1. Predicting uncertainty of traffic forecasts:
giving the policy-makers a range instead of a single number
Gerard de Jong – Significance and ITS Leeds
ETC 2009
November 2014

2. Contents of this presentation
■ Background and types of uncertainty affecting traffic
ETC 2009
forecasts
 Uncertainty prediction method
 Examples of outcomes (uncertainty margins)
 Netherlands national/regional models
 Some public transport project in Paris
 Fréjus Tunnel
p.2

3. ETC 2009
Background I
 Laplace, Pierre Simon
Théorie Analytique des Probabilités, 1812
‘The most important questions of life are indeed,
for the most part, really only problems of
probability.’
 Godfried Bomans (1913-1971):
‘A statistician waded confidently through a river
that on average was one metre deep ….
… He drowned.’
p.3

4. ETC 2009
Background II
 Usually only point estimates for transport volumes and
traffic flows, no uncertainty margins

In The Netherlands often 3-4 point estimates: for
different scenarios
 But for investments and policy-making, it is important
to know the range: robust decisions?
p.4

5. ETC 2009
Background III
p.5

6. Types of uncertainty (risk) affecting the
predictions
We are predicting Y using a model Y = f(’X , u)
ETC 2009
■ Input uncertainty (in X):
 Economic/demographic variables, e.g. GDP/capita,
population
 Policy variables: travel time and travel cost:
 (Policies of the decision-maker)
 Policies of other organisations, e.g. specific taxes,
safety measures, or competitors, e.g. competing
modes
p.6

7. Types of uncertainty (risk)
 Model uncertainty, e.g. in the model coefficients such as
impact of rail in-vehicle time on modal split
ETC 2009

Estimation error (in )
 Micro-simulation error (different model runs lead to different
choice outcomes)
 Specification error (e.g. different functional form f or
error distribution for u)
 Unexpected discrete events (e.g. fire in the Mont Blanc
tunnel, natural disaster, major strike, terrorist attack)
p.7

8. Contents of this presentation
■ Background and types of uncertainty affecting traffic
ETC 2009
forecasts
 Uncertainty prediction method
 Examples of outcomes (uncertainty margins)
 Netherlands national/regional models
 Some public transport project in Paris
 Fréjus Tunnel
p.8

9. ETC 2009
Methodology: reviews
■ de Jong et al. (2007) Uncertainty in traffic forecasts:
literature review and new results for The Netherlands,
Transportation, 34(4), 375-395
■ Rasouli and Timmermans (2012) Uncertainty in travel
demand forecasting models: literature review and
research agenda, Transportation Letters, 4, 55-73
p.9

10. ETC 2009
Methodology: reviews
■ de Jong et al. (2007) Uncertainty in traffic forecasts:
literature review and new results for The Netherlands,
Transportation, 34(4), 375-395
■ Rasouli and Timmermans (2012) Uncertainty in travel
demand forecasting models: literature review and
research agenda, Transportation Letters, 4, 55-73
 PhD thesis of Stefano Manzo (2014) at DTU Copenhagen
(supervised by Otto Anker Nielsen and Carlo Prato):
Uncertainty calculation in transport models and
forecasts
p.9

11. Methods for quantifying uncertainty I
 The literature on quantifying uncertainty in traffic
forecasts is fairly limited (compared to the number of
forecasts)
ETC 2009
 For input uncertainty:
 all studies use repeated model simulation
 usually with random draws for the inputs
 most studies ignore correlation between inputs
 some studies use long time series on the past to determine the
amount of variation and correlation in the input variables
 an alternative for this is a rule-based approach from directed
probabilistic graphical models (Petrik et al., IATBR, 2012)
p.10

12. Methods for quantifying uncertainty II
ETC 2009
 For model uncertainty:
 variances and covariances of parameters can come from the
model estimation
 Jackknife and Bootstrap methods to obtain proper variances
(some specification error)
 some studies use analytic expressions for the output variance
(due to using parameter estimates). Not a practical method for
complicated models
 repeated model simulations with random draws for parameter
values
p.11

13. Overview of common method for both input and
model uncertainty
■ Assume Normal (or triangular) distributions fo each
input variable and coefficient, if possible correlated with
each other
■ Take ‘random’ draws from multivariate Normal
distributions (Monte Carlo simulation)
 Insert the values drawn in the transport model and run
the model to obtain traffic forecasts
 Do this for many draws (e.g. 1000)
 Calculate summary statistics on the series of traffic
ETC 2009
forecasts obtained
p.12

14. Contents of this presentation
■ Background and types of uncertainty affecting traffic
ETC 2009
forecasts
 Uncertainty prediction method
 Examples of outcomes (uncertainty margins)
 Netherlands national/regional models
 Some public transport project in Paris
 Fréjus Tunnel
p.13

