Using @RISK for Traffic Forecast Analysis, London | 22.04.2008 TIS.PT – Transportes Inovação e...

Using @RISK for Traffic Forecast Analysis, London | 22.04.2008 TIS.PT – Transportes Inovação e Sistemas, S.A. Slide 1 | 29

Transportes, Inovação e Sistemas, S.A.Transportes, Inovação e Sistemas, S.A.

Av. da Republica, 35, 6º 1050-186 Lisboa | Portugal | www.tis.pt

Using @RISK for Traffic Forecast Analysis

Case Study: Marão Tunnel Concession

Palisade User Conference

London, 22nd April 2008

Inês Teles Afonso


Table of ContentsTable 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


Case Study PresentationCase Study Presentation

TUNNEL MARÃO CONCESSIONNational Politics

Strategy

Identical opportunities

of Development

Similar mobility

conditions

Traffic Forecast

in concession

sections

Main Objective

Traffic Study


Junction 3

Junction 5

Junction 1

Junction 4

IP4

IP4

A24/IP3

A24/IP3

A4/IP4

Penaguião

Amarante

IP4

EN2

EN304 EN313-2

VilaReal

EN15

A4/IP4

Carvalhais

CampeãQuintã

IP4

EN304EN210

EN15

EN101-5

EN210

EN312

EN101

EN101

EN15

MARÃO TUNNELMARÃO TUNNELCONCESSIONCONCESSION

MARÃO TUNNELMARÃO TUNNELCONCESSIONCONCESSION

Junction 2

A4/IP4

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

Vila Real



4 5


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

Note: These values doesn't correspond to the real project values

321

0

100.000

200.000

300.000

400.000

500.000

2012 2015 2018 2021 2024 2027 2030 2033 2036 2039

AADT.k

m

Section (1-2) Section (2-3) Section (3-4) Section (4-5)


Context – What is a traffic study?Context – What is a traffic study?

INPUTTransport Demand Characteristics

Traffic Study / Traffic Model

Traffic Forecasts for the study infra-structure

Finance Analysis(...income estimates)

Environmental Impact

AssessmentProject Analysis

OUTPUT

Transport Supply Characteristics


Context – What is a traffic study?Context – What is a traffic study?

INPUT

Traffic Study / Traffic Modal

OUTPUT

ANALYSIS

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.

Is it possible to present a clearer and

stricter outcome?


What are the advantages of using @RISK?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 variable

AAvariable variable

BBvariable variable

CC

Traffic Traffic

Model Model

Relations..Relations..

OUTPUOUTPU

TT

ANALYSIS


Traffic Modelling Model (VISUM) with @RISKTraffic Modelling Model (VISUM) with @RISK

4 minutes for a traffic

assignment

10.000 @RISK iterations

iterations duration

833 hours!

35 days!!!

SOLUTION

Draw adjustment curves

representing the relationship

between OUTPUT (traffic forecast)

and INPUT variables - Elasticity

Curves

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.


Traffic Modelling Model (VISUM) with @RISKTraffic Modelling Model (VISUM) with @RISK

Variable

OU

TP

UT

- A

AD

T.k

m

2. Traffic Assignments

3. Elasticity curves

adjustment

1. Change INPUT values


Methodology @RISK Application 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

variable Avariable A

Traffic Model Traffic Model


OUTPUTOUTPUT

variable Bvariable B variable Cvariable C variable Dvariable D


Junction 3

Junction 5

Junction 1

Junction 4

IP4

IP4

A24/IP3

A24/IP3

A4/IP4

Penaguião

Amarante

IP4

EN2

EN304 EN313-2

VilaReal

EN15

A4/IP4

Carvalhais

CampeãQuintã

IP4

EN304EN210

EN15

EN101-5

EN210

EN312

EN101

EN101

EN15

Junction 2

A4/IP4

Vila Real

OUTPUT Variable DefinitionOUTPUT Variable Definition

OUTPUT Variable

Traffic Forecast (AADT.km) for Tunnel Section (2011, 2020,

2030, 2040 and Accumulated Revenue)


