optimization of volume-delay functions

8/12/2019 Optimization of Volume-Delay Functions

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Optimization of Volume-Delay

Functions and Their Implementations in

VDOT Travel Demand Models

Symposium on Transportation Issues and Problems in the

Hampton RoadsHampton University, Hampton, VA 23668

October 1, 2010

Mecit CetinDepartment of Civil and Environmental Engineering

Old Dominion University


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Outline

Demand models

Project goals

Methods for capacity and FFS estimation Optimization of parameters in VDFs

Results

Summary


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Project Goals

Determine the best VDF to be used in demandmodels

Find the optimum parameters for the VDFs

Develop methods to estimate link capacities andFFS

Develop transferable models

Evaluate function performance: Hampton Roads,

Fredericksburg, Charlottesville Recommend models and VDFs to be used to

improve practice


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Volume Delay Functions (VDFs)

BPR :

Conical :

Akelik:


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VDFs

TT = f(V/C, FFS, a, b)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9

TravelTime

V/C

BPR

Conical

Akcelik


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Free Flow Speeds

Uninterrupted FFS=0.88*PS+14 (PS>50)

FFS=0.79*PS+12 (PS


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Identifying Signalized Intersections

Currently, signals are notmodeled

Used a simple rule based on

speed class to determine if a

node has a signal

Accuracy check: Out of 33

intersections in Norfolk

coded as signalized 3 do nothave signals in the field


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VDF Parameters

Current practice: BPR functions

VDF Parameters: Adjusted manually to

improve RMSE (root mean square error)


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Speed/Capacity Classes

For BPR function, there are 4*2 = 8 parameters to be

found

FreewaySpdClass Speed Capacity

11 55 1820

13 55 1820

15 60 1845

17 60 1875

19 63 1950

21 55 1820

23 55 1820

25 60 1845

27 60 1875

29 63 1950

Principal Arterial

SpdClass Speed Capacity

31 31 780

33 44 805

35 44 84537 47 860

39 56 890

Minor Arterial


41 33 650

43 31 710

45 37 71547 44 735

49 52 765

Collectors


51 30 480

53 32 480

55 33 49057 37 510

59 41 720


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Algorithm for Parameter Optimization

Use Genetic Algorithm (GA) to search for the

best combination of parameters that minimize

total RMSE

Run this for each demand model


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Genetic Algorithm System Diagram

AssignmentNew VDF

parameters

Link

Volumes

ValidationRMSE

Values

Genetic

Algorithm

Genetic AlgorithmSoftware

Travel Demand Model


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GA Solutions

Convergence over the number of runs

34.5

35

35.5

36

36.5

37

TotalRMSE

GA Iteration

a) Five Hampton Roads Model Runs with BPR

Function

30.5

31

31.5

32

32.5

33

33.5

34

TotalRMSE

GA Iteration

b) Five Charlottesville Model Runs with BPR

Function


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Optimized VDFsFreeways

Principal

Arterials Minor Arterials Collectors Total

RMSE

% RMSE

Improve

menta b a b a b a b

Hampton Roads Model

Default

BPR 0.15 6 0.3 5 0.3 4.5 0.3 4 35.9Optimum

BPR 0.4 4.8 0.24 7.1 0.58 4.3 0.53 4.4 34.05 5%

Optimum

Conical 1.99 1 8.84 1.7 3.58 1.1 8.09 0.6 32.34 10%

Charlottesville Model

Default

BPR 0.15 4 0.3 6 0.3 5.5 0.3 5 37.1OptimumBPR 1.43 4.4 1.37 4.6 1.42 4.6 0.52 9.1 30.7 17%

Optimum

Conical 6.99 1.7 6.45 1.8 8.13 1.9 12.86 1.5 29 22%

Fredericksburg Model

Default

BPR 0.15 4 0.2 10 0.05 10 0 1 34.7Optimum

BPR 0.31 4.2 1.04 4.1 0.32 7.6 0.47 7.9 32.9 5%

Optimum

Conical 1.25 1 15.87 1.9 13.04 1.8 1.18 1.7 34.1 2%

Optimized VDFs

provide significantly

better RMSE values

Optimizedparameter values

among the 3 TDMs

are not always

comparable


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Charlottesville Model Improvement

0%

10%

20%

30%

40%

50%

60%

70%

28%17%

37%

19%

11%

29%RM

SE

Default

Optimum

39%

Improvement


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Sensitivity of the GA

Population AvgRMSE 1 STDEV 1 Min 1 Max 1

10 31.02 0.13 30.9 31.2

20 31.14 0.25 30.9 31.5

30 31.08 0.13 30.9 31.2

Mutations

AvgRMSE

1

AvgRMSE

2 STDEV 1 STDEV 2 Min 1 Min 2 Max 1 Max 2

2 29.4 29.3 0.2 0.25 29.1 29 29.6 29.6

3 29.36 29.18 0.11 0.08 29.2 29.1 29.5 29.3

4 29.28 29.26 0.08 0.22 29.2 28.9 29.4 29.5

5 29.22 29.12 0.15 0.13 29 29 29.4 29.3

Results from the Conical multi mutation runs with random starting population 1 and 2

Results from the BPR multi population runsTests performed on

the Charlottesville

model


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Summary

Volume delay functions play an important role in travel

demand models

Link travel times can be estimated more accurately by

representing roadway capacity at finer detail

The GA method provides a solution to optimize VDF

parameters

Optimized functions as compared to existing ones perform

better

Conical function provides better RMSE values


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Acknowledgements

Research team: Asad Khattak, Mike Robinson,

Peter Foytik, Sanghoon Son

VDOT TDM Group: Jaesup Lee, Paul Agnello,

Jeremy Raw (now at FHWA)

optimization of volume-delay functions

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