CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Transport Modelling
CIVL5502 Transportation Engineering
The University of Western Australia
Lecturer: Dr. Chao Sun
1
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Part 1: Transport Supply &
Demand
2
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Why do we need transport models?
• Designs are often based on traffic volumes but how
do we know the future traffic, especially when you
make changes to the network?
• Traffic changes over time because of changes in
many factors, e.g. social & economic activities (fuel
price increase), individual preferences, government
policy (congestion charge, parking fees), land use,
real estate price
• Traffic responds to changes in supply
• How do we deal with all these uncertainties?
3
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
What’s a model
• Examples of a model
A model is ‘a simplified representation of a
part of the real world – the system of interest –
which concentrates on certain elements
considered important for its analysis from a particular
point of view’ (Ortuzar & Willumsen 1995, p2). 4
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
What’s a good model
• Does it capture the essence of the system that you
want to model?
• Does it replicate the behaviour of system?
•
•
Not everything. Only the things that you care about!
Not 100% accurate – be careful of overfitting!
•
Because it’s a model, not the real thing!
• Does it have the right level of abstraction?
• Predictive power - can it predict the system’s
behaviour?
5
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
What are transport models used for?
• Transport infrastructure planning
• Assessment of land use
development
• Assessment transport policy options
• Design of transport facilities
6
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Different Classes of Model
7
https://slideplayer.com/slide/13003088/79/images/7/Level+of+Effort+
Graphic+by+Daiheng+Ni.jpg
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Barcelo & Perarnau 2005
https://www.researchgate.net/
publication/242154775_METHO
DOLOGICAL_NOTES_ON_CO
MBINING_MACRO_MESO_AN
D_MICRO_MODELS_FOR_TRA
NSPORTATION_ANALYSIS
8
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
https://atap.gov.au/tools-techniques/travel9
demand-modelling/2-overview.aspx
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Transport Demand & Supply
P
Transport Cost
(generalised cost)
Inverse relationship btw Cost & Demand
Cost changes quantity
demanded along the curve
Shifters of demand:
1. Tastes & preferences
2. Num of customers
3. Price of related goods
(substitutes & complements)
4. Income
5. Expectations
Change in
Demand
(decrease)
Ref: https://www.youtube.com/watch?v=LwLh6ax0zTE
Change in
Demand
(increase)
Demand
Transport Demand
(numbers, types,
composition of users)
Q
10
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
•
Transport Demand
Transport demand is derived from
social/economic activities and their spatial
distributions in a region, and is characterised by the
regional demographics.
• The demand includes the numbers, types (i.e.,
passenger and freight), compositions of potential
transport users, and the transport cost
determines how much such potential become
eventuated.
Be careful of
induced demand
11
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Generalised cost
• All outlays perceived by the traveller for a given
trip, which can be expressed in monetary units
Most people
perceive waiting
& walking time
is perceived
much longer
than the real
time. What does
this mean for
PT?
Ref: Wikipedia
12
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Transport Demand & Supply
P
Transport Cost
(generalised cost)
Change in
Supply
(decrease)
Cost changes
quantity
supplied
along the
curve
Positive
relationship btw
Cost & Supply
Change in
Supply
(increase)
Supply
(Performance
function)
Ref: https://www.youtube.com/watch?v=ewPNugIqCUM&t=s
Transport Demand Q
(numbers, types,
composition of users) 13
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Transport Demand & Supply
Shifters of supply:
1.Price of resources
2.Num of producers
3.Technology
4.Taxes & Subsidies
5.Expectations
Ref: https://www.youtube.com/watch?v=ewPNugIqCUM&t=s
16
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Transport Demand & Supply
They interact through P (costs).
Driven by scarcity
Equilibrium
Q Transport demand (numbers, types,
compositions of transport users)
P Transport costs
Q0 Transport demand eventuated
P0 Transport costs eventuated
I Transport infrastructure
R Transport regulation
E Economic activities, including
their spatial distributions
D Demographics
f Demand functional form
g Supply functional form
The numbers, types,
compositions of transport
users and the corresponding
costs in the equilibrium state
are those that are going to
happen in reality (by theory).
