1. Transport Modelling
Traffic Flow Theory 2

2. Basis of Microsimulation
Car-following model
Lane-changing model
Gap-acceptance model
Lane-choice model
Models of intersection controls

3. Car-following models Models of individual vehicle following behaviour
In a single stream of traffic (lane disciplined)
No overtaking
Three main types:
Safety-distance model
“Action-points”: different rules for different driving states
Psycho-physical

4. Car Following Model hn+1t
The car following behaviour controls the motion of the vehicles.
The models assume that there is a correlation between vehicles in a range of inter-vehicle spacing, from 0 to about 100 to 125 meters.
Each driver in a following vehicle is supposed to be an active and predictable control element in the driver-vehicle-road system
xtn
xtn+1 t
hn+1t
xtn – xtn+1

5. Microscopic Traffic Flow Modeling
Car Following Theory-notations
n = the lead vehicle
n+1 = the following vehicle
= the position of vehicle n at time t
= the velocity of vehicle n at time t
= the acceleration of vehicle at time t
= time interval for update
IIT Bombay
Traffic flow modelling - I
Traffic flow modeling-I

6. Car Following Theories
Describe how one vehicle follows another in an uninterrupted flow
Describe how one driver react to the change in position of the vehicle ahead.
General motion car-following theory in the most popular

7. Car following theory : GM model
Microscopic Traffic Flow Modeling
Car following theory : GM model
response stimulus
= f ( dv, dx )
Basic assumptions : driver maintains safe distance or driver wants to drive at the desired speed
Traffic flow modeling-I

8. Microscopic Traffic Flow Modeling
Car following theory : GM model
Stimulus could be positive negative or zero α
Sensitivity Coefficient
IIT Bombay
Traffic flow modelling - I
Traffic flow modeling-I

9. Microscopic Traffic Flow Modeling
Car following theory : General Form
m speed exponent
l distance exponent
αl,m Sensitivity Coefficient
Traffic flow modeling-I

10. Microscopic Traffic Flow Modeling
Car following theory : Optimum Velocity
Vehicle will tend to maintain a safe speed which depends on the relative position, rather than relative velocity.
Traffic flow modeling-I

11. Microscopic Traffic Flow Modeling
Car following theory: Discussion
GM theory is the most popular because of its field agreement
The GM microscopic model can be derived mathematically from the macroscopic hydro dynamic model
OV models are more complex, but is behaviorally more accurate : driver can perceive relative space better than relative speed
Traffic flow modeling-I

12. Model requirements
Car Following Model
Agree with experimental evidence
Microscopic: individual vehicle trajectories
Macroscopic: q-k-u relationships
Be psycho-physically feasible
Posses local stability
Perturbations in behaviour of lead vehicle not causing following vehicle to collide
Possess asymptotic stability
Perturbations not magnified back over a line of vehicles

13. Variants and constraints
Car Following Model
Variable reaction times
Variable acceleration and deceleration
Variable or multiple lead vehicles
Lane-disciplined
Stable traffic flow: do not produce incidents

14. Gipps Car Following Model

15. The Gipps car-following model
Free flow model
Accelerate freely to desired speed
Safety-distance model
Driver maintains a speed n which will just allow him to stop in emergency without hitting the obstacle at distance S ahead

16. GM Car Following Model
Car Following Model
The research team developed 5 generations of car-following models; a general expression of is given by:
Response = Function (Sensitivity, Stimulus)
Response denotes the acceleration of the following vehicle due to a stimulus caused by the difference in speed of the lead and following vehicles.
Sensitivity is a behavioural parameter that might depend on speed difference and distance headway.

17. These models are based on the gap acceptance model.
Lane Changing Model
Lane changing might occur if there is a need for turning movement, speed change or on freeways to avoid exiting vehicles.
Lane-changing opportunities become available under light traffic conditions. However, ‘forced’ and ‘co-operative’ lane changing may also be performed under congested conditions.
These models are based on the gap acceptance model.
Discrete choice is also used to model lane changing behaviour.
A lane change is considered feasible if there is a gap of sufficient size in the target lane so that the vehicle can move into the target lane safely, without forcing other vehicles in the target lane to slow down significantly.

18. Lane-changing models Lane Changing Model
Models of individual drivers’ ability and propensity to change lanes
Lane-changing objectives, e.g.
To overtake a slower moving vehicle
To bypass an obstacle
To move off/into a reserved bus lane
To get-in-lane for next junction turning
To give-way to merging traffic
Decision-making behaviour:
Is it possible to change lane? (physically & safely)
Is it necessary to change lane? (for junction turning?)
Is it desirable to change lane? (to overtake?)

19. Lane changing can be of two types, mandatory and discretionary
Lane Changing Model
Lane changing can be of two types,
mandatory and discretionary
Lane changing model,
A lane change is considered feasible if there is a gap of sufficient size in the target lane so that the vehicle can move into the target lane safely, without forcing other vehicles in the target lane to slow down significantly.

20. Variants and constraints
Lane Changing Model
Variable lane-changing objectives
Variable hierarchical decision trees
Variable acceptable gaps
Look-ahead: anticipating a lane-changing needs a link ahead
Cooperative lane-changing
Courtesy yielding
Lane disciplined: no overtaking in between lanes or lane in opposite direction
A lane change is considered feasible if there is a gap of sufficient size in the target lane so that the vehicle can move into the target lane safely, without forcing other vehicles in the target lane to slow down significantly.

21. Gap Acceptance Model
Gap acceptance is an important element in most lane-changing models. In order to execute a lane-change, the driver assesses the positions and speeds of the lead and following vehicles in the target lane and decides whether the gap between them is sufficient.
Gap acceptance models are formulated as binary choice problems, in which drivers decide whether to accept or reject the available gap by comparing it to the critical gap (minimum acceptable gap).
A lane change is considered feasible if there is a gap of sufficient size in the target lane so that the vehicle can move into the target lane safely, without forcing other vehicles in the target lane to slow down significantly.

22. Gap Acceptance Model
Gap Acceptance Model
The subject vehicle tends to move from its current lane to target Lane, into the gap between 2 vehicles travelling in the target lane. When a driver wants to do lane changing, the critical lead gap and the lag gap are required to be acceptable for the driver. Otherwise, it is not safe for the driver to do the lane changing.

23. Sn = Speed of the subject vehicle
Gap Acceptance Model
subject= Vehicle which will do the lane-changing manoeuvre
lead and following= Lead and following vehicle of the subject vehicle
lead gap = Gap between the lead vehicle and the subject vehicle in the target lane
lag gap= Gap between the following vehicle and the subject vehicle in the target lane
front gap= Gap between the current lead vehicle and the subject vehicle in the subject lane
Sa and Sb = Speed of the lead and following vehicle
Sn = Speed of the subject vehicle
A lane change is considered feasible if there is a gap of sufficient size in the target lane so that the vehicle can move into the target lane safely, without forcing other vehicles in the target lane to slow down significantly.

24. Variants and constraints
Gap Acceptance Model
Time-dependent acceptable gap
Courtesy yielding
Individual gap acceptance: no shadowing effects (e.g. on approaching roundabouts)
Requires distinction of major/minor flows
A lane change is considered feasible if there is a gap of sufficient size in the target lane so that the vehicle can move into the target lane safely, without forcing other vehicles in the target lane to slow down significantly.