CALIBRATION OF THE GRAVITY MODEL FOR TRUCK FREIGHT … .pdf · CALIBRATION OF THE GRAVITY MODEL FOR TRUCK FREIGHT FLOW DISTRIBUTION by Shaohui Mao Dr. Michael J. Demetsky Research

CALIBRATION OF THE GRAVITY MODEL FOR TRUCK FREIGHT FLOW DISTRIBUTION

by Shaohui Mao Dr. Michael J. Demetsky

Research Report No. UVACTS-5-14-14 August 2002

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A Research Project Report For the Mid-Atlantic Universities Transportation Center (MAUTC) A U.S. DOT University Transportation Center Shaohui Mao Department of Civil Engineering Email: [email protected] Dr. Michael J. Demetsky Department of Civil Engineering Email: [email protected] Center for Transportation Studies at the University of Virginia produces outstanding transportation professionals, innovative research results and provides important public service. The Center for Transportation Studies is committed to academic excellence, multi-disciplinary research and to developing state-of-the-art facilities. Through a partnership with the Virginia Department of Transportation’s (VDOT) Research Council (VTRC), CTS faculty hold joint appointments, VTRC research scientists teach specialized courses, and graduate student work is supported through a Graduate Research Assistantship Program. CTS receives substantial financial support from two federal University Transportation Center Grants: the Mid-Atlantic Universities Transportation Center (MAUTC), and through the National ITS Implementation Research Center (ITS Center). Other related research activities of the faculty include funding through FHWA, NSF, US Department of Transportation, VDOT, other governmental agencies and private companies. Disclaimer: The contents of this report reflect the views of the authors, who are responsible for the facts and the accuracy of the information presented herein. This document is disseminated under the sponsorship of the Department of Transportation, University Transportation Centers Program, in the interest of information exchange. The U.S. Government assumes no liability for the contents or use thereof.

CTS Website Center for Transportation Studieshttp://cts.virginia.edu University of Virginia

351 McCormick Road, P.O. Box 400742Charlottesville, VA 22904-4742

434.924.6362

III

ABSTRACT

This research investigates the Gravity Model application for the statewide freight

flow distribution process at a commodity level. In earlier studies, an inventory system

was established and key commodities of Virginia were found. Freight flow production

and attraction equations were then developed for Virginia counties. Here the Gravity

Model was applied in the distribution stage for the key commodities. Four commodity

flow scenarios at statewide and interstate level were considered to define flows within

and between Virginia and external regions. Friction factors were calculated and calibrated

for both internal-internal flows and external-internal flows for the truck mode at the

county level. Here friction factors were calculated with regression analysis using the log-

form of the gamma function and calibrated with the trip length distribution and root mean

squared error method. K-factors were introduced to adjust the flows and aid in the

predictive ability of the model. The model then was tested in the forecasting mode.

Freight flow production and attraction equations were applied with socio-economic

factors to forecast future productions and attractions. After the productions and

attractions were determined for the year 2003, the calibrated Gravity Model was applied

to forecast freight flow distribution. This research shows that the Gravity Model is

appropriate for forecasting freight flows in terms of commodity flow tonnage. These

outputs need to be adjusted to show mode and vehicle flows, which need to be addressed

in future research.

IV

ACKNOWLEDGEMENTS

The authors acknowledge the support for this research from the UTC-Mid-Atlantic

Universities Transportation Center and the Virginia Transportation Research Council.

V

TABLE OF CONTENTS

List of Tables VII List of Figures VIII

CHAPTER 1: INTRODUCTION 1.1 Introduction 1

1.2 Problem Statement 2 1.3 Objective 3 1.4 Organization of The Thesis 3 CHAPTER 2: LITERATURE REVIEW 4 CHAPTER 3: DATA SOURCES 8 3.1 The Reebie TRANSEARCH 1998 Freight Data 8 3.2 GIS ArcView Files 10 3.3 Distance Data 10 3.4 Population and Employment Data 11 3.5 Other Data 11 CHAPTER 4: METHODOLOGY 13 4.1 Freight Flow Scenarios 14 4.2 Truck Trip Impedance and Observed Freight Flow Matrix 17 4.3 Trip Length Distribution and Average Trip Length 18 4.4 Friction Factor Calibration 18 4.5 Future Year Freight Flow Forecasting 21 CHAPTER 5: GRAVITY MODEL CALIBRATION 22 5.1 Overview 22 5.2 STCC 3500, Machinery Excluding Electrical 23 5.2.1 Internal-Internal (I-I) Flows Distribution 23 5.2.2 External-Internal (E-I) Flows Distribution 25 5.2.3 External Flows Between Virginia and BEA Regions 27 5.2.4 External Flows Between Virginia and Census Divisions 29 5.3 Comparison of The Goodness of Fit Measures 31 CHAPTER 6: FORECASTING FUTURE FREIGHT FLOW 38 6.1 Forecasting Socio-economic Factors 38 6.2 Forecasting Future Productions and Attractions 39 6.3 Forecasting Freight Flow Using The Gravity Model 43 CHAPTER 7: SUMMARY AND CONCLUSIONS 45 7.1 Summary 45

VI

7.2 Conclusion 45 7.3 Limitations and Recommendation 46 REFERENCES 48 APPENDIX A The Impedance Matrix Sample (STCC3200) 51

VII

LIST OF TABLES

Table Title Page

3.1 Key Commodities in Virginia 9

5.1 STCC3500 Goodness of Fit (I-I) 24

5.2 STCC3500 Goodness of Fit (E-I) 26

5.3 STCC3500 Goodness of Fit (Scenario 3) 28

5.4 STCC3500 Goodness of Fit (Scenario 4) 30

5.5 Goodness of Fit Measures Comparison for Scenario 1 (I-I) 32

5.6 Goodness of Fit Measures Comparison for Scenario 2 (E-I) 33

5.7 Goodness of Fit Measures Comparison for Scenario 3 35

5.8 Goodness of Fit Measures Comparison for Scenario 4 36

6.1 Population Estimation (Example) 39

6.2 Productions in the year 2003 (Sample) 40

6.3 STCC2900 Freight Attractions in 1998 (Example) 42

6.4 STCC2900 Growth Factors in 2003 (Example) 43

6.5 STCC 3200 I-I Flow Forecasting (Sample) 44

VIII

LIST OF FIGURES

Figure Title Page

3.1 Mapblast.com Distance Query 11

4.1 Scenario 1: Virginia counties and adjacent counties 15

4.2 External Stations in Scenario 2 16

4.3 Scenario 3: Virginia and other states and BEA regions 16

4.4 Scenario 4: Virginia and Census Divisions 17

5.1 STCC3500 TLF After 5 Iterations (I-I) 23

5.2 STCC3500 TLF After K-factor Adjustment (I-I) 24

5.3 STCC3500 TLF After 5 Iterations (E-I) 25

5.4 STCC3500 TLF After K-factor Adjustment (E-I) 26

5.5 STCC3500 TLF After 5 Iterations (Scenario 3) 27

5.6 STCC3500 TLF After K-adjustment (Scenario 3) 28

5.7 STCC3500 TLF After 5 Iterations (Scenario 4) 29

5.8 STCC3500 TLF After K-adjustment (Scenario 4) 30

1

CHAPTER 1

INTRODUCTION

1.1 Introduction

Since the passage of the Intermodal Surface Transportation Efficiency Act of 1991

(ISTEA), freight modeling has become increasingly important for statewide and

metropolitan transportation planning. The importance of freight flow on statewide and

metropolitan transportation practices was further stressed in the Transportation Equity

Act for the 21st Century (TEA-21) in 1998. Freight transportation also plays an important

role in the state economy. The 1997 Commodity Flow Survey showed that there were

more than 255 million tons and 123 billion dollars worth of commodities shipped by the

transportation network in the Commonwealth of Virginia. (The new commodity flow

survey is being conducted during the year 2002.) Truck is a very important mode of

transport for Virginia-originating commodities, and therefore for the Virginia economy.

