Transport Modelling Traffic Flow Theory 2

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

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

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

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

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

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

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

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

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

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

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

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

Gipps Car Following Model

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

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.

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.

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?)

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.

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.

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.

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.

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.

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.