17
https://www.youtube.com/watch?v=ewPNugIqCUM&t=s
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Transport Demand & Supply
Shifting Demand & Supply
Demand curve describes how
price changes demand;
Supply curve describes how
demand changes price.
Q
https://www.youtube.com/wa
tch?v=V0tIOqU7mc&list=PLD5BC727C84E254E5
18
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Transport Demand & Supply
Beware of induced demand:
diverted demand & new demand
https://www.youtube.com/wa
tch?v=QzgviOpWi74
Q
19
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Travel Demand Management (TDM)
Enhance the attractiveness of alternatives to SOV
Please read ‘Travel Demand Management’ in course material
20
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Social Marginal Cost
By DavidLevinson - Own work, CC BY-SA 3.0,
https://commons.wikimedia.org/w/index.php?curid=5004157
• http://www.traffic-simulation.de/
21
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
The Perth model results
The regulations can include
measures such as congestion
charge that the government
adopts to internalise some
externalities of a transport
system.
22
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Congestion Charge
Please watch:
Economics of Land Transport in Singapore Managing Traffic Congestion in Singapore
https://www.youtube.com/watch?v=gyJdfY4d
3eM
By VK35 at English Wikipedia, CC BY 2.5,
https://commons.wikimedia.org/w/index.php?curid=3797602
https://www.wbur.org/onpoint/2019/04/0
4/new-york-congestion-pricing-traffic
A very interesting TED talk:
Jonas Eliasson: How to solve traffic
jams [pay attention to VDF in his
talk]
https://www.youtube.com/wa
tch?v=CX_Krxq5eUI
23
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Brasses Paradox and Social Costs
• In the 2019 class, I have played a game based on the following version of
the Brasses Paradox https://www.youtube.com/watch?v=8mlH9bnvWVE .
Students managed to replicate the same results.
• Here’s a longer video describe the paradox
https://www.youtube.com/watch?v=cALezV_Fwi0 and links it to the Nash
Equilibrium, although I don’t necessarily agree with her statement of
AVs will just solve the paradox.
• Related problems are The Prisoner's Dilemma
https://www.youtube.com/watch?v=t9Lo2fgxWHw & The Tragedy
of the Commons https://www.youtube.com/watch?v=tLnA0AO2lXA
• These problems tell us individuals could be entirely rational but still
produce a lose-lose situation so the whole group is worse-off
• Just as explained in the social marginal cost slide, the misalignment
between the individual’s interests and societal interests is often the root
cause of our transport problems.
25
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Part 2: 4-step models
26
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Representation of the Transport
Network
• Model scope can vary from multiple
countries, several regions in a county, a
whole city, or a local area in a city/town.
• The geographic coverage and resolution
need be represented accordingly so that the
spatial distribution of transport demand and
infrastructure can be modelled by mathematical
expressions.
27
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Zone Centroids
The whole area is divided into zones, each of
which acts a single unit to generate and
attract trips:
• If a centroid acts as a point generating
traffic, it is called a trip origin.
• If a centroid acts as a point attracting
traffic, it is called a trip destination.
A zone is represented by its
centroid.
Source: Ortúzar, J. D. and Willumsen, L. G.:
Modelling Transport, 3rd edition, p. 117, John
Wiley & Sons, Ltd.
28
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Links & Nodes
Links
Each road section is represented a link, which has
homogeneous characteristics, such as road width,
pavement conditions and others. If a road sections has with
heterogeneous characteristics along its length, it needs to
be represented by two or more homogenous links, with node
in between.
Nodes
When road links intersect or a road section is broken down
into more links, the corresponding locations of these 29
intersections or changes are called nodes.
