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

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

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 ( ): ‘A statistician waded confidently through a river that on average was one metre deep …. … He drowned.’ p.3

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

ETC 2009 Background III p.5

ETC 2009 Types of uncertainty (risk) affecting the predictions We are predicting Y using a model Y = f(’X, u) ■ 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

ETC 2009 Types of uncertainty (risk)  Model uncertainty, e.g. in the model coefficients such as impact of rail in-vehicle time on modal split  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

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

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

ETC 2009 Methods for quantifying uncertainty I  The literature on quantifying uncertainty in traffic forecasts is fairly limited (compared to the number of forecasts)  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

ETC 2009 Methods for quantifying uncertainty II  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

ETC 2009 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 forecasts obtained p.12

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

Case study: A16 motorway near Rotterdam

ETC 2009 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 ( ; 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 p.15

ETC 2009 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  Distribution over zones p.16

ETC % confidence intervals for pkm by mode for Reference 2020 (input, model, total uncertainty) p Car driver Car passenger Train BTM Slow Total

ETC 2009 Outcomes for vehicle flows on selected links for Reference 2020 p.18

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

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

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

ETC 2009 Fréjus tunnel application  Road connection in the Alps between France and Italy  Private operator; toll and subsidies from France and 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

ETC 2009 Variables and coefficients that are varied (Fréjus) ■ GDP (distinguishing 3 time periods up to 2050)  When will Lyon-Turin HSR service (passengers, freight) open? 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

ETC 2009 Uncertainty margins passenger forecasts p.24

ETC 2009 Uncertainty margins freight forecasts p.25

ETC 2009 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: ; freight: )  regulatory measures (volume cap for road freight through tunnels): timing ( ) and size p.26

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