For all commodities originating in Virginia, the truck mode carries about 77% of the

weight and 83% of the value (3). Freight cargo is expected to increase in the future and

its impact on the state highway network needs to be addressed.

In order to cope with problems associated with increasing freight transport, state

planners need better planning models. There are several practices of freight transportation

modeling in several states. Planners usually use the four-step approach, which includes

freight generation, distribution, modal split and route assignment. Both commodity-based

and vehicle-based models have been used. In the distribution stage, the Gravity Model

was generally applied for vehicle trips rather than commodity flow. This research will

focus on the commodity-based freight distribution at the statewide level.

2

The Commodity Flow Survey (CFS) data from the U.S. Bureau of Census and the

commodity flow data from Reebie and Associates are commonly used for freight flow

planning. To test the Gravity Model, some researchers used traffic counts and screen line

data to compare actual flow with the calculated values. This method is efficient for

vehicle trips, but this validation method may be hard to apply or cannot be applied to the

commodity-based model because it is needed to measure the commodity value or weight

instead of the number of trucks carrying the commodity. Otherwise, it must be

determined what is carried in each load, the number of each load and load factors to

determine each commodity flow.

1.2 Problem Statement

Once the freight flow production and attraction equations were derived in a

previous study (5), a method was needed for forecasting flows among production and

attraction points. Here, to be consistent with transportation planning forecasting,

alternative means for freight distribution need to be examined.

1.3 Objective

The objective of this research is to investigate a commodity-based model for

distributing freight flow to and from Virginia for the truck mode. The commodity flow

data are organized now and four scenarios featuring different region size for the model

application are set up. Not only the statewide freight flow is distributed, but also the

freight flow between Virginia and external regions is considered. Using forecasted socio-

economic factors; the projections of freight production and attraction of each zone have

3

been calculated and calibrated. Accordingly, future year freight flow will then be

forecasted. The whole process is based on the commodity flow data, rather than on truck

trips.

1.4 Organization of The Thesis

The organization of this thesis is as follows. In chapter two, the literature is

reviewed, followed by chapter three, which introduces the data used. Chapter four

describes the methodology used. Beginning with chapter five, the Gravity Model is

calibrated, and then in chapter six, future year forecasting results are showed. Finally, in

chapter seven, the results are analyzed and conclusions are made.

4

CHAPTER 2

LITERATURE REVIEW

Freight planning models can be classified into commodity-based models and trip-

based models (9). The commodity-based model estimates the freight tonnage production

and attraction at each zone, and estimates the tonnage flow between origin-destination

pairs. Usually, the commodity is classified and aggregated according to cargo that is

similar in nature and transport properties. It is commonly believed that commodity-based

models best reflect the economic factors affecting freight flows (9). Some practices in

the states of Indiana, Wisconsin, Kansas and Texas have been based on such commodity

flow data (6, 9,10,13, 19). In the case of Wisconsin, the input-output (I-O) model was

used for planning and the Gravity Model was applied in the distribution stage with truck-

trip data that was converted from commodity flow data (10). An entropy model (fully

constrained gravity model) was used in Indiana to distribute the traffic based on the 1993

Commodity Flow Survey data (13). The Kansas statewide freight model was based on

agricultural commodity flow data. The commodity flow was converted to truck trips and

the external-internal and internal-external flows were distributed using the Gravity Model

(6). The models above converted commodity flow data to truck trips for distribution.

In contrast, trip-based (vehicle-based) models focus on vehicle traffic. The vehicle

trips are generated, distributed, and assigned to the highway network. Traffic count data

are used to verify the model. Trip-based models focus on vehicle trips, not commodity

flow, and so may fail to recognize the cargo types and economic effects on the freight

5

flow (9, 19). A trip-based model has been applied in Phoenix (21). Usually commodity

flow can approximately be converted to vehicle trips (9).

No matter at which level the model is applied, a statewide freight-planning

network usually includes these flows (6, 10,12, 19):

1. Internal-Internal: Both origin and destination zones are within the state area.

2. External-Internal: Either the origin or the destination is outside the state area.

3. External-External: Both origin and destination are outside the state area.

The external station method is applied to distribute the External-Internal and

External-External flows just as in passenger planning. External stations are assumed to be

located where major highways intersect the state border. The flows that pass through the

external stations include the external-internal and external-external flows (6, 8).

In conventional passenger planning, the Growth-Factor Model, Gravity Model

and Intervening Opportunity model have been applied to the distribution process. The

growth-factor model expands the existing interzonal flows by means of zonal growth

factors. If only the trip end and trip interchange data at the origin and destination are

available, the Growth-Factor model can be applied. This model is a simple process that

does not consider any trip impedance. In freight planning practice, the Growth-Factor

model is used to establish rough estimates of the statewide growth in freight flow (6). For

external-external flow distribution where the socio-economic data are not available, the

Growth-Factor model may be applied (10).

The Gravity Model is widely adopted in statewide freight trip distribution (6, 10,

11, 12, 14, 20). However, previous practices on freight flow distribution often faced the

difficulty of data shortage.

6

The Gravity Model is calibrated by comparing the trip length distribution and

average trip length to the observed values (8, 9, 10, 11, 12, 14, 16). It was found that the

shape of the trip length distribution (TLD) curve is relatively smooth and unimodal in

urban and suburban freight movements. But freight movements in the intercity level lead

to irregular and multimodal TLDs (9). Calibration results using “selected links” data

showed that the Gravity Model did well in Wisconsin based on truck trips, although the

observed TLDs were from “selected links” of the whole network.

Traffic count data were compared with the distribution results of the Gravity Model

(10, 12). But for the commodity-based gravity model, it is difficult to count the particular

commodity freight flow using the traffic count data. In this case, Gravity Model results

should be compared to reliable commodity flow survey data such as the Reebie

TRANSEARCH database. On the other hand, commodity flow may be converted to truck

flow using vehicle-loading factors, and the traffic count data may be used to verify the

calibration results. (6,11)

The Intervening Opportunity model may be another choice for freight flow

distribution. This model assumes that each destination has a specific probability, and the

total travel time from origin to destination should be minimized (18). This model is more

complicated than the Gravity Model and may be suitable, although no literature showed

applications to freight flow distribution.

Researchers in Texas used a fractional split distribution model for the statewide

commodity flow analysis to stress the socio-economic effect in the freight flow pattern

(19). This approach “estimates the fraction of commodity consumed at each destination

zone that originates from alternative production zones” (9).

7

In the previous studies, the truck mode generally was analyzed in the freight flow

distribution stage using traffic count data and truck trips that were converted from the

commodity flow data. The remaining option is to apply the commodity flow data directly

for the truck mode using the Gravity Model.

8

CHAPTER 3

DATA SOURCES

The data sources used in this freight flow distribution study include:

1. The Reebie TRANSEARCH 1998 freight data set (commodity flow data

designated for Virginia)

2. GIS ArcView files of Virginia and other states of United States

3. Highway distance data from Mapblast.com

4. Population data from the U.S. Census Bureau

5. Employment data from the U.S. Census Bureau and Minnesota IMPLAN Group

6. Other data such as income from the Weldon-Cooper Center

3.1 The Reebie TRANSEARCH 1998 Freight Data

The 1998 Reebie TRANSEARCH data was the primary source of commodity flow

data. The 1997 Commodity Flow Survey data was consulted to confirm the accuracy of

and add additional detail to the TRANSEARCH data set. The Reebie TRANSEARCH

data for Virginia was based on nationwide data with a focus on Virginia and was much

more detailed than the CFS data. This database had a sample size of 50 million shipments.