INPUT Variables DefinitionINPUT Variables Definition

INPUT Variables

GDP Annual Variation Rate (after

2009)

Toll value f(VAT)

Value of Time (VoT) Variation Rate

Fuel Cost Annual Variation Rate

GC= l (length).Co (Operational Cost) + t (travel time).VOT +

l.T(unit toll)

Traffic growth factors

Transport Demand

Generalized Cost


Probability Distribution for INPUT Variables Probability Distribution for INPUT Variables



OUTPUTOUTPUT

variable Avariable A variable Bvariable B variable Cvariable C variable Dvariable D 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.



GDP Annual Variation Rate (after 2009)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

Normal distributionMean= 2,3%Standard Deviation = 0,5%

To avoid to have

negative values of

traffic, which is a non

sense, the distribution

was truncated.



Fuel Cost Variation RateFuel Cost Variation RateIt 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

Weibull distributionPercentile 5% = 0,8Percentile 50% = 1Percentile 95% = 1,5

The modelled variable

consists of the Fuel

Cost Variation until

2020.



Value of Time (VoT) Variation RateValue of Time (VoT) Variation RateVoT is one of the most decisive parameters for the route choice

model;

Research on VoT growth over time indicates annual growth

Triangular Distributionminimum = 0,3Most likely = 0,7Maximum = 1

ranging from 30% to

100% of annual GDP

growth rateIn the deterministic

approach it was used

70%



Toll valueToll = €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 distributionPercentile 5% = 0,18Percentile 50% = 0,21Percentile 95% = 0,23


Correlation Analysis Between INPUT VariablesCorrelation 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 VAT and Fuel Costs


Interaction between INPUT and OUTPUT variablesInteraction between INPUT and OUTPUT variables

GDP rate

AA

DT

.km

Fuel Cost rate

AA

DT

.km

Toll f (VAT)

AA

DT

.km

Value of Time

AA

DT

.km

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




OUTPUTOUTPUT

variable Bvariable B variable Cvariable C variable Dvariable Dvariable Avariable A



OUTPUTOUTPUT





OUTPUTOUTPUT



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


200 225 250 275 300

5% 90% 5% 253,4292 279,3718

Mean=267450,7

Distribution for AADT.km TUNNEL / 2011/F16

Val

ues

in 1

0^ -

5

Values in Thousands

0

1

2

3

4

5

6

Mean=267450,7

200 225 250 275 300 0 125 250 375 500

5% 90% 5% 260,5224 408,8325

Mean=338624,3

Distribution for AADT.km TUNNEL / 2020/O16

Val

ues

in 1

0^ -

6

Values in Thousands

0

1

2

3

4

5

6

7

8

9

Mean=338624,3

0 125 250 375 500

0 175 350 525 700

5% 90% 5% 322,8853 556,4628

Mean=444670,7

Distribution for AADT.km TUNNEL / 2030/Y16

Val

ues

in 1

0^ -

6

Values in Thousands

0

1

2

3

4

5

6

Mean=444670,7

0 175 350 525 700 0 200 400 600 800

5% 90% 5% 357,5827 615,0895

Mean=490997,5

Distribution for AADT.km TUNNEL / 2040/AI16

Val

ues

in 1

0^ -

6

Values in Thousands

0,0000,5001,0001,5002,0002,5003,0003,5004,0004,5005,000

Mean=490997,5

0 200 400 600 800

Results Analysis – Output Distributions GraphsResults Analysis – Output Distributions Graphs

