# TRAFFIC PERFORMANCE MODELS I: TRAFFIC FLOW THEORY AND SIMULATION APPROACHES - PowerPoint PPT Presentation

PPT – TRAFFIC PERFORMANCE MODELS I: TRAFFIC FLOW THEORY AND SIMULATION APPROACHES PowerPoint presentation | free to view - id: 81dae-ZDc1Z

The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
Title:

## TRAFFIC PERFORMANCE MODELS I: TRAFFIC FLOW THEORY AND SIMULATION APPROACHES

Description:

### time-mean speed ut: average speed of vehicles crossing a point of the roadway ... time-mean speed space-mean speed (typically ut = 1.06 1.12us) ... – PowerPoint PPT presentation

Number of Views:1201
Avg rating:3.0/5.0
Slides: 76
Provided by: hariskout
Category:
Tags:
Transcript and Presenter's Notes

Title: TRAFFIC PERFORMANCE MODELS I: TRAFFIC FLOW THEORY AND SIMULATION APPROACHES

1
TRAFFIC PERFORMANCE MODELS I TRAFFIC FLOW
THEORY AND SIMULATION APPROACHES
• Haris N. Koutsopoulos
• Northeastern University
• M.I.T. Summer Professional Program 1.10s
• Modeling and Simulation for Dynamic
Transportation Management Systems
•  July/August 2003
•

2
Outline
• Basic Elements
• Macroscopic models
• Traffic Stream Models
• Continuum Models
• Microscopic models
• Car Following Models
• Lane Changing
• Traffic Simulation Models

3
Basic Elements of Traffic Flow Theory
• flow (q) number of vehicles crossing a point
per unit of time
• speed (u)
• time-mean speed ut average speed of vehicles
crossing a point of the roadway
• space-mean speed us average speed of vehicles
over a roadway segment at any given time, or
based on average time it takes to cross the
segment
• concentration
• density (k) number of vehicles per unit length
• occupancy (o) percent of time a point of the
• space headway (s) distance between two
consecutive vehicles
• time headway (h) time between passage of two
consecutive vehicles

4
Measurements
• Fixed Point
• Fixed Time (aerial photograph)
• Moving observer

5
Time-Space Diagram Analysis at a Fixed Position
6
Time-Space Diagram Analysis at a Fixed Time
7
Measurements
• Flow
• Density

8
Measurements
• Time-mean speed

At a fixed location, time T ui instantaneous
speed
• Space-mean speed

Observation at fixed location over time T
Instantaneous photograph, speeds over section of
length L
• time-mean speed ? space-mean speed (typically
ut 1.06 1.12us)

9
Fundamental Relationship
• q us ? k
• where,
• q flow
• us space-mean speed
• k density

10
Traffic Stream Models
• Objective
• Provide fundamental relationships among
macroscopic traffic stream characteristics for
uninterrupted flow conditions
• speed-density
• flow-density
• speed-flow

11
Field Data (Holland Tunnel, Eddie 63)
12
Relationships
• Structure
• Single regime same functional form under all
traffic conditions
• Multiple regime different models for different
traffic conditions

13
Examples
• Single regime models
• Greenshields model

uf, kj, parameters to be calibrated
14
Examples
• Single regime models
• Greenbergs model ?
• Underwoods model ?

uf, kj, km, parameters to be calibrated
15
Examples
• Multiple regime models
• Edies model
• Uncongested region
• Underwoods model
• Congested region
• Greenbergs model
• Discontinuity

16
Speed-Density Relationships
17
Flow-Density Relationships
18
Speed-Flow Relationships
19
Empirical Results
• Hall et. al. (1992)

20
Speed-Flow Relationship
Source HCM 2000
21
Continuum Flow (Kinetic) Models
• Conservation of flow
• density at time t k
• density at time tdt kdk
• conservation of flow qdt kdx (q dq)?dt
(kdk)?dx

22
Continuum Flow (Kinetic) Models, contd
• First order models (Lighthill and Whitham,
Richards, LWR)

Conservation of flow
Basic equation of flow
Equilibrium speed (e.g. Greenshields
speed-density model)
q flow u space-mean speed k density g(x,t) gen
eration rate
23
Solution of First Order Models
• Problem
• Given a set of initial and boundary conditions,
• e. g. k0 k(x0, 0)
• Find k(x,t)
• Solution
• Exact solution is based on the method of
characteristics (waves) lines with the same
density