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Zone Connectors
A zone centroid is connected to the road network
by one or more connectors. The connectors can be
a real road or simply a nominal or virtual road
30
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
A simple Perth model
Image credit: Google Maps
31
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
A simple Perth model
External
zone
internal
zone
32
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Simplified Transport User’s Decision
Making Process
• Should a journey (either a passenger trip or a
freight shipment) be made or not?
• Which destination should be chosen?
• What transport mode should be used?
• What route should be taken?
• When should the journey start?
33
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Simplified Transport User’s Decision
Making Process
• In reality, these decisions could be made sequentially
or simultaneously.
• Or they are divided into subsets, with decisions being
made simultaneously within a subset and sequentially
between subsets
• It depends on the specific type and purpose of a
journey.
• However, in most transport models these decisions are
treated as a sequential process.
3
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
4 of 5 basic choice
decisions are modelled,
with
departure time decision
being either ignored or
treated roughly by breaking
a day into several
modelling periods, such as
morning peak, shoulder,
off-peak and afternoon
peak periods.
35
What’s the difference btw a journey and a trip
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
The 4-Step Model
The model consists of a set
of sub-models representing
the 4 stages in transport
decisions.
Attention: you’re NOT
doing this for your
assignment!
(Ortuzar & Willumsen 1994)
36
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
1. Trip-generation/attraction model
This model produces the number of trips
generated from an origin zone and the number of
trips attracted to a destination zone:
Origins could
become
destinations
and vice versa
Conservation equation
to model a closed
system (through the use
of external zones)
38
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
1. Trip-generation/attraction model
As indicated in Eq. 1 and 2, input into the tripgeneration/attraction model includes:
• Population
• Economic activities, such as retail floor areas,
employments, students, GDP and so on
• Car ownership
• Household income
• Others
39
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
1. Trip-generation/attraction model
A linear regression model:
Ti = b0 + biz1i + b2z2i + … + bkzki
Ti : trips generated
bk: coefficient for characteristic k, estimated from travel
surveys
zki: characteristic k (income, employment, number of
household members, car ownership)
Cross-classification models (look-up tables for trip
generation rates) are also used.
40
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
An trip attraction/generation example
Why the difference?
41
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Trip generation manual
Day care centre (7-9am)
•
•
•
Different land use
types have different
generate rates
Heavy industries vs.
light industries.
Which has higher
generates rates?
What’s the average
trip gen rates of
Perth households?
42
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
1. Trip-generation/attraction model
OD matrix
Empty
The output of the trip-generation/attraction model is the number of trips
generated from and the number of trips to individual
zones, which can be expressed by the above matrix format.
Origin  Generation
Destination  Attraction
Total generation = total attraction
43
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
2: Trip distribution model
It distributes the total number of trips generated from zone i to
individual destination zone j, populating the empty cells in Table 1
into Table 2 in such way that
44
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
2: Trip distribution model
A key issue in distributing the number of trips generated from an
origin zone to individual destination zones is to choose a
proper functional from which simulates:
• the traveller’s destination choice behaviour or
• the physical phenomenon of trip distribution over
origin-destination pairs (OD pairs), which may not
necessarily be based on any behavioural consideration.
45
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
2: Trip distribution model
Why is this the highest?
Ortúzar, J. D. and Willumsen,
L. G.: Modelling Transport, 3rd
edition, p. 173, John Wiley &
Sons, Ltd.
46
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
2: Trip distribution (gravity) model
Based on Newton's law of universal gravitation
(Wikipedia By I, Dennis Nilsson, CC BY 3.0,
https://commons.wikimedia.org/w/index.php?curid=3455682)
Distance decay: the interaction
between two locales declines as
the distance between them
increases (Wikipedia) but the
friction function could be more
complicated.
Major Origins or Destinations
have stronger “fields”, e.g. CBD
has the largest catchment
Normally non-linear
Used for calibration
47
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
2: Trip distribution model
Use all model parameters to reproduce the trip length distribution
48
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
2: Trip distribution model
The point of lowest
friction but why?