The database was compiled using surveys to the freight shippers and carriers, and

considering public data such as the CFS (5).

The procured TRANSEARCH database for Virginia provided the following data:

1. Commodity flows among Virginia counties and between Virginia counties

and adjacent counties in Maryland, West Virginia and Washington, D.C. at

the four-digit Standard Commodity Classification Code (STCC) level.

9

2. Commodity flows between Virginia counties and other states and BEA

regions at the four-digit STCC level.

3. Commodity flows between Virginia counties and census divisions at the four-

digit STCC level

4. Commodity flow data for the following modes: truck, rail, water and air

Key commodities in Virginia are listed at the aggregated two-digit STCC level.

These key commodities are listed as in Table 3.1.

STCC Commodity

3700 Transportation Equipment

2800 Chemicals or Allied Products

3600 Electrical Machinery, Equipment, or Supplies

3500 Machinery, excluding Electrical 2000 Food and Kindred Products

2600 Pulp, Paper, or Allied Products

3000 Rubber or Miscellaneous Plastics Products 3200 Clay, Concrete, Glass or Stone Products

2400 Lumber or Wood Products, excluding Furniture

1100 Coal

1400 Non-metallic Ores and Minerals, excluding Fuels

2300 Apparel or Other Finished Textile Products or Knits

2100 Tobacco Products, excluding Insecticides 2700 Printed Matter 2900 Petroleum or Coal Products

Table 3.1 Key Commodities in Virginia

(Source: James J. Brogan. Application of a Statewide Intermodal Freight Planning Methodology)

10

Because STCC 1400 production and attraction equations are not available using

regression analysis (5), this commodity is neglected in the distribution analysis.

3.2 GIS ArcView Files

GIS data of Virginia counties and cities, as well as other states, are available to the

public from the U.S. Census Bureau and the National Atlas website. The ArcView files

have been downloaded from the National Atlas website: http://nationalatlas.gov,

including county, city and state coverage. These ArcView files were inputted to

determine the center of each region in ArcView 3.2.

3.3 Distance Data

The impedance in the Gravity Model is defined to be the centroidal distance

between origin and destination zones. In GIS ArcView3.2, the distance between two

zones can be measured using the TIGER file. On the other hand, there is available

distance data from some online map and travel service companies like Mapblast.com and

Mapquest.com. The distance data from Mapblast.com provides the actual travel route

based on the shortest path assumption. For example, as shown in Figure 3.1, the distance

between Dunnsville, VA and Jamestown, NC is 252.56 miles and travel time is not

needed for this research.

11

Figure 3.1 Mapblast.com Distance Query

(Source: www.mapblast.com)

3.4 Population and Employment Data Population data for Virginia counties and cities was obtained from the U.S. Bureau

of Census. The employment data at the county level in Virginia were procured from the

Minnesota IMPLAN Group and aggregated to a two-digit STCC level (5). Missing data,

such as total employment, was obtained from the Bureau of Census website.

3.5 Other Data

12

Per-capita income data, and county and city size data, were obtained from the

Weldon-Cooper Center for Public Service at the University of Virginia. This socio-

economic data was then used in the freight production and attraction forecasting (5).

13

CHAPTER 4

METHODOLOGY

The methodology for distributing freight flow for Virginia is listed below. Flow of

each key commodity of Virginia was considered. The results of the calculations are

discussed in Chapters five to seven.

The literature review reveals that the Gravity Model is the most appropriate model

for freight flow distribution. This is because that trip impedance is not considered in the

Fratar Model, and Intervening Opportunity Model is “cumbersome and somewhat

arbitrary” in the calibration process, sometimes hard to converge (22). The Gravity

Model predicts that the flow between two zones is: 1).directly proportional to the flow

generations of each zone and 2).inversely proportional to a function of the spatial

separation between these two zones (8, 16). The Gravity Model is formulated as follows:

∑=

= n

jijijj

ijijjiij

KFA

KFAPT

1

where

ijT = flow from zone i to zone j

iP = flow productions in zone i

jA = flow attractions in zone j

ijF = the friction factor relating to the spatial separation between zone i

and zone j

14

ijK = an optional zone-to-zone adjustment factor

4.1 Freight Flow Scenarios

The Reebie TRANSEARCH database provided freight flow within Virginia and

between Virginia counties and external zones. The counties and cities in Virginia are

numbered from 1 to 136. The adjacent counties in Maryland, West Virginia and

Washington, D.C. are numbered from 137 to 168. BEA regions and other states are

numbered from 169 to 193. The Census divisions are numbered from 194 to 200. Alaska

and Hawaii are treated as one zone: 201.

Because it is difficult to assume the center position of zone201 (Alaska plus

Hawaii), and the flows are essentially not in the truck mode, this zone has been neglected.

For the remaining 200 zones, there are great differences in terms of zone size. To

calculate the internal-internal and external-internal flow distribution, four scenarios have

been set based on the relative sizes of these regions.

1. Virginia counties and adjacent Counties in WV, MD and DC (I-I).

2. Virginia counties and external stations (E-I).

3. Virginia (as one zone) with other states and BEA regions.

4. Virginia (as one zone) with the external census divisions.

These scenarios are illustrated in Figures 4.1 to 4.4. Scenario 2 is used to distribute

the external-internal flow. The eleven external stations are assumed to be located where

major highways intersect the state border. Scenario 3 and 4 are used to show directional

flow at the state level. Through-flow (External-External) is not distributed here. The

Growth Factor model may be applied to predict the through flow in the future.

15

External-Internal flow is converted to flow between external stations and internal

zones based on the shortest path assumption. For example, flow between Albemarle

County and Florida can be assumed to travel on I-95 and external station 5 takes this flow.

All E-I flows are assigned to external stations first, and then distributed to internal zones.

Figure 4.1 Scenario 1: Virginia counties and adjacent counties

16

Figure 4.2 External Stations in Scenario 2

Figure 4.3 Scenario 3: Virginia and other states and BEA regions

17

Figure 4.4 Scenario 4: Virginia and Census Divisions

4.2 Truck Trip Impedance and Observed Freight Flow Matrix Travel distance is used as the truck trip impedance. Using ArcView GIS to

determine the center city of each zone, these city pairs are inputted into a query in the

Mapblast.com database, and the distance between them is obtained. Using the nearest

neighbor technique, the intrazonal travel impedance is assumed to be equal to one-half

the distance from this zone to its nearest neighbor zone (8, 19). The impedance matrix

examples are listed in Appendix A.

The observed freight flow matrix is used in the calibration, and freight flow

productions and attractions at each zone are calculated. The observed freight flow

matrixes for key commodities were obtained from the previous work (5). However,

because the flow data of Virginia is at the county level, the flow matrix in scenario 3 and

18

scenario 4 must be transformed to the state level. Therefore the internal flow of Virginia

will be calculated by adding up the flows in the136 zones in Virginia. Flows from

Virginia to an external zone are calculated by summing up flows from each Virginia

County to this external zone. Obtaining the flow from an external zone to Virginia can be

performed similarly.

4.3 Trip Length Distribution and Average Trip Length

The trip length distribution is calculated by accumulating the flow between each

pair of zones according to the travel impedance between zones, therefore the percentage

of total flow in each travel impedance increment can be obtained. The average trip length

is the weighted mean value of travel impedance, with the flow as the weight.

4.4 Friction Factor Calibration

The Gamma function for friction factor is applied (8).

ijctbijij eatF −= (1)

where

ijt = The travel impedance, and a , b, c are coefficients.