24
Solution of First Order Models
• Properties
• characteristics (waves) are straight lines along
which the density is constant (equal to the
density at the initial point they emanate from)
• a disturbance at a point propagates along the
characteristic through that point
• a disturbance travels at a speed given by the
slope of the characteristic

25
Solution of First Order Models
26
• Shockwave speed

27
• If (A, B) (2, 1) w21 is positive (shockwave
moves forward)
• If (A, B) (3, 2) w32 is negative (shockwave
moves backward)

28
Example Traffic Lights
time
29
Shockwaves at Traffic Lights (red)
Stopping waves
uw
A
qA
Flow (q)
B
D
qD 0
kj
kA
Density (k)
30
Shockwaves at Traffic Lights (green)
Starting waves
uw
C
qB qmax
Flow (q)
B
D
kj
kC
31
Discussion on First Order Models
• Issues
• driver differences
• motion through a shock
• stability
• Implications
• light traffic
• desired speed
• platoon formation
• restricted traffic
• instantaneous change of speed
• stop and go instabilities

32
High Order Continuum Flow Models
• Attempt to represent the acceleration of the
traffic stream
speed, reaction time,)

33
High Order Continuum Flow Models
• Example Paynes model

conservation of flow
basic equation of flow
dynamic speed equation
• where,
• T reaction time, relaxation parameter
• ? anticipation parameter
• f(k) equilibrium speed (speed-density model)
• Rate of change of speed is a function of
• Convection (tendency to travel upstream with
current speed)
• Relaxation to equilibrium
• Anticipation (impact off density ahead)

34
Microscopic Models
• Car-following
• Lane changing
• Gap acceptance

35
Car-Following Models
Common Model Response(t) sensitivity?stimulus(t
-T) T reaction time Stimulus ?v (relative
speed), ?x (relative distance) Sensitivity
function of ?x, speed, traffic conditions Response
acceleration, speed
36
Car-Following Models
GM models (Herman, Gazis)
acceleration of vehicle n at
time t ?, l, m parameters
37
Car-Following Models
• Distance-based models (Newell)
• Stimulus is a function of relative distance
• Psycho-physical spacing model (Wiedemann, 1974)
• reaction based on relative speed-relative
distance combinations
• General acceleration models
• Ahmed, Ben-Akiva, Koutsopoulos (2002)
• Multiple regimes of traffic
• Free flowing
• Car-following
• Time headway threshold and reaction time
distributions

38
General Acceleration, contd
• Ahmed, Ben-Akiva, Koutsopoulos (2002)
• Car following
• Free flowing
• Distributed headway threshold and reaction time

39
Car-following and Traffic Stream Models
mgt
• Are car-following and traffic stream models
consistent?
• Under steady-state, single lane conditions
integration of car-following models results in
traffic stream models

40
Flow Models Derived from Car-Following Models
41
Lane Changing Models
• Mandatory and discretionary lane-changing
• mandatory getting off the current lane in order
to continue on the desired path (e.g. exiting),
or to avoid lane closure
• discretionary attempting to achieve desired
speed, avoid following trucks, avoid merging
traffic, etc.

42
Lane-changing, contd
• Ahmed, Ben-Akiva, Koutsopoulos (1999)
• Mandatory and discretionary
• 3 levels
• Decision to consider lane change
• Target lane choice for DLC
• Random utility framework
• Gap acceptance
• Forced merging

43
Dimensions of Lane Changing
44
Gap Acceptance
• Critical Gap
• if available gap lt critical gap reject the gap
• if available gap gt critical gap accept the gap
• Critical gap is a function of
• Relative speed
• First gap
• Number of gaps rejected
• Remaining length (mandatory lane changing)
• Other opportunities
• Traffic conditions

The Critical Gap is Function of explanatory
variables Gng (t) expXng (t)?g ?ng (t)
45
Limitations of Existing Models
• Independent behaviors
• Acceleration and lane-changing
• Mandatory and discretionary lane changing
• Reactive
• No anticipation
• Myopic
• No planning

