The radial toll highway R-2: An application of stochastic assignment. Henning Stührmann, EPYPSA.

The radial toll highway R-2: An application of stochastic

assignment.

Henning Stührmann, EPYPSA

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Situation

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Plano R-2

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IMD TOTAL: 116.084% PESADOS: 10,47

IMD TOTAL: 165.093% PESADOS: 9,24

IMD TOTAL: 107.230% PESADOS: 10,55

INTESIDAD MEDIADIARIA: 14.354

INTESIDAD MEDIADIARIA: 65.434

INTESIDAD MEDIADIARIA: 74.842

INTESIDAD MEDIADIARIA: 147.845

INTESIDAD MEDIADIARIA: 132.385

Basic Model structure

• Based on Home based survey for the whole province of Madrid

• Models for car only, no mode split as PT infrastructure already well established in base year (1996)

• Three periods– Morning Peak 7-10– Off-Peak 6 to 7, 10-18 and 21 to 24– Afternoon Peak 18.00 - 21.00

• Calibration demandj with counts

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Counts

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Hourly Traffic on Workdays

0

1.000

2.000

3.000

4.000

5.000

6.000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24Hour

km 12,15 to MADRID

km12,15 to ZARAGOZA

km 37,7 to ZARAGOZA

km 37,7 to MADRID

km 116 to ZARAGOZA

km 116 to ZARAGOZA

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Toll System

• 10 Ptas/km as day mean• Analysis of first assignments and counts from N-II

=> two different highways => two toll systems

• Outer part closed system

• Inner part open system

AM-Peak Off-Peak PM-Peak Night

12,15 12,15 12,15 4

AM-Peak Off-Peak PM-Peak Night

15 7,5 15 7,5

Plano R-2

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Outline of the Stochastic Assignment

1. Understand Toll – No Toll facilities as two different modes

2. Two sub-networks: Toll has access to all links, No Toll has NO access to toll facilities

3. Initialise Toll No-Toll Split arbitrarily4. Two class assignment (Toll and No Toll) to

get generalized cost and toll matrices (add. Options)

5. Apply modal split functions for all classes6. Return to step 4, until convergence

Assignment: classes

• Differentiate Internal and external trips• Internal trips: 3 socio-economic classes• External trips: long-distance and mid-distance

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Assignment: Split functions (1)

• Kirchhoff type functions:

•

• Generalized Cost includes a component of function cost, assumed to be the same for all classes

• Different α for external and internal trips

anij

apij

a

C

CPpij

1

1

nijanij

aij

pijapij

GCC

VoT

PGCC

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Assignment: Split functions (2)

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Toll - No Toll Splitt Function

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2

Percieved Cost: Toll/(No Toll)External Trips a=5

Internal Trips a=8

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Assignment: Implementation

• Series of nested macros• Allows to easily change part of the procedure,

e.g. split functions, convergence or output• Convergence usually after 3 steps, 30 min per

time period and scenario

Assignment: Strengths and drawbacks

• Unlimited number of classes

• Easy to use different split functions for different classes

• Very difficult to implement different tolls at one toll both, you would need to assign an additional class.

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Average Daily Traffics

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Future Development

• Split Functions• Additional classes with different tariffs and

split functions => Airport Access

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