The log form of this function is a linear form.

ijijij ctbLntLnaLnF −+= (2)

The initial values of friction factors are assumed to be 1. Regression analysis is

performed to determine the coefficients value.

The criteria for convergence are:

19

1). Trip length distribution curves of the calculated and observed should be

relatively close to each other. In other words, the friction factors in the current

iteration are almost the same as the friction factors in the next iteration.

2). The difference between the observed average trip length and calculated

average trip length is less than 10%.

If the calculated trip length distribution and average trip length do not meet the

criteria, the friction factors are adjusted by the iterative procedures.

i

obsii TT

FF =+1 (3)

where

1+iF = The friction factor for iteration 1+i

iF = The friction factor for iteration i

obsT = The observed flow

iT = The calculated flow for iteration i

Then the adjusted friction factor values are converted to integer values and the log

form of the gamma function equation is applied to obtain smoothed values using equation

(2). Values of constants a, b, and c are determined using regression analysis. Here ijt is

the impedance of O-D pair ji − , which is the travel distance data in this research. One

thing should be noted that before the regression analysis, friction factors with the same

impedance value must be merged so that there are no identical impedance values in the

regression. New friction factor values are obtained from this regression analysis and they

are the initial values for the next iteration.

20

The calculated trip length distribution and the observed trip length distribution are

compared each other. If the two curves fit well, the iteration is considered to have

converged. At the same time, the calculated average trip length and the observed one

should have a difference of less than 10%. In practice, the root-mean-squared-error

(RMSE) method is applied to determine the convergence condition. The RMSEs between

the calculated flow ijT values and observed values are determined. If the RMSE values

between two iterations remain stable, the iteration can be stopped. In this research, it was

found that after 5 iterations, the RMSE value had less than 10% difference in most cases.

However the trip length distribution diagram after 5 iterations still showed some

difference between the observed and calculated values. To solve this problem, the K-

factor adjustment must be applied. Through the literature review, it is clear that the K-

factor has some relation with socio-economic conditions. An experimental equation can

be used to calculate the K-factor (16). The mechanism of the K-factor is still not very

clear and there are no perfect strategies for dealing with it. By the K-factor adjustment,

the final distributed flow matrix can be determined.

ijij

ijijij RX

XRK

−

−=

11

(4)

where

Rij = ratio of observed flows to the gravity model result for the flows from

zone i to zone j.

ijX = ratio of OD flows to the total OD flows leaving zone i

21

This formula is applied if 10 percent to 40 percent of the flow is leaving a zone.

For other conditions, Rij should be used as the K-factor (16).

4.5 Future Year Freight Flow Forecasting

Freight flow production and attraction equations from previous studies (5) were

applied. The equations are based on socio-economic factors regression analysis. To

project freight flow in 2003 (5 years after 1998), socio-economic factors such as

population were forecasted for 2003 with the average growth rate from data of ten years

(from 1991 to 2000). Assuming the freight generation equations and Gravity Model

friction factors are still valid over a relatively short period, future freight generation data

can be predicted and distributed. K-factors in 1998 are used to adjust the final freight

flow.

22

CHAPTER 5

Gravity Model Calibration

5.1 Overview

Obtaining the friction factor distribution is the main part of the Gravity Model

calibration process. The observed origin-destination (O-D) flow data is important.

Fortunately, the detailed O-D matrices can be derived from the TRANSEARCH database.

This means that the calibration can be performed by spreadsheet software with

conventional procedures or professional software packages like TRANPLAN. Microsoft

Excel 2000 is used for the calibration process.

Since there is no recommended value for freight flow distribution available, the

initial values of friction factors are assumed to be equal to 1. The initial value will affect

the speed of convergence but usually several iterations may be enough (8). In the 1st

iteration, the distributed flow matrix is calculated using the Gravity Model equation and

the values are compared with the observed ones to adjust the friction factors using

equation (3) in Chapter four. If the reduction of RMSE between two continuous iterations

is less than 10%, the iteration can be stopped. It was found that after five iterations the

RMSE reduction was almost zero for all scenarios. Therefore, the Gravity Model was

calibrated in five iterations before applying the K-factor adjustment. The average trip

length is another measure. The criterion is that after the K-factor adjustment, the average

trip length should have a difference of less than 10% comparing with the observed value.

In this study, Internal-Internal (I-I) flows and External-Internal (E-I) flows of the

truck mode are distributed. The corresponding scenarios as stated in Chapter four are

scenario 1 and scenario 2. External flows at the state-level as shown in scenario 3 and

23

scenario 4 are also distributed to get a whole picture of the freight movement between

states. The following subsections describe the application of the Gravity Model to a

specific commodity, STCC3500 (Machinery excluding electrical). The same procedure

was applied to other commodities.

5.2 STCC 3500, Machinery Excluding Electrical

The Gravity Model was applied in each scenario for STCC3500.

5.2.1 Internal-Internal (I-I) Flows Distribution

Altogether 166 zones are defined as internal zones including the adjacent counties

of Maryland, Washington D.C., and West Virginia. The trip length distribution diagrams

after 5 iterations are illustrated in Figure 5.1 and Figure 5.2 respectively using no K-

factors, and then the K-factor adjustments.

Figure 5.1 STCC3500 TLF After 5 Iterations (I-I)

24

Figure 5.2 STCC3500 TLF After K-factor Adjustment (I-I)

It shows that after 5 iterations the calculated TLF and the observed TLF still do not

fit well. After applying the K-factor adjustment, the calculated TLF and the observed

TLF match within 10%. Other commodities’ TLFs show the same trend as STCC 3500.

At the same time, the RMSE decreased when K-factors were applied as shown in

Table 5.1. The difference of the average trip length is below 5%.

Observed

5th

Iteration K-factor Adjusted

Overall RMSE (ton) 2314 333.1

Percent RMSE 110% 16%

Average Trip Length (mile) 127.6 121.5 127.8

Difference of Average Trip Length 4.8% 0.2%

Table 5.1 STCC3500 Goodness of Fit (I-I)

25

Both the overall RMSE and percent RMSE decreased after K-factors were applied.

In the percent RMSE calculation, percent means the ratio of the difference between

observed and calculated flow to the observed value. In the calculation, if the absolute

value of the ratio is bigger than 5, it will be discarded. For example, the observed flow is

2 tons and the calculated one might be 12 tons or 0.3 tons, so the overall RMSE is not too

big but the percent RMSE is far away over 100%. These values are treated as abnormal

and discarded in the percent RMSE calculation. The percent RMSE value calculation has

excluded the abnormal values for all key commodities.

5.2.2 External-Internal (E-I) Flows Distribution In Scenario 2, eleven external stations at the state border with 136 Virginia

counties and cities were considered. E-I flows were distributed between external stations

and internal zones. The TLF curves are illustrated in Figure 5.3 and Figure 5.4.

Figure 5.3 STCC3500 TLF After 5 Iterations (E-I)

26

Figure 5.4 STCC3500 TLF After K-factor Adjustment (E-I)

The K-factor adjusted the flow very well. The average trip length and the RMSE

are listed in Table 5.2.

Observed 5th

Iteration

K-factor

Adjusted

Overall RMSE (ton) 1720.9 217.9



Difference of Average Trip Length 8.6% 0.3%

Table 5.2 STCC3500 Goodness of Fit (E-I)

The RMSE and average trip length showed the effectiveness of the K-factor. The

difference of the average trip length dropped from 8.6% to 0.3%.

