Transportes, Inovação e Sistemas, S.A.

1. Transportes, Inovação e Sistemas, S.A. Using @RISK for Traffic Forecast Analysis Case Study: Marão Tunnel Concession Palisade User Conference London, 22nd April 2008 Inês Teles Afonso Av. da Republica, 35, 6º 1050-186 Lisboa | Portugal | www.tis.pt

2. Table of Contents • Case Study Presentation • Context – What is a traffic study? • What are the advantages of using @RISK? • Traffic Modelling Model (VISUM) with @RISK • Methodology @RISK • Results Analysis • The data presented in this presentation was modified so that we could ensure the privacy of our client

3. Case Study Presentation • National Politics Strategy • TUNNEL MARÃO CONCESSION • Identical opportunities of Development • Similar mobility conditions • Traffic Study Main Objective • Traffic Forecast in concession sections

4. Case Study Presentation IP4 Vila Real Junction 4 Junction 5 EN312 EN210 A24/IP3 EN304 EN15 EN15 Quintã IP4 Campeã Junction 1 Junction 3 IP4 A4/IP4 A4/IP4 Amarante IP4 Vila Real MARÃO TUNNEL CONCESSION Carvalhais A4/IP4 EN2 EN15 Junction 2 EN210 EN101 EN313-2 EN304 Penaguião EN101-5 EN101 A24/IP3 • Main characteristics: • Connection between cities of Amarante and Vila Real • length → 30 km • Cross-Section → 2x2 • Free Flow Speed →100 km/h • Tolled motorway → open scheme with toll charge in road section → 3 - 4

5. Case Study Presentation • Traffic Model was built on the VISUM platform • The obtained results allow to predict the traffic demand on the studied sections over the period of analysis 4 5 1 3 2 • Note: These values doesn't correspond to the real project values

6. Context – What is a traffic study? Transport Demand Characteristics Transport Supply Characteristics INPUT Traffic Study / Traffic Model Traffic Forecastsfor the study infra-structure OUTPUT Finance Analysis (...income estimates) Project Analysis Environmental Impact Assessment

7. Context – What is a traffic study? • It is a very important issue to know the expected evolution for the traffic (OUTPUT) and what are the associated risks. • Usually we reflect the uncertainty of the model results in three scenarios such as “central”, “optimistic” and “pessimistic” allowing for a very limited deterministic analysis. INPUT Traffic Study / Traffic Modal OUTPUT • Is it possible to present a clearer and stricter outcome? ANALYSIS

8. What are the advantages of using @RISK? • YES! • Using @RISK, the OUTPUT (traffic forecast)is represented by a probability distribution which improves the quality of decision-making. • HOW? • With simulation (Monte Carlo simulation). In each iteration @RISK tries all valid combinations of the values of INPUT to simulate all possible outcomes (OUTPUT). variable A variable B variable C Traffic Model Relations.. OUTPUT ANALYSIS

9. Traffic Modelling Model (VISUM) with @RISK • PROBLEM • Due the complexity of traffic model, it takes some time to get its outcome (traffic forecast). Therefore it is not feasible to do a traffic assignment (VISUM) for each @RISK iteration. • 4 minutes for a traffic assignment • 10.000 @RISK iterations • iterations duration • 833 hours! • 35 days!!! • SOLUTION • Draw adjustmentcurves representing the relationship between OUTPUT (traffic forecast) and INPUT variables - Elasticity Curves

10. Traffic Modelling Model (VISUM) with @RISK • 2. Traffic Assignments • 3. Elasticity curves adjustment • 1. Change INPUT values OUTPUT - AADT.km Variable

11. Methodology @RISK Application • 1.OUTPUT Variable definition • 2. INPUT Variables • INPUT variables definition • Definition of the probability distribution for each one • Analysis of correlation between them • 3. Interaction between INPUT and OUTPUT variables • 4. @RISK Simulation • 5. Results Analysis

12. OUTPUT Variable Definition • OUTPUT Variable • Traffic Forecast (AADT.km) for Tunnel Section (2011, 2020, 2030, 2040 and Accumulated Revenue)

13. INPUT Variables Definition GC= l (length).Co (Operational Cost) + t (travel time).VOT + l.T(unit toll) • INPUT Variables • GDP Annual Variation Rate (after 2009) • Toll value f(VAT) • Value of Time (VoT) Variation Rate • Fuel Cost Annual Variation Rate Transport Demand Traffic growth factors Generalized Cost

14. Probability Distribution for INPUT Variables • Around each input variable, there was a very deep discussion to decide which probability distribution should the variable assume. • This discussion was based mainly on expert judgement.

