, which is one of the major strengths of the space-syntax approach. Finally, work is also underway to better define the route-choice model as a function of dynamic parameters such as queuing levels, crowd density, and visibility/signage. Acknowledgements; The author wishes to thank the architects on the Perterborough Academy project (Foster and Partners) and Dr. David Brocklehurst and Ms. Erica Calogero for their help on the project work discussed in this paper.

Proceedings, 6th International Space Syntax Symposium, İstanbul, 2007

Sharma; A Static-Dynamic Network Model for Crowd Flow Simulation

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Hillier, B., Penn, A., Hanson, J., Grajewski, T., Xu, J., 1993, “Natural Movement: Or Configuration and Attraction in Urban Pedestrian Movement”, Environment &Planning B: Planning & Design, vol 19, pp29-66. Kerridge, J., Hine, J., Wigan, M., 2001, “Agent-Based Modelling of Pedestrian Movements: The Questions that Need to be Asked and Answered”, Environment and Planning B: Planning and Design, vol. 28, pp. 327 – 341. Klüpfel, H., Meyer-König, T., 2003, “Characteristics of the PedGo software for crowd movement and egress simulation”, Int Conf. Ped. and Evac. Dyn., Greenwich. Owen, M., Galea, E.R., Lawrence, P.J., 1996, “The Exodus Evacuation Model Applied to Building Evacuation Scenarios”, J. Fire Protection Engr., 8(2), pp 65-86. Penn, A., Dalton, N., 1994, “The Architecture of Society: Stochastic Simulation of Urban Movement”, N. Gilbert, J. Doran (Ed.), Simulating Society: The Computer Simulation of Social Phenomena, UCL Press, London, Ch 5, pp85126. Penn, A., Hillier, B., Banister, D., Xu, J., 1998, “Configurational Modeling of Urban Movement Networks”, Environment and Planning B-Planning & Design, vol 25, no 1, pp. 59-84. Penn, A., Turner, A., 2002, “Space Syntax Based Agent Simulation”. Proceedings, 1st International Conference on Pedestrian and Evacuation Dynamics, University of Duisburg, Germany (Springer: Berlin) pp. 99–114. Raford, N., Ragland D.R., 2005, “Pedestrian Volume Modelling for Traffic Safety and Exposure Analysis: The Case of Boston, Massachusetts”, Paper UCB-TSC-RR-2005-TRB2, University of California Berkeley Traffic Safety Center. Raford, N., Ragland, D., 2003, “Space Syntax: An Innovative Pedestrian Volume Modeling Tool for Pedestrian Safety”, Paper 04-2977, Annual Meeting of the Transportation Review Board. Sharma, S. B., Brocklehurst, D. Westbury, P. S., 2004, “A Dynamic Network Model for Circulation and Evacuation”, Proceedings, Human Behaviour in Fire Symposium, InterScience Comm. Ltd, ISBN 095412166X. Swords, A., Goldman, L., Feldman, W., Erlich, T., Bird, W., 2003, “Analytical Framework for Prioritizing Bicycle and Pedestrian Investments: New Jersey’s Statewide Master Plan Update, Phase 2”, Paper 04-3905, Annual Meeting of the Transportation Review Board. Tecchia, F., Loscos, C., Conroy, R., Chrysanthou, Y., 2001, “Agent Behaviour Simulator (ABS): A Platform for Urban Behaviour Development”, GTEC'2001, Hong Kong. Teklenburg, J.A.F., Timmermans H.J.P., van Wagenberg, A., 1993, “Space Synax: Standardised Integration Measures and Some Simulations”, Environment and Planning B: Planning & Design, vol 20, no 3, pp 347–357. Thomas, G., Donikian, S., 2000, “Modelling Virtual Cities Dedicated to Behavioural Animation”, Computer Graphics Forum, vol 19, no 3, pp. 71-80. Thompson, P. A., 1994, “Simulating New Techniques for Modelling Crowd Movements” vol. I. PhD Thesis, University of Edinburgh, UK. Turner, A., 2000, “Angular Analysis: A Method for the Quantification of Space”, Working Paper 23, CASA, University College London, London.

Proceedings, 6th International Space Syntax Symposium, İstanbul, 2007