27

5.2.3 External Flows Between Virginia and BEA Regions

In the third scenario, Virginia is considered one zone. The intrazonal flow of

Virginia is obtained by summing up the I-I flow of 136 counties. Flows between BEA

regions and Virginia counties are merged to obtain flow data between Virginia and other

regions. The TLF are illustrated in Figure 5.5 and Figure 5.6.

Figure 5.5 STCC3500 TLF After 5 Iterations (Scenario 3)

28

Figure 5.6 STCC3500 TLF After K-adjustment (Scenario 3)

It shows that almost 30% of flow originated within 100 miles of Virginia. Even

without K-adjustment, the Gravity Model has a relatively good fit for mid to long-range

(1000-2000 miles) cargo flow.

The goodness of fit measures are listed in Table 5.3.

Observed 5th Iteration K-factor Adjusted

Overall RMSE (ton) 28776.1 8597.1



Difference of Average Trip

Length

28.5% 1.4%

Table 5.3 STCC3500 Goodness of Fit (Scenario 3)

29

The RMSE dropped from 143% to 25% after K-factor adjustment. The difference

of average trip length was lowered from 28.5% to 1.4%.

5.2.4 External Flows Between Virginia and Census Divisions

Census divisions in this scenario cover all the BEA regions and their areas are

much larger than that of Virginia. Similar to scenario 3, Virginia is considered one zone.

Impedance is assumed to be the distance between two zone-centers. The TLF comparison

is illustrated in Figure 5.7 and Figure 5.8.

Figure 5.7 STCC3500 TLF After 5 Iterations (Scenario 4)

30

Figure 5.8 STCC3500 TLF After K-adjustment (Scenario 4)

From the figures above, it can be seen that the Gravity Model converged after 5

iterations and the two TLF curves fit relatively well for most ranges even without K-

factor adjustment. The RMSE and average trip length values are listed in Table 5.4.

Observed 5th Iteration K-factor Adjusted

Overall RMSE (ton) 124026 39577



Difference of Average Trip

Length 5.8% 1.3%

Table 5.4 STCC3500 Goodness of Fit (Scenario 4)

31

The RMSE dropped from 114% to 21% after K-factor adjustment. The differences

of the average trip length are both less than 6%.

5.3 Comparison of The Goodness of Fit Measures

The goodness of fit measures for each scenario are listed in Table 5.5, 5.6, 5.7 and

5.8. No TLF curves are showed below but they are similar to those for STCC 3500. After

the K-adjustment, curves usually fit very well. For Scenario 4, there are no available data

for STCC2000 (Food and kindred products), STCC2400 (Lumber or wood product), and

STCC1100 (Coal). The “average trip length difference” in the table is the relative

percentage difference between the calculated value and the observed value.

Commodity Measure Observed 5th Iteration K-factor adjusted

Transportation Equipment Average Trip Length

/Difference 137.8 120.9 (12.2%) 137.5 (0.2%)

(STCC3700) Percent RMSE 119% 15%

Chemicals or Allied Products

Average Trip Length /Difference 131.1 120.9 (7.8%) 130.3 (0.6%)


Electrical Machinery, Equipment or Supplies



Food and Average Trip Length

/Difference 121.7 117.6 (3.3%) 119.3 (2%) Kindred Products


Pulp, Paper or Allied Products



Rubber or Miscellaneous Average Trip Length

/Difference 159 129.2 (19%) 160.4 (0.9%) Plastic Products


Clay, Concrete, Glass or Average Trip Length

/Difference 131.1 128.2 (2.2%) 127.8 (2.5%) Stone Products


32

Lumber or Wood Products,

Average Trip Length /Difference 158.5 128.6 (19%) 160.5 (1.3%)

excluding Furniture (STCC2400) Percent RMSE 115% 19%

Coal Average Trip Length

/Difference 302.4 287.7 (4.9%) 303.2 (0.3%) (STCC1100) Percent RMSE 62% 27%

Apparel or Other Finished Textile Products or Knits



Tobacco Products, Average Trip Length

/Difference 134.9 129.7 (3.9%) 135.2 (0.2%) excluding Insecticides


Printed Matter Average Trip Length

/Difference 81.7 87 (6.5%) 77.3 (5.4%) (STCC2700) Percent RMSE 131% 29%

Petroleum or Coal Products



Machinery, excluding Average Trip Length

/Difference 127.6 121.5 (4.8%) 127.8 (0.2%)

Electrical (STCC3500) Percent RMSE 110% 16%

Table 5.5 Goodness of Fit Measures Comparison For Scenario 1 (I-I)

Table 5.5 shows that the average trip lengths in Scenario 1 are mostly less than 160

miles. But for STCC1100 (Coal), the average trip length is around 300 miles. In fact, coal

is transported mainly by rail mode; only 5% is by truck mode according to 1998

TRANSEARCH data. The origin zones include Buchanan County, Dickenson County,

Lee County, Russell County, Tazewell County, and Wise County in Virginia, with

Alleghany County and Garrett County in Maryland, and Grant County in West Virginia

among 166 zones in this scenario.

The K-factor adjustment shows good results. The percent RMSEs dropped from

over 100% to less than 30% for almost all commodities. The difference of the average

trip length dropped to less than 3%.

33



/Difference 257.1 244.6 (5.1%) 264 (2.7%) (STCC3700) Percent RMSE 129% 13%

Chemicals or Allied Products Average Trip Length

/Difference 218.9 188.7 (13.8%) 224.1(2.3%) (STCC2800) Percent RMSE 126% 17%





/Difference 224.3 211.2 (5.8%) 225.7 (0.6%) Kindred Products

(STCC2000) Percent RMSE 125% 12% Pulp, Paper or Allied

Products Average Trip Length

/Difference 219.8 184.3 (16%) 230.2 (4.7%) (STCC2600) Percent RMSE 125% 26%


/Difference 226.2 213.1 (5.8%) 227.3 (0.5%) Plastic Products (STCC3000) Percent RMSE 125% 13%


/Difference 218.2 189.7 (13%) 223.8(2.6%) Stone Products (STCC3200) Percent RMSE 131% 28%

Lumber or Wood Products, Average Trip Length

/Difference 214.4 196.2 (8.5%) 215.2 (0.4%) excluding Furniture





Average Trip Length /Difference 233.2 214 (8.2%) 234.2 (0.4%)



/Difference 248 232.8 (6.1%) 249.7 (0.7%) excluding Insecticides




Petroleum or Coal Products Average Trip Length



/Difference 264.9 242 (8.6%) 265.7 (0.3%) Electrical (STCC3500) Percent RMSE 141% 21%

Table 5.6 Goodness of Fit Measures Comparison For Scenario 2 (E-I)

34

Table 5.6 shows that the average trip lengths in Scenario 2 are mostly less than 260

miles. There are 136 zones in Virginia and 11 external stations at the border in this

scenario. The K-factor adjustment shows good result. The percent RMSEs dropped from

over 100% to less than 30% for all commodities. The difference of the average trip length

dropped to less than 5%.