After this point,
F(c) declines
with distance!
49
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
3. Modal split model
It simulates the choice of transport modes by
travellers, of which the modal choice behaviour
has been the core for model development.
Given a trip matrix, such as Table 2, and attributes
or characteristics of various modes in question as
input, the modal split model produces M modespecific trip matrices, each for a mode among
the M modes available for travellers.
50
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
3. Modal split model
Mathematically, this process can be expressed as
follows:
to develop a set of mode shares for each OD pair (Pijm).
logit
Modal split models with various forms, such probit,
, nested logit, and HEV models
have been developed over last thirty plus years. The fundamental of these models is the
random utility theory pioneered by Daniel L. McFadden,
who won He won the Nobel Prize in economics (year 2000) for
his contribution to the development of the random utility theory for discrete choice models.
51
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Discrete Choice
•
Daniel L. McFadden (1937-) received the prize for “his development of theory and
methods for analyzing discrete choice.” Before McFadden’s work,
empirical economists … tended to assume that the variables … were
continuous. But what if one is studying the demand for … people’s choice of
travel modes for getting to work? ... In 1965, one of his graduate students at
Berkeley was analyzing thesis data on the California state highway department’s
choices on where to put freeways and asked for his help. Freeway
placement is an example of a discrete, rather than a continuous,
choice.
•
McFadden tested his model with data on people’s transportation choices
before the Bay Area Rapid Transit (BART) system was built in the San
Francisco Bay Area. While the official forecast was 15 percent, McFadden used
his model to predict that only 6.3 percent of Bay Area travelers would use BART.
The actual number turned out to be 6.2 percent.
https://www.econlib.org/library/Enc/bios/McFadden.html
52
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
3. Modal split model
The basic assumption of random utility theory in the context of
a traveller will select a mode that
generates the most utility. Utility represents a
modal choices is that
consumer's preferences.
The problem then becomes one of developing an expression for
the utility generated by various mode alternatives.
Because it is unlikely that individual travellers’ utility functions can
be specified with certainty, the unspecifiable portion is assumed
to be random.
53
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
3. Modal split model
Deterministic component
Random component
Random to the analysts but not to the travellers
coefficients in the utility function (βm1, …, βmk ) can be estimated with data
collected from traveller surveys
54
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
A sample utility function
Vcar = 0.25 – 1.21IVT – 2.5ACC – 0.3C/I + 1.1NCAR
IVT: in-vehicle travel time
ACC: access time
C/I: cost/income
NCAR: number of cars (per household)
• Utility is derived from the characteristics of the
•
•
alternative modes and those of the traveller
Sensitivity: ACC has approximately twice the impact of a
unit change on IVT and > 7 times the impact of C/I
Mode/alternative specific constant represents
unobserved or not modelled characteristics
55
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Two important characteristics of Utility
• Utility combines the cost with the other features
• Utility makes completely different alternatives
comparable
56
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
3. Modal split model
The probability that a traveller will choose some alternative
mode m, is equal to the probability that the given
alternative’s utility is greater than the utility of all
other possible alternatives.
The probabilistic component arises from the fact that the
unspecifiable portion of the utility expression is not known to
the analyst and is assumed to be a random variable. The basic
probability statement is
57
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
3. Modal split model
The function form of the choice probability depends on the
distribution of the unobservable component εim. If
it is assumed that εim independently (i.e., for i ≠ s) and
identically follows a Gumbel distribution as shown in Figure
7, then the probability for individual i to choose mode
alternative m is
In general, error terms are normally
distributed. However normal distributions
are not bounded which creates a lot of
mathematical complexities. Gumbel is a
necessary simplification at that time to drive
this closed form. Now we can use normal
distribution because of modern computing
58
power (use Monte Carlo simulation).
