TRANSPORT MODELLING 23 November 2010 [email protected] Transport Modelling Traffic Flow Theory 2

TRANSPORT MODELLINGTRANSPORT MODELLING23 November 2010

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Transport Modelling

Traffic Flow Theory 2


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Basis of Microsimulation

• Car-following model• Lane-changing model• Gap-acceptance model• Lane-choice model• Models of intersection controls


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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


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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

Car

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hn+1t

xtn – xt

n+1

xtn

xtn+1

t


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IIT Bombay Traffic flow modelling - I 5/44

Car Following Theory-notations

n = the lead vehicle

n+1 = the following vehicle

= the position of vehicle n at time t

ntxntvnta

= the velocity of vehicle n at time t= the acceleration of vehicle at time t

= time interval for updatet

Microscopic Traffic Flow Modeling


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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


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Car following theory : GM model

response stimulus

ttna

1

= f ( dv, dx )

Basic assumptions : driver maintains safe distance or driver wants to drive at the desired speed



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IIT Bombay Traffic flow modelling - I 8/44


Car following theory : GM model

)]()([)(1tvtvtta

nntn

Stimulus could be positive negative or zero

α Sensitivity Coefficient


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Car following theory : General Form

l

ntt

n

nt

ntm

ntt

mltn

tt

xx

vvva

)(

)(

1

11,

m speed exponent

l distance exponent

αl,m Sensitivity Coefficient


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Car following theory : Optimum Velocity

ndesirednnvva

1

Vehicle will tend to maintain a safe speed which depends on the

relative position, rather than relative velocity.

nnoptvxv

)(

1


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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


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Model requirements

• 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


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Variants and constraints

Variable reaction timesVariable acceleration and deceleration Variable or multiple lead vehicles

Lane-disciplinedStable traffic flow: do not produce incidents


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Gipps Car Following Model

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The Gipps car-following model

Free flow modelAccelerate freely to desired speed

Safety-distance modelDriver maintains a

speed which will just allow him to stop in emergency without hitting the obstacle at distance S ahead

Ld

vTvS

2

2

Gipps' First Car Following Model (v(0)=0,Vn=20m/s, an=1.7m/s/s, T=1sec)

0

5

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15

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25

0 5 10 15 20 25 30 35

Time (second)

Sp

ee

d v

(t)

(m/s

)


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GM Car Following Model

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• 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.


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Lan

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• 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.


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Lane-changing models

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?)

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Lan

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• Lane changing can be of two types,mandatory and discretionary

Lane changing model,


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• 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


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• 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).

Gap

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Gap Acceptance Model

Gap

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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.


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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

Gap

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• Time-dependent acceptable gap• Courtesy yielding

• Individual gap acceptance: no shadowing effects (e.g. on approaching roundabouts)

• Requires distinction of major/minor flows


Gap

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Documents

TRANSPORT MODELLING 23 November 2010 [email protected] Transport Modelling Traffic Flow Theory 2