/Difference 429 367.1 (14.4%) 478.3 (11.5%) (STCC3700) Percent RMSE 138% 34%

Chemicals or Allied Products Average Trip Length



Average Trip Length /Difference 493.6 546 (10.6%) 486.2 (1.5%)



/Difference 198.3 166.3 (16%) 207.8 (4.8%) Kindred Products

(STCC2000) Percent RMSE 138% 29% Pulp, Paper or Allied

Products Average Trip Length



/Difference 329.9 361.9 (9.7%) 330.9 (0.3%)

Plastic Products (STCC3000) Percent RMSE 142% 30%


/Difference 174.5 143 (18%) 176.2 (1%) Stone Products (STCC3200) Percent RMSE 131% 17%

Lumber or Wood Products, Average Trip Length

/Difference 194.3 169.9 (12.6%) 197.9 (1.9%) excluding Furniture





Average Trip Length /Difference 413.7 548.7 (32.6%) 387 (6.5%)



/Difference 350.3 277.2 (20.9%) 348.9 (0.4%) excluding Insecticides


35


/Difference 277.4 274.1 (1.2%) 282 (1.7%) (STCC2700) Percent RMSE 144% 28%


/Difference 248.2 148.2 (40.3%) 246.4 (0.7%)



/Difference 426.2 547.7 (28.5%) 420.4 (1.4%) Electrical (STCC3500) Percent RMSE 141% 21%

Table 5.7 Goodness of Fit Measures Comparison For Scenario 3

Table 5.7 shows that the average trip lengths in Scenario 3 are irregular ranging

from 170 miles to 500 miles. The zones in this scenario include Virginia State as one area

and other BEA regions and states that are illustrated in Figure 4.3. For STCC3600

(Electrical machinery and equipment), the average trip length is almost 500 miles. This is

because the flows between New York, Texas and Tennessee are huge. On the contrary,

for STCC3200 (Clay, concrete, glass or stone products), the largest flows are usually

within each zone or between adjacent zones, therefore the average trip length is around

170 miles. After the K-factor adjustment, the percent RMSEs dropped from over 100% to

less than 40% for almost all commodities. The difference of the average trip length

dropped to less than 6% for almost all commodities.



/Difference 572.2 588 (2.8%) 589.3 (3%) (STCC3700) Percent RMSE 166% 16%

Chemicals or Allied Products




Average Trip Length /Difference 583.2 645.4 (10.7%) 566.3 (3%)


36

Pulp, Paper or Allied Products




/Difference 571.1 644.9 (12.9%) 566.4 (0.8%) Plastic Products



/Difference 330.4 363.5 (10%) 330.4 (0) Stone Products (STCC3200) Percent RMSE 163% 46%

Apparel or Other Finished Textile

Average Trip Length /Difference 516 585.8 (13.5%) 510 (1.2%)

Products or Knits (STCC2300) Percent RMSE 103% 15%


/Difference 206.6 190.9 (7.6%) 225 (8.9%) excluding Insecticides



/Difference 444 517.8 (16.6%) 445.2 (0.3%) (STCC2700) Percent RMSE 129% 6%


/Difference 372.2 386.7 (3.9%) 372.2 (0) (STCC2900) Percent RMSE 122% 0%


/Difference 571.2 604.1 (5.8%) 563.5 (1.3%) Electrical (STCC3500)


Table 5.8 Goodness of Fit Measures Comparison For Scenario 4

Table 5.8 shows that the average trip length in Scenario 4 are from 200 miles to

580 miles. The zones in this scenario include Virginia State and census divisions

illustrated in Figure 4.4. For STCC2100 (Tobacco products), the average trip length is

around 200 miles because the largest flows are within Virginia State. After the K-factor

adjustment, the percent RMSEs dropped from over 100% to less than 40% for almost all

commodities. The difference of the average trip length dropped to less than 10% for all

commodities.

37

For almost all scenarios of every key commodity, the K-factor adjustment showed

effective results. After five iterations, the RMSE and the difference of the average trip

length had large values for most commodities. After the K-factor adjustment, the RMSE

usually dropped to 30% or less and the difference of the average trip length dropped to

10% or less.

38

CHAPTER 6

Forecasting Future Freight Flow

The calibration of the Gravity Model provided a set of friction factors and K-

factors for each key commodity in each scenario. Assuming the friction factors and K-

factors do not change in time, the Gravity Model can be used to predict future year

commodity freight flows. The source data is from 1998; truck freight flow for the year

2003 is forecasted.

6.1 Forecasting Socio-Economic Factors

Freight production and attraction equations use socio-economic factors such as

population and employment. For example, the freight attraction equation for STCC3700

(Transportation equipment) is as follows (5):

29.765 (Industry Employment) + 2.772 (Total Employment) - 25.359 (Population/Square

Mile) - 79.539 (Motor Freight & Warehousing Employment) - 38.677 (Air Transportation

Employment) + 219.258 (Water Transportation Employment)

Annual growth rates of employment were obtained with the employment data from

the IMPLAN Group, Minnesota (5). The only additional information needed is the

forecasting of population data. Using the population data between 1990 and 2000 from

the U.S. Bureau of Census, the average annual growth rate can be determined. The

estimated population in 2003 then can be calculated. Table 6.1 shows an example of the

population estimation.

39

Region County Name

Industry Employment Annual

Growth Rate%

1990-2000 Population

Growth Rate%

Population Annual Growth

Rate

Estimated Population in

2003

1 Accomack -0.59 20.8 0.019097 35443.772

2 Albemarle -0.18 16.2 0.0151459 84520.864

3 Alleghany -0.16 0.9 0.0008628 12198.489

4 Amelia 0 29.7 0.0263758 11808.241

5 Amherst -0.46 11.6 0.0110386 31737.113

6 Appomattox 0 11.4 0.0108749 13863.854

7 Arlington 0.87 10.9 0.0103625 186652.39

8 Augusta -0.16 20.3 0.0186272 67746.846

9 Bath -0.16 5.2 0.0050713 5016.2822

10 Bedford -0.46 32.5 0.0285636 64320.574

11 Bland 0.5 5.5 0.0053499 6930.4458

12 Botetourt 0.43 22.0 0.0201034 31549.635

13 Brunswick 0 15.2 0.0142614 17942.456

14 Buchanan 0.5 -13.9 -0.014854 26843.387 15 Buckingham 0 21.4 0.0195499 16127.006 16 Campbell -0.46 7.5 0.007291 52196.909

17 Caroline -0.59 15.1 0.0141727 23660.682

18 Carroll 0.5 10.3 0.0098327 29270.555

19 Charles City 2.06 10.3 0.0098072 7446.6511

20 Charlotte 0 6.7 0.0065135 12663.478

21 Chesterfield 2.06 24.0 0.0217443 273839.48

22 Clarke 0.87 4.6 0.0044626 13066.697

23 Craig 0.5 16.4 0.0153419 5268.1635

24 Culpeper 0.87 23.3 0.0211531 36733.233

Table 6.1 Population Estimation (Example)

6.2 Forecasting Future Productions and Attractions

By applying the freight flow production and attraction equations with factors in

2003 values; productions and attractions can be determined. However, before using the

Gravity Model to distribute truck commodity flows, these productions and attractions

40

have to be split to the truck mode as shown in Table 6.2. The truck mode percentage for

each commodity was obtained from the 1998 TRANSEARCH database (5).