1 2

3 4





0 200 400 600 800

5% 90% 5% 357,5827 615,0895

Mean=490997,5

1 2

3 4


Distribution for AADT.km TUNNEL / 2011/F16

Values in 10^ -5

Values in Thousands

0

1

2

3

4

5

6

Mean=267450,7

200 225 250 275 300200 225 250 275 300

5% 90% 5% 253,4292 279,3718

Mean=267450,7

Distribution for AADT.km TUNNEL / 2020/O16

Values in 10^ -6

Values in Thousands

0

1

2

3

4

5

6

7

8

9

Mean=338624,3

0 125 250 375 5000 125 250 375 500

5% 90% 5% 260,5224 408,8325

Mean=338624,3

Distribution for AADT.km TUNNEL / 2030/Y16

Values in 10^ -6

Values in Thousands

0

1

2

3

4

5

6

Mean=444670,7

0 175 350 525 7000 175 350 525 700

5% 90% 5% 322,8853 556,4628

Mean=444670,7

Distribution for AADT.km TUNNEL / 2040/AI16

Values in 10^ -6

Values in Thousands

0,0000,5001,0001,5002,0002,5003,0003,5004,0004,5005,000

Mean=490997,5

0 200 400 600 800

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



The uncertainty of the model

increases with time

This evolution is an intuitive

perception

But the stochastic model allows to

see that the uncertainty is bigger for

the lower demand values

2010 2020 2030 2040

AADT.k

m

Percentile 5%

Percentile 50%

Percentile 95%

Percentile 5% Percentile 95%

-5% 4%

-24% 20%

-28% 25%

-28% 25%


Results Analysis – Tornado Graphs Results Analysis – Tornado Graphs

Regression Sensitivity for AADT.km TUNNEL /2011/F16

Std b Coefficients

VAT (Toll charge) / SIMULA.../C10-,227

VOT (relation GDP & VOT) /.../C13 ,242

Fuel Cost Annual Evoluatio.../C7-,281

GDP Annual Evoluation Tax .../C4 ,766

-1 -0,75 -0,5 -0,25 0 0,25 0,5 0,75 1

Regression Sensitivity for AADT.km TUNNEL /2020/O16

Std b Coefficients





-1 -0,75 -0,5 -0,25 0 0,25 0,5 0,75 1 Regression Sensitivity for AADT.km TUNNEL /2030/Y16

Std b Coefficients





-1 -0,75 -0,5 -0,25 0 0,25 0,5 0,75 1

Regression Sensitivity for AADT.km TUNNEL /2040/AI16

Std b Coefficients





-1 -0,75 -0,5 -0,25 0 0,25 0,5 0,75 1

1 2

3 4


Results Analysis – Tornado Graphs Results Analysis – Tornado Graphs Regression Sensitivity for AADT.km TUNNEL /

2011/F16

Std b Coefficients





-1 -0,75 -0,5 -0,25 0 0,25 0,5 0,75 1

Regression Sensitivity for AADT.km TUNNEL /2020/O16

Std b Coefficients





-1 -0,75 -0,5 -0,25 0 0,25 0,5 0,75 1

Regression Sensitivity for AADT.km TUNNEL /2030/Y16

Std b Coefficients





-1 -0,75 -0,5 -0,25 0 0,25 0,5 0,75 1

Regression Sensitivity for AADT.km TUNNEL /2040/AI16

Std b Coefficients





-1 -0,75 -0,5 -0,25 0 0,25 0,5 0,75 1

1 2

3 4

These results shows

the importance of the

uncertainty of the

INPUT variables on

uncertainty of output

outcome

What factors cause higher uncertainty on 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


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%

Results Analysis - RevenuesResults Analysis - Revenues


ConclusionsConclusions

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.


ConclusionsConclusionsThe 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


Results Analysis – Tornado Graphs Results Analysis – Tornado Graphs

Thank You


Transportes, Inovação e Sistemas, S.A.Transportes, Inovação e Sistemas, S.A.

Av. da Republica, 35, 6º 1050-186 Lisboa | Portugal | www.tis.pt

Using @RISK for Traffic Forecast Analysis

Case Study: Marão Tunnel Concession

Palisade User Conference

London, 22nd April 2008

Inês Teles Afonso

Using @RISK for Traffic Forecast Analysis, London | 22.04.2008 TIS.PT – Transportes Inovação e...

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