Microscopic Pedestrian Flow Modeling

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Microscopic Pedestrian Flow Modeling

• From Experiments to Simulation

Prof. Dr. Ir. S. P. Hoogendoorn Dr. Winnie
Daamen Ir. M.C. Campanella www.pedestrians.tudelf
t.nl
Faculty of Civil Engineering and Geosciences
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Problem background

• Research goals develop tools / microscopic
  simulation models to
• describe and predict pedestrian flow operations
• in different types of infrastructure (urban
  areas, airports, railway stations, buildings)
• in case of different situations (peak-hours,
  off-peak period, emergencies and evacuation
  emphasis on crowds)
• With the final aim to assess a new infrastructure
  design / changes in design / evacuation plan in
  terms of
• Comfort, efficiency, safety

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Behavioral levels in walker theory

• The walking theory behind our models can be
  divided into three inter-related levels
• Strategic level, involving activity scheduling
  and (global) prior route choice (which activities
  to do in which order, where to perform these
  activities, and how to get there)
• Tactical level, involving choice decisions during
  while walking (e.g. choice of the ticket window
  with the shortest queue)
• Operational level, walking, waiting, performing
  activities

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Route choice in continuous space

• Wi(t,x) minimum cost of getting from any
  location x to destination area Ai satisfies
  Hamilton-Jacobi-Bellman partial differential
  equation
• Prior route choice is assumed equal for all
  pedestrians sharing the same destination area Ai

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Schiphol Plaza example

• Figure shows iso-value function curves for buying
  item (before leaving by using exits 1-5)
• Also user-equilibrium dynamic assignment to
  include traveler response to traffic conditions

Hoogendoorn, SP, Bovy, PHL (2004). Dynamic
user-optimal assignment in continuous time and
space, Transportation Research Part B - 38 (7),
pp. 571-592.
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En-route decisions

• Rerouting due observable delays (congestion)
• Example choice of turnstile
• Turnstile is chosen that gives best trade-off
  between walking distance and waiting time

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Empirical / experimental facts of walking

• Substantial body of research on pedestrian flow
  operations both from viewpoint of individual
  pedestrians and collective flow
• Examples microscopic facts
• Free walking speed of pedestrians and dependence
  on internal and external factors (age, gender,
  purpose of walking, inclination, temperature)
• Relation required spacing and walking speed
• Example macroscopic facts
• Fundamental relation between flow, density and
  speed
• Capacity estimations for hallways, doors,
  revolving doors, etc.
• Self-organization phenomena

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Walking experiments
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Self-organization

• In pedestrian flow, several self-organized
  patterns can be observed which are fundamental
  for modeling pedestrian flow
• Formation of dynamic lanes in bi-directional
  flows (or in case of faster / slower pedestrians)
• Formation of diagonal stripes in crossing flows
• Zipper effect in long oversaturated bottlenecks
• Arc formation and the faster is slower effect
• Self-organization has been studied empirically
  and experimentally
• Some examples

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Lane formation bi-directional flows
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Lane formation bi-directional flows
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Crossing flows
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Crossing flows
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Bottleneck experiment
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Zipper formation in bottlenecks
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Walker operations during emergency

• Although panic does generally not occur (less
  than 10 of all cases), the wish to leave a
  building as quickly as changes the nature of the
  walking operations (adaptive behavior)
• Excellent experimental and simulation research on
  emergent traffic conditions has been done by
  Peschl (1971), Stapelfeldt (1976) and Helbing
  (2004)
• An important effect is the so-called
  faster-is-slower effect / arc formation
  pedestrians with a stronger wish to leave the
  building (or leaving it more quickly) cause
  increased forces on other pedestrians possibly
  leading to arc formation or tripping pedestrians

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Example experiments
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Self-organization theory

• Theory of self-organization
• Pedestrian economicus
• Minimize predicted disutility (or maximize
  pay-off) of walking
• Expect some user-equilibrium state can
  unilaterally take an action to improve his / her
  condition
• Differential game theory predicts occurrence of
  Nash equilibrium
• Hypothesis self-organized phenomena are such
  self-organized states