Region County Name STCC 3700

STCC 2800

STCC 3600

STCC 3500

STCC 2000

1 Accomack 82.768205 345805.57 0 1364.8343 351.57918 2 Albemarle 4944.4315 28473.625 9267.1682 1914.4846 0

130 South Boston 0 0.0 0 0 0 131 Staunton 1913.2038 1,419.8 2829.1763 2210.6488 206.65579 132 Suffolk 10232.031 334,129.9 0 0 28612.644

133 Virginia Beach 18218.95 26,336.4 2031.3778 25287.904 129192.97

134 Waynesboro 246.7263 3,828.4 235.01597 10229.85 3675.9545

135 Williamsburg 2626.0379 7,497.8 273.23886 43.691962 501.80626 136 Winchester 24075.387 65,258.1 12181.774 14041.932 89791.94

Truck Mode 86% 80% 93% 83% 98%

Production in 2003 (Truck Mode)

Region County Name STCC 3700

STCC 2800

STCC 3600

STCC 3500

STCC 2000

1 Accomack 71.180656 283,560.6 0 1132.8124 344.5476 2 Albemarle 4252.2111 23,348.4 8618.4665 1589.0222 0

130 South Boston 0 0.0 0 0 0 131 Staunton 1645.3553 1,164.2 2631.1339 1834.8385 202.52267 132 Suffolk 8799.5468 273,986.5 0 0 28040.391

133 Virginia Beach 15668.297 21,595.8 1889.1814 20988.96 126609.11

134 Waynesboro 212.18462 3,139.3 218.56485 8490.7753 3602.4354

135 Williamsburg 2258.3926 6,148.2 254.11214 36.264328 491.77014 136 Winchester 20704.833 53,511.6 11329.05 11654.804 87996.101

Table 6.2 Productions in the year 2003 (Sample)

Another issue that needs to be addressed is that the production and attraction

equations are based on internal flow between 136 Virginia counties and cities. There are

41

no available data to determine the productions and attractions in the adjacent zones in

scenario 1 and external stations in scenario 2. To forecast the future I-I and E-I flow, it

was assumed that the future productions and attractions at these zones could be calculated

using the average growth rates of the 136 Virginia zones productions and attractions.

However, there are some “outliers” when using the freight production and

attraction equations (5). The production and attraction equations are based on regression

analysis of the 1998 TRANSEARCH database. When applying these equations to the

base year (1998), there are some result values that are not reasonable. For example, as

shown in Table 6.3, the freight attraction estimation of Region 8 (Augusta County) is –

29.78 tons in the base year, but the actual value should be 326,552 tons. This negative

value should be considered to be an outlier. Similarly, if the growth factor (which is

defined as the ratio of estimated value divided by the actual value in the base year) is

bigger than 2.0 or less than 0.5, the corresponding region is assumed to be an outlier. For

example, in Table 6.3, the estimated attraction is 10,019 tons for Campbell County, but

the actual value is 76,268 tons. The error is relatively unacceptable. The growth factor is

0.13. Therefore, this value is considered to be an outlier. In the forecasting step, these

regions will not be considered in the average growth factor calculation.

42

Region County Name Total Tons

Terminating (1998)

Estimated Tons Terminating

(1998)

Growth Factor Non-outlier

1 Accomack 34,760 17429.612 0.501431 0.501431 2 Albemarle 32,158 33341.065 1.0367965 1.0367965 3 Alleghany 1,315 2,617.5 1.9899064 1.9899064 4 Amelia 2,208 1,594.0 0.7220188 0.7220188 5 Amherst 39,103 22,602.9 0.5780312 0.5780312 6 Appomattox 3,749 4,642.7 1.2384736 1.2384736 7 Arlington 83,171 83,815.2 1.0077481 1.0077481 8 Augusta 326,522 -29,774.1 0 Out 9 Bath 291 536.2 1.8426315 1.8426315

10 Bedford 34,109 43,480.7 1.2747569 1.2747569 11 Bland 1,038 3,210.8 3.0932747 Out 12 Botetourt 15,749 20,563.9 1.3057657 1.3057657 13 Brunswick 5,864 5,091.8 0.8683286 0.8683286 14 Buchanan 18,610 20,970.6 1.1268578 1.1268578 15 Buckingham 4,295 3,810.7 0.8872877 0.8872877 16 Campbell 76,268 10,018.9 0.1313646 Out 17 Caroline 8,612 5,845.4 0.6787276 0.6787276 18 Carroll 10,127 8,519.1 0.8412292 0.8412292 19 Charles City 4,577 1,486.3 0.3247698 Out 20 Charlotte 3,151 3,054.2 0.9691759 0.9691759 21 Chesterfield 253,806 253,139.1 0.9973712 0.9973712 22 Clarke 4,408 3,072.6 0.6971174 0.6971174 23 Craig 0 618.8 0 Out 24 Culpeper 16,894 14,023.8 0.8301166 0.8301166

Table 6.3 STCC2900 Freight Attractions in 1998 (Example)

For the future year prediction, as shown in Table 6.4, the outliers in 1998 are

omitted. It was assumed that the commodity flow growth rate over a five-year period

would be less than 1000%. Therefore, if the growth factor is bigger than 10.0 or less than

0.1, the corresponding region is considered to be an outlier too. The final average growth

factor can be calculated from these non-outliers.

43

Region County Name Total Tons

Terminating (1998)

Estimated Tons Terminating

(2003)

Growth Factor Non-outlier

1 Accomack 34,760 17200.723 0.4948461 0.501431 2 Albemarle 32,158 76690.992 2.3848355 1.0367965 3 Alleghany 1,315 9,602.8 7.3002371 1.9899064 4 Amelia 2,208 1,302.9 0.590151 0.7220188 5 Amherst 39,103 23,460.4 0.5999594 0.5780312 6 Appomattox 3,749 1,398.4 0.3730345 1.2384736 7 Arlington 83,171 636,614.0 7.6542995 1.0077481 8 Augusta 326,522 366,643.8 Out Out 9 Bath 291 -127.6 0 1.8426315

10 Bedford 34,109 49,710.4 1.4573972 1.2747569 11 Bland 1,038 3,361.9 Out Out 12 Botetourt 15,749 22,189.7 1.4090005 1.3057657 13 Brunswick 5,864 1,306.8 0.2228568 0.8683286 14 Buchanan 18,610 22,761.4 1.2230851 1.1268578 15 Buckingham 4,295 3,557.9 0.8284202 0.8872877 16 Campbell 76,268 304,030.9 Out Out 17 Caroline 8,612 5,782.9 0.6714623 0.6787276 18 Carroll 10,127 5,983.2 0.5908202 0.8412292 19 Charles City 4,577 1,450.0 Out Out 20 Charlotte 3,151 2,300.6 0.7300392 0.9691759 21 Chesterfield 253,806 208,652.1 0.8220918 0.9973712 22 Clarke 4,408 2,244.1 0.5091591 0.6971174 23 Craig 0 386.7 Out Out 24 Culpeper 16,894 -229,877.1 0 0.8301166

Table 6.4 STCC2900 Growth Factors in 2003 (Example)

6.3 Forecasting Freight Flow Using The Gravity Model

Since the productions and attractions for each zone in scenario 1 and scenario 2 are

determined, the standard Gravity Model formula featuring the K-factor can be applied.

The I-I flow (Scenario 1) and E-I flow (Scenario 2) are forecasted. A sample of part of

the forecasted flow for Scenario 1 is showed in Table 6.5.

44

The prediction is based on the assumption that the friction factor and K-factor for

future years remain the same in a short period. In the freight generation step, there are

outliers using regression analysis equations. To calculate the average growth rate, some

assumptions have to be adopted. Nevertheless, the Gravity Model provides a way to

forecast future freight flow with the consideration of socio-economic effects. It presents a

reasonable solution for looking at trends of alternatives analysis.

