3Phase theory introduction

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3Phase theory introduction
Peter Los Frank Zuurbier Huizhao Tu
TRAIL Course The Physics of Traffic
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DEFINITIONS

• Traffic variables e.g. flow (q), (vehicle) speed
  (v), time/space gap (g), density (?)
• Traffic (control) parameters e.g. weather, road
  conditions (alignment, width, etc) vehicle
  characteristics
• Traffic state A state characterized by certain
  set of variables and parameters
• Traffic phase set of traffic states in with a
  specific (unique) spatiotemporal features

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DEFINITIONS
UPstream backwards
DOWNstream forward
IN flow
OFF flow
OUT flow
ON flow
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DEFINITIONS

• FRONT
• a region where a spatial transition is performed
  between different traffic
• a) states
• b) phases
• Downstream front edge of the state forwards the
  direction of traffic flow
• Upstream front edge of the state backwards the
  direction of traffic flow

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DEFINITIONS
direction of traffic flow
Variable (speed, flow, etc)
distance
upstream front
downstream front
state UP
state IN
state DOWN

• width ? length !!!

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MEASUREMENTLocal traffic variables

• by double induction loops we measure variables
• ?ti length of pulse (and pause)
• ?ti time lag between 2 loops
• ? vi , di speed length of vehicle
• ? ? , g time and distance gap
• ? macroscopic traffic flow
• q, ? and v (temporal) speed of flow???

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MEASUREMENT

• at bottlenecks(control parameters change)
• to be able observe the spatiotemporal changes

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FUNDAMENTAL DIAGRAMempirical observations
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FUNDAMENTAL DIAGRAMModels

• (Deterministic) Macroscopic
• L-W-R (1955-56), Prirogine (1959)Payne (1971)
  and further developments
• (Deterministic) Microscopiccar following
  acceleration gap
• optimal velocity accel. gap speed
  difference
• inteligent driver accel. speed gap ?
  speed
• Stochastic
• Gipps (1981) safe distance
• cellular automata

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FUNDAMENTAL DIAGRAMShock-wave theory

• Conservation of number of vehicles
• based on the particle conservation law
• Shock-wave formula ?1(v1-vp) ?2(v2-vp)
• Velocity of the shock-wave

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FUNDAMENTAL DIAGRAM LWR model

• Lighthill Whitham (1955) and Richards (1956)
• the flow (q) is a function of the density (?)
• qq(?) i.e. only one independent variable
• Conservation balance formula
• solution Kinematic waves

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PROBLEMS OF FD APPROACH

• it works only in homogeneous steady-states
• i.e. same distances, same time-dependent speed
• describes the free-flow well-enough
• at higher density presents only averaged
  characteristics of congested patterns(not
  considering noise and perturbations)

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FUNDAMENTAL DIAGRAM 2-phase theory

• Prirogine and Herman (1971)
• concept of collective flow in FD-aproach
• 2-phase traffic flow theory
• - free flow and
• - collective flow at higher densities
• synchronization of vehicle speed (probability of
  passing is a monotonous decreasing function of
  density)

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FUNDAMENTAL DIAGRAM Moving jams scenarios

• Herman et al. and KomentaniSasaki (1958-59)
• ideas of statistical physics to explain the
  moving jams
• instabilities (driver behaviour
  over-decelaration)
• critical point (density)
• KernerKornhauser (1994)
• Metastable traffic flow - below the critical
  density

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WIDE MOVING JAM
direction of traffic flow
Variable (speed, flow, etc)
distance
upstream front
downstream front
state UP
state IN
state DOWN

• WMJ width of state in gtgt width of fronts

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FUNDAMENTAL DIAGRAMMoving jam characteristics

• J-line determined by characteristics of free
  flow by accelerating from the standstill
• independent parameters(only if free
  outflow!)?del , qout , ?min , vmax
• point j is the treshold of metastability

qmax
j
unstable
qout
J - slope vg
stablefree flow
?min
?max
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FUNDAMENTAL DIAGRAM Metastability of free flow

• line K
• vup lt vg
• the width of jam decreases
• line N
• vup gt vg
• .the width of jam increases

n ?n qn
qmax
qout
N
K
?min
?max