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Walker model NOMAD

• Aims derive model which is continuous in
  timeand space model, describing acceleration
  a(t) of pedestrian p
• Two sub-models
• Physical interactions model (short range
  interactions), describing normal and tangential
  forces between pedestrians and between
  pedestrians and obstacles (Helbing et al,2000)
• Control model (long range interactions),
  describing decisions made by pedestrians based on
  predictions of future state of system (including
  actions of other pedestrians)

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Physical model
normal force

• Pedestrians are represented as circles with a
  certain radius
• Pedestrians are to a certain extent compressible
• When a physical interaction between two
  pedestrians occur, both a normal (repellent)
  force and a tangential force (friction) acts on
  the pedestrians
• Friction increases with increasing compression
  (like a squash-ball)
• The model is instantaneous (no noticeable delay)
• Holds equally for interactions between
  pedestrians and obstacles

friction
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Control model derivation

• Control model describes long-range / non-physical
  interactions between pedestrians (differential
  game)
• Dynamics are determined by the control decisions
  of pedestrians, where pedestrians are assumed to
  be optimal controllers that minimize predicted
  walking cost (or pay-off) given expected
  reactions of other pedestrians (opponents)
• Commercial models (i.e. Legion) make similar
  assumptions

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Zero acceleration game

• Optimal acceleration strategy zero acceleration
  game
• Shows smooth acceleration towards desired
  velocity and distance dependent repelling forces
  caused by opponents which are too near to p
• Note this is exactly the Social-Forces model of
  Helbing!

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Model characteristics

• Model captures all empirically established
  pedestrian flow features
• Realistic speed dependent space requirements
• Emergent behavior (lane-formation, striping,
  arc-formation)
• Distinction between different types of
  pedestrians can be made
• Besides repulsion, specific pedestrians can also
  attract each other

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Example application evacuation

• Reproducing faster-is-slower effect?
• NOMAD / Social-Forces pedestrians are
  compressible particles exerting friction on
  each other when touching
• Friction increases with level of compression
• In case of emergency / evacuation pressure /
  friction between pedestrians / pedestrians and
  infrastructure increases due to
• Increased desire to get out / walk at the desired
  speed / increase of the desired speed
• Higher demand of pedestrians aiming to get out of
  the facility
• See research of Helbing and Molnar, Hoogendoorn
  and Daamen

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Desired speed and escape features

• Arc-formation modeling

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Desired speed and escape features

• Increasing desired speed leads to increase of
  time needed to leave and decrease in capacity

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Simulation example (NOMAD)

• Example simulation using NOMAD

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Simulation example (NOMAD)

• Design solution reduce pressure by adding
  obstacle
• Similar solutions in ruptures of grain silos
  (break force networks)

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Does it work in practice?
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Advanced model calibration

• Model has been calibrated on a microscopic level
  using data from walking experiments using a newly
  developed calibration method
• Calibrated results indicated
• Large inter-pedestrian differences in parameters
  describing walking behavior
• Importance of including anisotropy
• Existence of a finite reaction time (of approach
  0.3 s)

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Advanced model calibration

• Anisotropic retarded model
• Plausible model parameters
• Reaction time approx. 0.3 s

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Summary

• Differential game theory was applied to derive
  mathematical model describing pedestrian
  behavior
• Model captures fundamental characteristics of
  pedestrian flows
• Besides a walker model, the microscopic
  simulation model NOMAD also features
• Models for en-route route choice / activity area
  choice
• Models for route choice and destination choice in
  continuous time and space

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Future work

• Improved models for pedestrian behavior near
  entrances (doors, revolving doors, turnstiles,
  etc.) dedicated walking experiments have been
  performed to this end!
• Improving efficiency of route choice modeling
• Improving numerical efficiency of walker modeling
• Including other kinds of traffic (bicycles, cars,
  etc.) in the model
• Freeware version of NOMADj will be available soon
  at the TU Delft pedestrian website
  (www.pedestrians.tudelft.nl)
• Please visit website for all publications

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