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
3. Modal split model
59
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Example 1
A simple work-mode-choice model is estimated from data in a small urban
area to determine the proportions of individual travellers selecting various
modes. The mode choices include automobile drive-alone (DL), automobile
shared-ride (SR), and bus (B), and the utility functions are estimated as
where cost is in dollars and time is in minutes. Between a residential area
and an industrial complex, 4000 workers (generating vehicle-based trips)
depart for work during the peak hour. For all workers, the cost of driving an
automobile is $4.00 with a travel time of 20 minutes, and the bus fare is 50
cents with a travel time of 25 minutes. If the shared-ride option always
consists of two travellers sharing costs equally, how many workers will take
each mode?
60
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Example 1: Solution
Note that the utility function coefficients logically indicate that as
modal costs and travel times increase, modal utilities decline and,
consequently, so do modal selection probabilities (see Eq. 15).
Substitution of cost and travel time values into the utility
expressions gives Mode specific
Relative
constants
utility –
the
difference
matters so
UB can be
0
BTW, for those who drive, do you know what buses routes are
61
available to you? Perception = Reality
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Example 1: Solution
Substituting these values into Eq. 15 yields
Multiplying these probabilities by 4000 (the total number of
workers departing in the peak hour) gives 2564 workers driving
alone, 944 workers sharing a ride, and 492 taking a bus.
62
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
4. Traffic Assignment Model
• Number of trips between OD pairs are
determined but which routes should they take?
• To simulate the route choice of travellers
• The end product is the “predicted” total number
of vehicles on each road link of the network in
question
63
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Deriving Vehicular OD Matrix
Passenger OD Matrix
(from Step 3)
f – avg veh occupancy (passenger/veh)
Vehicle OD Matrix
A simple network
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
14
Generic traffic assignment model
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
vehicle trips on route k between i & j
Route
Link
Origin
total vehicle trips between
i&j
Destination
Key assumptions
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
• Trip maker chooses a route btw i & j , which is
perceived to give the maximum utility
• The maximisation of utility is normally associated with
the shortest travel time, which depends on:
• Link performance functions
• Whether perfect information is assumed
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Link performance functions
• What’s the performance given the flow?
• Constant link travel times
• Flow has no impact so use free flow travel time
• Variable link travel times
VDF: Volume delay function
𝑽 𝜷
𝑻𝒍 = 𝑻𝟎 [𝟏 +∝∗
]
𝑪
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Classification of assignment models
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Perfect information
• Perceived TT = actual TT
• Perception = Reality
Link TT
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Perfect info & constant
link TT
shortest time route btw i & j
if link l is on the
shortest time
route
num of veh travelling along the shortest route
btw i & j
All-Or-Nothing (AON) assignment:
• For an OD pair: All flows assigned to shortest path;
• Others get nothing
• A link might get 0 veh for one OD but might get from others
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Perfect info & variable link TT
For an OD pair:
• Trips are spread over multiple routes
• Each has equal TT as the result of different traffic
vol assigned
• Wardrop user equilibrium:
The travel time between a specified origin and destination on all
used routes is the same and is less than or equal to the travel time
that would be experienced by a traveller on any unused route.
Or:
No user can save time by switching routes
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Perfect info & variable link TT
Equal TT for all used routes btw ij
set of used routes btw i & j
TT of route k is the sum of its link TT
0 or 1
Vol on all routes add up to total demand btw ij
Vol link l = all traffic assigned to it by all OD pairs
Deterministic User Equilibrium (DUE) assignment
• Only assign trips to shortest (time) paths
• Don’t get confused with Dynamic User Equilibrium
A DUE example
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Equal TT
q < q*
q > q*
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
DUE assignment
R1: 10km @ 100km/hr
+2 min for every 500veh
4,500 veh
City
Suburb
R2: 5km @ 75km/hr
TT increase with the square of 103 veh/hr
Step 1: Determining free-flow travel times
DUE assignment
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
R1: 10km @ 100km/hr
+2 min for every 500veh
City
4,500 veh
Suburb
R2: 5km @ 75km/hr
TT increase with the square of the number of 103 veh/hr
Step 2: link performance functions
DUE assignment
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
If total traffic flow q < q* all traffic needs to be
assigned to Route 2 under DUE
q* can be obtained by solving the equation for route
2:
q* > q so assign to both routes
DUE assignment
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
DUE assignment
It can also be solved using calculus!
