3Phase Theory

1
3Phase Theory

• und why all zhe otzher mohdellss arrrh wronghh

Trail 3Phase Theory
2
The beginning

• Kerner starts working with FD but changes his
  mind due to empirical data
• Old theory cans explain the spatiotemporal
  patterns Mainly the F-S-J transitions
• Kerner briefly discusses other theories

3
Kerners critique on existing theories

• LWR
• FD is an unperturbed noiseless limit case,
• Allows any kind of shockwave,
• Only characteristic WMJ speed
• Shockwaves are instantaneous,
• No reaction delay
• Inability to model self formation of wide moving
  jams

4
Kerners critique on existing theories

• Models with Moving Jam emergence
• Some models allow F-J transition but no F-S-J
• Different behavior on on-ramps than observed
• Models with variety of vehicles/characteristics
• No F-S-J transition
• Multiclass Macroscopic suffer from FD limitation
• Microscopic simulation does not need multi
  vehicle class (he will show in part III)

5
Why 3Phase theory is qualitative?

• Qualitative research is one of the two major
  approaches to research methodology in (social)
  sciences. Qualitative research involves an
  in-depth understanding of phenomena and the
  reasons that govern the phenomena (why,how)
• Hypotheses is a suggested explanation of a
  phenomenon

6
Qualitative 3Phase theory

• Based on empirical data,
• Hypotheses are suggested which explain them,

7
Spatio Temporal patterns 3 phases

• F free flow
• J wide moving jam,
• characteristic speed (-16 km/hr), propagates
  upstream through bottlenecks
• independent on initial conditions or demand
• S synchronized flow, vehicles have tendency to
  synchronize speed, but diverse spatiotemporal
  patterns

8
Driving behavior

• Observed common behavioral characteristics of
  drivers in traffic flow (pg 99)
• A drivers ability to recognize if space gap
  between preceding vehicle is increasing or
  decreasing
• If space gaps between vehicles are not too large,
  the drivers ability is unchanged even if
  difference in speed between vehicle and preceding
  vehicle is negligible
• Drivers can maintain a time independent space gap

9
Qualitative 3Phase theory

• Based on empirical data,
• Hypotheses are suggested which explain them,

10
Fundamental hypothesis

• Given Observed spatiotemporal patterns and user
  behavior, a fundamental hypotheses regarding
  synchronized flow is stated
• Hypothetical steady speed states of synchronized
  flow, i.e., synchronized flow states in which all
  vehicles move at the same distance from one
  another and with the same time-independent speed,
  cover a two-dimensional region in the
  flow-density plane (2D).

11
Fundamental hypotheses
Steady speed state

• Speed 1n densities

12
Fundamental hypotheses
Steady density state

• Density 1n speeds

13
Fundamental hypotheses
Free flow
Breakdown phenomena
Synchronized flow

• Speed is better indicator, but NO characteristic
  speed

14
Fundamental hypotheses
Multi lane
Single lane

• Multi lane has higher speeds because vehicles can
  overtake -gt gap in metastable region

15
Fundamental hypotheses
Steady speed state
S-up

• Upper bound due to safe distance, minimal gap
• Lower bound due to speed adaptation

16
Fundamental hypotheses
Lower boundary Synchronization distance
Speed adaptation
S-low

• Speed adaptation, if distance gt synchronization
  distance, then vehicle can accelerates until
  desired speed if it cant pass a preceding
  vehicle it will tend to adapt its speed to this
  vehicle (synchronize).

17
Fundamental hypotheses
Wandering effect
Perturbation

• Fluctuation in braking or acceleration -gt
  perturbation
• Small enough perturbations do not need to grow in
  SP
• Steady state does NOT exist in SP -gt dynamic
  synchronized flow state

18
Fundamental hypotheses
Complex dynamic interactions

• Steady states are hypothetical -gt do not exist
• SP is a dynamic pattern

19
Fundamental hypotheses
Higher frequency of MJ emergence

• In higher speeds, WMJ does not need to occur
• In Lower speeds, frequency of MWJ occurrence is
  higher

20
Empirical basis of 3phase theory

• Reproducibility
• Hard to reproduce empirical behavior data w.r.t
  the distance gap, speed adaptation etc
• Easier to reproduce spatiotemporal patterns
• Therefore spatiotemporal data is regarded as
  empirical basis for 3Phase theory

21
Empirical basis of 3phase theory

• 3 Traffic phases F, S, J
• J propagates upstream through BN with Vg
• When density high -gt
• SP flow can lie above line J
• Onset of congestion is F-gtS transition
• F-gtJ does not exist!
• WMJ can occur spontaneously in S-gtJ
• Low vehicle speed in S -gt higher frequency of
  S-J
• In S with high speed, J does not necessarily
  occur
• WMJ occur only due to F-gtS-gtJ

22
Discussion

• Data collection
• Kerner says low local speeds are bad measurable,
  and due to heterogeneity density is already a bad
  estimate. Still uses local speed to estimate
  density, how bad is this ? (Kerner gives no
  explanation)
• All spatiotemporal patterns are the result of
  interpolation of loop data, how sensitive are the
  patterns to interpolation ?
• All data from one motorway, reproducibility ?

23
Discussion

• Spatio temporal patterns
• Terminology is not straightforward
• The Pinch effect is badly described
• First in SP, later also in WMJ (pg 45)