15. Probability Distribution for INPUT Variables • GDP Annual Variation Rate (after 2009) • The source for GDP before 2009 was the Bank of Portugal • After 2009 it is considered a stochastic variable • To avoid to have negative values of traffic, which is a non sense, the distribution was truncated. Normal distribution Mean= 2,3% Standard Deviation = 0,5%

16. Probability Distribution for INPUT Variables • Fuel Cost Variation Rate • It was considered that the likeliness of fuel prices reaching very high levels in the long or medium term is higher than that of regressing to lower levels • The modelled variable consists of the Fuel Cost Variation until 2020. Weibull distribution Percentile 5% = 0,8 Percentile 50% = 1 Percentile 95% = 1,5

17. Probability Distribution for INPUT Variables • Value of Time (VoT) Variation Rate • VoT is one of the most decisive parameters for the route choice model; • Research on VoT growth over time indicates annual growth • ranging from 30% to 100% of annual GDP growth rate • In the deterministic approach it was used 70% Triangular Distribution minimum = 0,3 Most likely = 0,7 Maximum = 1

18. Probability Distribution for INPUT Variables • Toll value • Toll = €0,07.(1+VAT).(paid length) • The toll value is changed when VAT changes. VAT is the INPUT variable; • In 2007 Portuguese VAT was 21%; • It is not likely that VAT can increase much more; • The probability of simulating a lower VAT than the most likely is higher than getting a higher most likely value Weibull distribution Percentile 5% = 0,18 Percentile 50% = 0,21 Percentile 95% = 0,23

19. Correlation Analysis Between INPUT Variables • The correlation matrix was constructed considering the following variable relations: • Negative correlation between GDP and VAT, and GDP and Fuel Costs • Positive correlation between GDP and VoT • Positive correlation between VATandFuel Costs

20. Interaction between INPUT and OUTPUT variables • GDP Annual Variation Rate and VoT Annual Variation rate have positive elasticity with the traffic forecast, which means that when they increase, the traffic demand on the Tunnel also increases • Fuel Cost and Toll Annual Variation Rate have negative elasticity with the traffic forecast. Their growth implies a traffic demand decrease on the Tunnel

21. The data presented in this presentation was modified so that we could ensure the privacy of our client

22. Results Analysis – Output Distributions Graphs 1 2 Traffic Model Traffic Model 3 4 Traffic Model Traffic Model

23. Results Analysis – Output Distributions Graphs • The red line represents the deterministic output (traffic forecast.km) of the Traffic Model. • The deterministic outcome is always on the right side of the mean value of the distribution. • This means that traffic study may have assumed optimistic values

24. Results Analysis – Output Distributions Graphs • The uncertainty of the model increases with time • This evolution is an intuitive perception • But the stochastic model allowsto see that the uncertainty is bigger for the lower demand values

25. Results Analysis – Tornado Graphs 2 1 4 3

26. Results Analysis – Tornado Graphs • These results shows the importance of the uncertainty of the INPUT variables on uncertainty of output outcome • What factors cause higher uncertaintyon the traffic forecast? • GDP is the INPUT with more influence. Fuel Costs are the second most influential and become more relevant until 2020 where the variable value remains constant

27. Results Analysis - Revenues • What is the possibility of having the revenues 15% less than the deterministic forecast? • The model allows to estimate that that outcome can occur with a probability of 13%

28. Conclusions • With Deterministic model: • The outcome sensitivity analysis is given by deterministic results by changing the values of the input variables; • It is not possible to measure the probability of those results. • With stochastic approach (@RISK) • The outcome sensitivity analysis is based on a probabilistic distribution; • It improves the deterministic analysis answering to the following questions: • what are the expected variation for the traffic forecast results? • what are the factors that cause higher uncertainty on the traffic forecast? • What are the risks of having less revenue than the deterministic forecast? • For all of these, the decision (expert and client) can obtain a more transparent and accurate approach of the outcome presented by traffic model using @RISK analysis software.

29. Conclusions • The undertaken analysis allow to identify the main RISKS associated with the Concession Traffic Forecast. • Usually, on the deterministic model we assume the most likely values for the input variables. • The @RISK results, in this case, allows to observe that the deterministic outcome could have been too optimistic • The information supplied by @RISK analyses allows to add information to the traffic forecast results, improving the interpretations of the results • In future analysis we remain with two main challenges: • to accurately replicate the relevant relations of the traffic model in Excel (VISUM with @RISK) • to improve the methodology for the setting of the probability distributions

30. Results Analysis – Tornado Graphs Thank You

31. Transportes, Inovação e Sistemas, S.A. Using @RISK for Traffic Forecast Analysis Case Study: Marão Tunnel Concession Palisade User Conference London, 22nd April 2008 Inês Teles Afonso Av. da Republica, 35, 6º 1050-186 Lisboa | Portugal | www.tis.pt