Microscopic Traffic Flow Models

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Microscopic Traffic Flow Models

• Its probabilistic nature and its consequences for
  subsequent congestion

Physics of Traffic
Qing Ou email Q.Ou_at_tudelft.nl
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Topics

• The earlier microscopic models (CA, CF)
• KKW model

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Cellular Automaton (CA) Model

• Space is divided into cells
• Time is discrete
• Rules
• CA Models are used to described discrete
  dynamical systems

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1D CA Model for Microscopic Traffic

• Nagel Schreckenberg (NS) Model
• A road is divided into L cells numbered by 1,2L
• Time is discrete
• Vehicle with integer velocity v0,1,Vmax

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Rules for NS Model

• Acceleration viltVmax, then vi? vi 1
• Slowing down if vigtdi then vidi, (dixi1-xi-1
  and xi is the position of vehicle i )
• Stochastic deceleration with probability p,
  vi(gt0)? vi -1
• Position updating xi? xi vi
• (Introduction of probability make it difficult
  to get analytic solution to this model)

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Fukui Ishibashi (FI) Model

• Velocity updating vi?min(di, Vmax)
• Position updating xi? xi vi
• An analytical relation between average velocity
  and average density

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Car Following (CF) Model

• Three main types
• GHR model
• Safety-distance model (Gipps model)
• Linear model
• Psycho-physical (e.g. GM models)
• Reactionfollowersensitivityfollowerstimulus

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Car Following (CF) Model

• The basic ideas about car following model can be
  summarized
• The function represents the stimulus to the
  vehicle, and this stimulus is composed by the
  speed of the vehicle speed difference and gap
  between the vehicle and the leading vehicle

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Gazis-Herman-Rothery (GHR) model

• GHR Model well-known in late fifties and sixties
• which considers relative spacing and speeds
  between vehicle n and n-1.
• c, l, m are constants and T is driving
  reaction time

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Best combination of m and l regarding GHR model

• m0.8, l2.8 (May and Keller, 1967)
• m-0.8, l1.2 (Heyes and Ashworth, 1972) data
  from Mersey tunnel in UK
• m0.6 , l2.4 (Ceder and May, 1976) a far large
  number of data sets
• replaced by , S is jam
  spacing and A valued from 0 to 10 indicating free
  flow to congestion
• Now seldom used for large number of contradictory
  findings as to correct m and l.

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Car Following (CF) Model

• Safety Distance Model
• Driver maintains a speed v which will just allow
  him
• to stop in emergency without hitting the obstacle
  at
• distance S ahead

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Linear Model

• Acceleration
• Desired following distance
• Share the similar disadvantages with GHR model

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Two Lane Model (Symmetry)

• The single lane model results in platooning with
  slow vehicles followed by faster ones.
• The most important elements of the two lane
  model
• Symmetry
• Stochasticity
• Direction of Causality

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Basic rules for lane changing

• Look ahead if somebody is in your way
• Look on the other lane if it is any better there
• Look back on the other lane if you would get in
  somebody elses way

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Technical rule for lane changing

• T1 how far you look ahead on
  your lane
• T2 ahead on the other lane
• T3 back on the other
  lane
• T4
• When all conditions are satisfied, lane changing

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The main parts of complete microscopic model

• Motion rules
• Lane changing rules
• Stochastic ingredients

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Microscopic three-phase traffic theory (KKW Model)

• Earlier traffic flow theories and models are in a
  serious conflict with many of these empirical
  spatiotemporal traffic pattern features
• Introduction of three-phase traffic theory to
  explain all eimpirical spatiotemporal congested
  pattern.
• Free flow
• Synchronized flow
• Wide moving jam

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Main rules in KKW Model

• Vehicle Motion rules
• Lane changing rules
• Random acceleration and deceleration rules
• The biggest feature in KKW model
• Synchronization distance (page 100)
• (E q16.29
  page410)

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Main rules in KKW Model

• Vehicle Motion rules

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Main rules in KKW Model

• Lane changing rules
• Incentive conditions (Eq16.75 p420)speed
• Security conditions (Eq16.77 p421)gap
• depending on the function

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Main rules in KKW Model

• Stochastic part of KKW model

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Main behavioral model assumptions and model
parameters

• In synchronized flow, a driver accepts a range of
  different hypothetical steady state speeds at the
  same space gap to the preceding vehicle.

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Main behavioral model assumptions and model
parameters

• A driver tends to adjust the speed to the
  preceding vehicle within the synchronization
  distance

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Main behavioral model assumptions and model
parameters

• Over-acceleration effect
• It is responsible for an F?S transition and the
  related Z-shaped dependence of vehicle speed on
  density
• The simulation of the vehicle over-acceleration
  effect is made through the use of random vehicle
  fluctuations
• Over-Deceleration effect
• This random effect of the vehicle
  over-deceleration is responsible for moving jam
  emergence.
• (Stochastic part of model, page 426)

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Main behavioral model assumptions and model
parameters

• A driver in synchronized flow does not accelerate
  before the preceding vehicle has begun to
  accelerate.
• Moving in synchronized flow, a driver comes
  closer to the preceding vehicle over time that
  explains the pinch effect in synchronized flow.
• (Stochastic time delay of acceleration and
  deceleration, page 426)

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Conclusion

• Three-phase theory can explain empirical features
  of phase transitions and congested patterns at
  freeway bottlenecks.
• Models based on this theory is formed by the
  introduction of a synchronization distance
• The synchronization distance depends on
  time-dependent vehicle speeds.
• Safety conditions, driver time delays, stochastic
  behavior, lane changing rules should be well
  adjusted

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• Thank you!