46
Other Traffic Performance Models
• Delay models
• Queuing theory (deterministic and stochastic
approaches)
• Empirical models
• Simulation models
• Synthesis of traffic theory models, delay models,
traffic dynamics representation

47
Simulation Models
• Definition
• the process of designing a model of a real
system and conducting experiments with this model
for the purpose either of understanding the
behavior of the system or of evaluating various
strategies (within the limits imposed by a
criterion or set of criteria) for the operation
of the system (Shannon, 1975)
• Approaches
• Discrete event
• synchronous
• Asynchronous
• Continuous time
• Hybrid

48
Simulation Models
• Functionality and level of detail
• Network representation
• Flow representation
• Traffic dynamics
• Support of control strategies
• Surveillance
• Travel behavior/demand
• Overall structure
• Event-based
• Time-based
• Output
• Measures of effectiveness (MOEs)

49
Level of Detail
• Based on their flow and traffic dynamics
representation traffic simulation models are
characterized as
• Macroscopic
• Fluid representation of flow
• Time and space discretization
• Mesoscopic
• Individual vehicle representation
• Continuous space
• Usually discrete time
• Microscopic
• Individual vehicle representation
• Traffic dynamics through vehicle interactions and
movements
• Nanoscopic
• Many common elements with microscopic
• Detailed representation of vehicle dynamics

50
Overall StructureTime- vs. Event-Based Simulation
• Time-based models advance the clock at fixed
intervals ?t
• ?t may be different for different processes
• choice of ?t important for
• Efficiency
• Accuracy
• Event-based models maintain an event list. First
event in the list is processed next
• sequencing of events may be difficult
• less control over efficiency

51
Macroscopic Model Characteristics
• In effect numerical solutions to continuum flow
models
• Usually deterministic
• Common for evaluation of freeway corridor
operations
• Traffic dynamics
• queuing theory
• kinetic theory
• simple input/output
• simple continuum
• high order continuum
• Basic approach
• numerical solution of kinetic equations
• discretization of space and time

52
General Approach
• define a grid of points (n, j) in the time-space
domain
• replace derivatives by finite differences
• Forward, Backward, Central
• Lax-Friedrichs scheme
• Codunovs finite difference approximation

53
Macroscopic Model Example
• Numerical solution based on Laxs method

?j coefficient for converting flow to density
(e.g. ?t/?xj)
54
Paynes model (High Order)
55
Macroscopic Models Examples
56
NETCELL (Daganzo)
• Characteristics
• Dynamic evolution of multi-commodity traffic over
large scale freeway networks
• Links divided into cells traversed in one
simulation step (under free flow speed)
• Consistent with hydrodynamic theory of flow (cell
transmission model)
• Time-based, with an event list
• Inputs
• network geometry
• incidents
• O-D flows
• routing information

57
NETCELL, contd
• Principles (example)

58
NETCELL, contd
cell i1
cell i-1
ni(t1) ni(t) yi(t) - yi1(t)  yi(t) min
ni-1(t), Qi(t), Ni(t) - ni(t)
• l length of cell
• ni(t) number of vehicles in cell i at time t
• Ni(t) max number of vehicles in cell i
• Qi(t) capacity flow into i for time interval t,
and
• yi(t) number of vehicles that flow from cell i-1
to cell i in (t, t1)
• Note results are independent of the processing
order of cells

59
• Debate first order vs. high order models
• theoretical considerations
• empirical evidence
• Recent developments include
• effects due to lane drops
• freeway-to-freeway interactions
• bus effects
• Importance of method for numerical solution
• Numerical solution requires appropriate
discretization of time and space

60
• data requirements
• execution speed
• Usual output aggregate measures of performance
• queue lengths
• speed contours
• total delay
• total travel time
• fuel/pollution statistics

61
Mesoscopic Traffic Simulation Models
• Flow Representation
• individual vehicles or groups of vehicles with
similar characteristics (packets)
• Traffic Dynamics
• fluid approximation
• queuing theory
• Network Representation
• integrated networks or corridors
• lane-based
• Traffic Control
• aggregate by equivalent capacities
• Detailed
• Structure
• time-based

