Traffic stream models

1
Traffic stream models

• CE740 Traffic Engineering

2
Traffic stream models

• Macroscopic
• Expression of the average behaviour of the
  vehicles at the specific location and time
• Mesoscopic
• Small group of traffic entities with activities
  and interactions
• Microscopic
• space-time behaviour of the systems entities
  (i.e. vehicle and drivers)

3
Traffic stream models

• Macroscopic Stream Models
• Greenshield's model
• Greenberg's logarithmic model
• Underwood's exponential model
• Pipe's generalized model
• Multiregime models

4
Greenshield's model

• Linear speed-density relationship

Relation between speed and density
5
Greenshield's model

• Description
• v mean speed
• k density
• vf free flow speed
• kj jam density
• When density becomes zero, speed approaches free
  flow speed

Two parameter model
6
Greenshield's model

• Relation between speed and flow

7
Greenshield's model

• Relation between flow and density

8
Greenshield's model

• Boundary conditions
• Maximum flow
• Density corresponding to max. flow
• Speed corresponding to max. flow
• Model parameters
• Jam density
• Free flow speed

9
Greenshield's model

• Density corresponding to max. flow
• We have
• Differentiating

10
Greenshield's model

• Maximum flow
• Speed corresponding to max. flow

11
Greenshield's model

• Calibration
• Determination of model parameters
• Free flow speed (vf)
• Jam density (kj)
• where x is density and y denotes speed

12
Greenshield's model

• Calibration
• Using linear regression method

OR
a is
13
Greenshield's model

• Example
• Calibrate Greenshields model using the data give
  in the table
• Find the maximum flow
• Find the density corresponding to a speed of 30
  km/hr

14
Greenshield's model
15
Greenberg's model

• Logarithmic relation
• Advantage
• Analytical derivation
• Good at congestion
• Drawbacks
• Infinite speed
• Poor at low densities

16
Underwood's model

• Exponential Model
• Advantage
• Good at low speed
• Drawbacks
• speed is zero only at infinity density
• Poor at high densities

17
Pipes' model

• Generalized Model
• When n is 1 Pipes model resembles Greenshields
  model

18
Multiregime model

• Eddies Two Regime Model
• Based on field data (Chicago)

Regime 2 Logarithmic
Regime 1 Exponential
19
Multiregime model

• Eddies Two Regime Model
• Based on field data (Chicago)

20
Multiregime model

• Eddies Two Regime Model

Greenshields Model
21
Multiregime model

• Three Regime Model
• Free flow
• Normal
• Congested

22
Thee Dimensional Model

• Simultaneous treatment of q k v

23
Shock waves

• Traffic along a stream can be considered similar
  to a fluid flow

Shock wave Stream characteristics
24
Shock waves

• Flow- Density curve

Speed of Shock Wave
25
Shock waves

• Time Distance diagram

26
Conclusion

• Concerns
• The current status of mathematical models for
  speed-flow concentration relationships is in a
  state of flux
• The models that dominated for nearly 30 years are
  incompatible with the data currently being
  obtained
• but no replacement models have yet been developed
• Lieu 1999, Traffic-Flow Theory
• US DOT, Federal Highway Administration
• http//www.tfhrc.gov/pubrds/janfeb99/traffic.htm

27
Conclusion

• Trends
• Despite those words of caution, it is important
  to note that there have been significant advances
  in understanding traffic stream behavior since
  1980s leading to a better understanding of
  traffic operation
• Efforts to implement ITS will provide challenges
  for applying this improvement
• Equally important, ITS will likely provide the
  opportunity for acquiring more and better data to
  advance understanding of traffic operations

28
Thank You

• tomvmathew_at_gmail.com