15. Case study: A16 motorway near Rotterdam

16. Method used in Dutch study for input uncertainty
 List input variables in tour frequency models, mode-destination
models and expansion procedure:
 income, car ownership, car cost/km, jobs by sector, population
by age group; household size, occupation, education
 Use existing time series (1960-2000; 20-year moving
averages) as source on variances and covariances
 Draw input values from multivariate normal distribution
(with correlations; generated using Choleski
decomposition)
 Run models for many different sets of inputs
ETC 2009
p.15

17. Method used in Dutch study for model uncertainty
 Variances and covariances for parameters from
estimation (including Bootstrap) of the tour frequency
and mode-destination choice models
 Draw parameters from multivariate normal distribution
 Run models for many different sets of parameters
 Sources of variation that were not included:
 Uncertainty in base matrices
 Errors in licence holding and car ownership models
 Errors in assignment and time of day procedures
ETC 2009
 Distribution over zones
p.16

18. 95% confidence intervals for pkm by mode for
Reference 2020 (input, model, total uncertainty)
ETC 2009
p.17
140
130
120
110
100
90
80
70
60
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
Car driver Car passenger Train BTM Slow Total

19. Outcomes for vehicle flows on selected links for
Reference 2020
ETC 2009
p.18
Standard deviation
for input uncertainty
(% of mean)
Standard deviation
for model uncertainty
(% of mean)
Standard deviation
for input and model
uncertainty (% of
mean)
A20
Rotterdam-Gouda 4.1 0.3 4.3
A20
Gouda-Rotterdam 4.6 0.6 4.7
A2
Amsterdam-Utrecht 8.3 1.3 8.3

20. Contents of this presentation
■ Background and types of uncertainty affecting traffic
ETC 2009
forecasts
 Uncertainty prediction method
 Examples of outcomes (uncertainty margins)
 Netherlands national/regional models
 Some public transport project in Paris
 Fréjus Tunnel
p.19

21. ETC 2009
Main results in Paris
■ New element: input uncertainty in policy variables, such
as transport cost and different time components by
mode (partly own policy; partly determined by others)
 As in the Dutch application, the macro-economic
variation (part of input uncertainty) is the most
important source of outcome uncertainty
 The possible variation in transport time and cost by
mode (partly own policy; partly determined by others)
also important
 Uncertainty of model coefficients relatively more
important than in The Netherlands
p.20

22. Contents of this presentation
■ Background and types of uncertainty affecting traffic
ETC 2009
forecasts
 Uncertainty prediction method
 Examples of outcomes (uncertainty margins)
 Netherlands national/regional models
 Some public transport project in Paris
 Fréjus Tunnel
p.21

23. Fréjus tunnel application
 Road connection in the Alps between France and Italy
 Private operator; toll and subsidies from France and
ETC 2009
Italy
 Part of the TEN-T
 Competes with Mont-Blanc tunnel, mountain passes,
railway lines and future Lyon-Turin high-speed rail
service (passengers, freight)
 New: inclusion of time dimension (uncertainty margins
as long-term predictions over time)
p.22

24. Variables and coefficients that are varied (Fréjus)
■ GDP (distinguishing 3 time periods up to 2050)
 When will Lyon-Turin HSR service (passengers, freight) open?
ETC 2009
And its prices?
 When will Fréjus Safety Tunnel open?
 Competing conventional and container rail routes: when will
increased capacity become available?
 EU environmental policies (e.g. volume cap on trucks through
tunnels)
 Alternative-specific coefficients (for routes)
 Other model coefficients (elasticities, mode/route choice)
p.23

25. Uncertainty margins passenger forecasts
ETC 2009
p.24
Passenger vehicles Frejus + Mont Blanc tunnel corridor
350
300
250
200
150
100
50
0
2007
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
2031
2033
2035
2037
2039
Volume index (2007 = 100)

26. Uncertainty margins freight forecasts
ETC 2009
p.25
Freight vehicles Frejus + Mont Blanc tunnel corridor
200
180
160
140
120
100
80
60
40
20
0
2007
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
2031
2033
2035
2037
2039
Volume index (2007 = 100)

27. What do we conclude from the Fréjus graphs?
 Uncertainty increases over time, …
 … but not at a constant rate
 Important sources of uncertainty:
 opening of Lyon-Turin HSR (passengers: 2018-2024;
ETC 2009
freight: 2023-2030)
 regulatory measures (volume cap for road freight
through tunnels): timing (2023-2030) and size
p.26

28. ETC 2009
Concluding remarks
 Most traffic forecasts do not quantify uncertainty
 Methods exist for both input and model uncertainty
(Monte Carlo simulation, repeated model runs)
 Case studies: input uncertainty dominates model
uncertainty
 Policy variables (actions of other decision-makers) can
be included
 Time dimension can be included (uncertainty margins
over time). Especially for PPP projects one would like to
know time path of forecasts and uncertainty
p.27