Imperfect info
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Perception ≈ Reality
Err term for route k btw i & j
Independently & identically follows a Gambel distribution
Model parameter
Add up link TT to get route TT
Allocating trips using a Logit choice model
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Imperfect info & constant link TT
Multiple-routes assignment model
Typically applies to rural roads:
• Most travellers chose actual shortest path but not
all
• When θ →∞, it converges to AON
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Imperfect info & variable link TT
Spreading of traffic due to:
• Imperfect info
Multiple-routes model doesn’t have these
• Traffic level
Stochastic User Equilibrium (SUE)
•
•
•
∞
When θ →
, it converges to DUE
When traffic is light, it converges to the Multiple-Route traffic assignment
model
When both are true, it converges to AON
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Classification of assignment models
Zone 1
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
𝑶𝒊 =
O1 = fo(X1)
𝑫𝒋
D1 = fd(X1)
R1,3 2
Zone 2
O2 = fo (X2)
D2 = fd(X2)
R1,3 1
R1,3 3
O3 = fo (X3)
D3 = fd(X3)
Zone 3
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
http://etc.ch/pfrH
Route choice experiments
85
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Summary &
discussions
93
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
The four-step modelling framework
(Ortuzar & Willumsen 1994)
94
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Use models for rational decision making
(Ortuzar & Willumsen 1994)
95
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Modelling and systems thinking
(Ortuzar & Willumsen 1994)
96
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Modelling and systems thinking
(Ortuzar &
Willumsen 1994)
97
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
The 'land-use transport feedback cycle'
This calls for
integrated land
use & transport
models
Wegener, M. 1996
https://www.researchgate.net
/publication/265028805_Redu
ction_of_CO2_Emissions_of_
Transport_by_Reorganisation
_of_Urban_Activities/figures
98
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
A case study
First mile & last mile problem
(Mungundan, Radhakrishnan, 2018: EVALUATING THE IMPACT OF INCREASING
99
‘PARK AND RIDE’ AT PERTH TRAIN STATIONS)
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
A case study
• How would increasing PnR supply change PT
patronage?
(Mungundan, Radhakrishnan, 2018: EVALUATING THE IMPACT OF INCREASING
‘PARK AND RIDE’ AT PERTH TRAIN STATIONS)
100
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
The “optimal” model complexity
(Ortuzar & Willumsen 1994)
101
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Debate about models and their
“accuracy”
The links below are about climate change but you can easily
image people having the same argument about transport
models
• http://www.abc.net.au/news/2016-08-
16/professor-brian-cox-vs.-senator-malcolmroberts/7746576 Round 3 @ 2:30 @4:00 @4:41
• https://www.theguardian.com/australianews/2016/aug/16/qa-brian-cox-brings-graphsmalcolm-roberts
•
102
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Use and Abuse of Models
Inspired by the book Use and Abuse of Statistics
https://www.questia.com/library/83108/use-and-abuse-of-statistics
• How and in what circumstances they
may be used
• How they should not be used
• Dangers of misinterpretation
• Difficulties which beset the modellers
path of investigation
• Black art?
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Is Newtonian physics correct?
How about Theory of Relativity &
quantum physics?
All models are wrong but some
are useful,
so use them carefully!!!
Where’s the biggest weakness of all models?
104
CIVL5502 - Transportation Engineering – UWA - CRICOS Provider Code: 00126G
Weakness of models
Assumptions
• Why do models always have
assumptions?
Data:
•
•
Your model can only be as good as your data
“Garbage in garbage out”
Verification & calibration