62
Mesoscopic Simulation Models Examples
• Microscopic version has also been developed

63
Microscopic Traffic Simulation Models
• Detailed
• Synthesis of models
• Driving behavior
• Travel behavior
• Control and routing strategies
• Driver classes
• Integrated networks (freeways, urban streets)
• Usually time-based (e.g. 0.1 sec. time step)
• Stochastic

64
Microscopic Traffic SimulationApplication Needs
65
Microscopic Traffic SimulationFunctionality
Needs
66
Examples of Microscopic Simulation Models
• AIMSUN 2 Universitat Politècnica de Catalunya,
Spain
• ANATOLL ISIS and Centre dEtudes Techniques de
lEquipement France
• ARTEMiS University of New South Wales, School of
Civil Engineering Australia
• ARTIST Bosch Germany
• CASIMIR Institut National de Recherche sur
les Transports et la Sécurité France
USA
• DRACULA Institute for Transport Studies,
University of Leeds UK
• FLEXSYT II Ministry of Transport
Netherlands
• FREEVU University of Waterloo, Department
USA
• HUTSIM Helsinki University of
Technology Finland
• INTEGRATION Queens University, Transportation
• MELROSE Mitsubishi Electric Corporation
Japan
• MICROSIM Centre of parallel computing (ZPR),
University of Cologne Germany
• MICSTRAN National Research Institute of Police
Science Japan
• MITSIMLab Massachusetts Institute of
Technology USA
• NEMIS Mizar Automazione, Turin
Italy

67
Examples of Microscopic Simulation Models, contd
• PADSIM Nottingham Trent University NTU UK
• PARAMICS The Edinburgh Parallel Computing Centre
• PHAROS Institute for simulation and
training USA
• PLANSIM-T Centre of parallel computing (ZPR),
University of Cologne Germany
• SIGSIM University of Newcastle UK
• SIMDAC ONERA Centre d'Etudes et de Recherche
de Toulouse France
• SIMNET Technical University Berlin
Germany
• SISTM Transport Research Laboratory,
Crowthorne UK
• SITRA-B ONERA Centre d'Etudes et de Recherche
de Toulouse France
• TRANSIMS Los Alamos National Laboratory USA
• THOREAU The MITRE Corporation USA
• VISSIM PTV System Software and Consulting GMBH
Germany

A detailed description of microscopic models can
be found in www.its.leeds.ac.uk/smartest
68
TRANSIMS Microsimulation
intersection with multipleturn buffers (not
internallydivided into grid cells)
single-cell vehicle
multiple-cell vehicle
7.5 meter ? 1 lane cellularautomaton grid cells
69
TRANSIMS Microsimulation, contd
• For all particles i simultaneously
• IF ( vi gt gapi ? deceleration)
• ELSE IF (vi lt vmax ? acceleration)
• ELSE (vi vmax and vi lt gapi ? free-flow)

70
Nanoscopic Simulation Models
• General characteristics
• detailed driver behavior
• detailed vehicle dynamics model
• detailed vehicle-drive interactions

71
Applications of Traffic Simulation Models
• Evaluation at the planning and policy level
• Evaluation at the operational level
• traffic control
• intersection/urban street operations
• freeway corridors
• ITS
• Automated Highway Systems (AHS)
• Public transportation
• Design
• Optimization

72
Applications of Traffic Simulation Models
• Real time decision support systems
• Prediction
• Strategy design/evaluation
• route guidance
• traffic control
• Research and development
• New concepts and algorithms
• Role
• used independently
• elements of larger systems
• supply representation

73
Applications of Traffic Simulation Models

74
Summary
• Integrated networks
• Traffic dynamics
• queue build-up and spillbacks
• Travel behavior and demand
• Driver characteristics and vehicle classes
• Dynamic Traffic Management
• Trends
• Hybrid models

75
• Model complexity
• inputs
• Calibration
• Validation
• program is a close approximation to reality
• Estimation and calibration
• Output analysis
• large amounts of output
• interpretation of results
• Sources of error
• functional
• distributional
• independence
• aggregation
• boundary effects