Region 1 2 3 4 5 6 7 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 3 0 0 0.0 0 0 0 0 4 562.303 0 0.0 0 0 0 475.804 5 5.823 5 0.0 0.0504 0.768 0.0538 7.112 6 0 0 0.0 0 0 0 0 7 2858.757 2,369 0.0 12.116 262.194 0 2124.4678 0 0 0.0 0 0 0 0 9 0 0 0.0 0 0 0 0

10 0 0 0.0 0 0 0 0 11 0 0 0.0 0 0 0 0 12 83.127 187 0.0 1.276 20.709 4.263 169.364 13 0 0 0.0 0 0 0 0 14 25.334 18 0.0 0 0 0 17.566 15 0 0 0.0 0 0 0 0 16 0 0 0.0 0 0 0 0 17 0 0 0.0 0 0 0 0 18 0 0 0.0 0 0 0 0 19 0 0 0.0 0 0 0 0 20 0 0 0.0 0 0 0 0 21 628.569 859 0.0 6.227 77.555 5.486 783.785 22 0 0 0.0 0 0 0 0 23 0 0 0.0 0 0 0 0

Table 6.5 STCC 3200 I-I Flow Forecasting (Sample)

45

CHAPTER 7

Summary and Conclusions

7.1 Summary

The Gravity Model application for statewide freight flow distribution at a

commodity level was the focus of this research. In earlier studies, an inventory system

was established and key commodities in Virginia were found. Freight flow production

and attraction equations were developed for Virginia counties. The Gravity Model was

applied here in the distribution stage for the key commodities in order to add additional

data about the distribution of freight on Virginia’s highway network. Friction factors

were calibrated for both internal-internal and external-internal flows for truck freight at

the county level. Freight flow between Virginia and other external regions also was

distributed. Using the log-form of the gamma function, friction factors were calculated

with regression analysis and calibrated with Trip Length Distribution and Root Mean

Squared Error methods. The K-factor was introduced to adjust the flows and aid in the

predictive ability of the model. The model then was tested in the forecasting mode.

By forecasting the population data first, freight flow production and attraction

equations were applied with socio-economic factors to forecast future productions and

attractions. After the productions and attractions were determined for the year 2003, the

Gravity Model was successfully applied to forecast freight distribution.

7.2 Conclusion

46

1. The Gravity Model is appropriate to use for the truck freight distribution using

the commodity flow data. Previous studies by other researchers usually focused on

vehicle trips when applying the Gravity Model. This model was not applied before for

STCC two-digit level in statewide and between state and other regions. The calibration of

the Gravity Model needs observed flow data for each Origin-Destination pair. With the

detailed TRANSEARCH commodity flow data, observed flow matrices of each scenario

can be obtained and friction factors can be calibrated using the travel distance as the

impedance.

2.The K-factor plays an important role in Gravity Model calibration. In the

calibration, if the RMSE value between two iterations has a difference of less than 10%,

the iterations are considered to have converged. However, at the same time, the TLF

curves of observed and calculated flows do not fit well; therefore factors other than the

spatial distance should be considered. The K-factor is the zone-to-zone adjustment factor.

When K-factors are applied to Gravity Model equations, the calculated flow is adjusted

for each O-D pair. The final calculated average trip length and the calculated TLF better

fit with observed values.

7.3 Limitations and Recommendation

The Gravity Model was applied in this research only for the truck mode. In the

forecasting stage, friction factors and K factors were assumed to remain unchanged in the

future. Therefore, following these limitations, it is recommended that future research:

1. Develop K-factors that are associated with social-economic conditions.

47

K-factors were used in this research. However, the mechanism of the K-factor is

still not clear. The formula to calculate K-factors seems to have no direct relation to

socio-economic concepts. Future flow was predicted using the same K-factors from the

base year. The actual relationship between K-factors and time periods needs to be

addressed. GIS representations for social-economic conditions of each O-D pair might

assist in providing a close look at K-factors and the implementation of K-factors.

2. Apply the Gravity Model to other modes.

In this research only the truck mode is analyzed. There are key commodities that

are transported mainly by rail or water modes. Applying the Gravity Model to these

networks might be helpful.

3. Investigate freight flows in 4-digit STCC level

Commodities at the 2-digit STCC level group vary in terms of both weight and

value at the 4-digit STCC level. Showing the distribution of each commodity at the 4-

digit STCC level might show better results using the Gravity Model than the results

found at the 2-digit STCC level. Several important commodities in the key commodity

group can be investigated to verify accuracy.

4. Supplement commodity flow data to develop disaggregate flow dimensions.

With the directional distribution of flows, the commodity flow data can be

disaggregated to supplement the traffic count data. If empty truck trip data can be

obtained from weigh stations, the impact of truck freight flow on the statewide highway

network can be estimated more accurately because all truck trips would be accounted for

and not merely the loaded truck trips.

48

REFERENCES

1. Transportation Equity Act for the 21st Century. U.S. Public Law 105-178. 105th

Congress, Washington, D.C., 1998.

2. Intermodal Surface Transportation Efficiency Act of 1991. U.S. Public Law 102-

240. 102nd Congress, Washington, D.C., 1991.

3. U.S. Department of Transportation. Bureau of Transportation Statistics. 1997

Commodity Flow Survey. Washington, D.C., 1999.

4. Christopher J. Eatough, et al. A Methodology for Statewide Intermodal Freight

Transportation Planning. Report 99-R12, Virginia Transportation Research

Council, Charlottesville, VA 1998.

5. James J. Brogan. Application of a Statewide Intermodal Freight Planning

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6. U.S. Department of Transportation. Quick Response Freight Manual. USDOT,

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51

APPENDIX A

The Impedance Matrix Sample (STCC3200)

Region 1 2 3 4 5 6 7 1 16 N/A N/A N/A N/A N/A 183 2 N/A N/A N/A N/A N/A N/A N/A 3 339 107 N/A 162 78 103 223 4 201 N/A N/A N/A N/A N/A 136 5 284 52 N/A 93 9 31 160 6 258 N/A N/A N/A N/A N/A N/A 7 183 111 N/A 136 160 N/A 2 8 N/A N/A N/A N/A N/A N/A N/A 9 N/A N/A N/A N/A N/A N/A N/A 10 N/A N/A N/A N/A N/A N/A N/A 11 N/A N/A N/A N/A N/A N/A N/A 12 335 103 N/A 139 68 80 219 13 175 142 N/A 52 116 84 179 14 506 274 N/A N/A N/A N/A 390 15 N/A N/A N/A N/A N/A N/A N/A 16 N/A N/A N/A N/A N/A N/A N/A 17 202 104 N/A N/A N/A N/A 82 18 419 187 N/A 210 N/A N/A 303 19 N/A N/A N/A N/A N/A N/A N/A 20 N/A N/A N/A N/A N/A N/A N/A 21 183 90 N/A 24 103 82 127 22 N/A N/A N/A N/A N/A N/A N/A 23 N/A N/A N/A N/A N/A N/A N/A 24 N/A N/A N/A N/A N/A N/A N/A

STCC 3200 Impedance Matrix of Scenario 1 (Example) Unit: mile

52

Region 1 2 3 4 5 6 7 1 N/A N/A N/A N/A N/A N/A N/A 2 N/A N/A N/A N/A N/A N/A N/A 3 N/A N/A N/A N/A N/A N/A N/A 4 N/A N/A N/A N/A N/A N/A N/A

136 N/A N/A N/A N/A N/A N/A N/A E1 485 252 N/A 275 211 216 368 E2 419 187 N/A 208 146 150 302 E3 161 108 N/A N/A N/A N/A 110 E4 202 N/A N/A N/A N/A N/A N/A E5 155 136 N/A 84 151 119 177 E6 21 N/A N/A N/A N/A N/A N/A E7 181 134 N/A N/A 210 203 8 E8 267 137 175 N/A 158 206 76 E9 330 98 N/A 172 119 145 192 E10 364 132 25 194 102 127 247 E11 447 214 N/A N/A N/A 177 330


53

Region Virginia 169 170 171 172 173 174 Virginia 90 425 276 320 179 182 266

169 425 84 168 302 623 558 671 170 276 168 77 153 475 410 561 171 320 302 153 77 413 291 470 172 179 623 475 413 46 101 91 173 182 558 410 291 101 33 187 174 266 671 561 470 91 187 46 175 939 1333 1184 N/A 773 799 698 176 489 890 785 697 315 411 247 179 286 536 451 481 258 352 289 180 348 370 276 358 409 487 441 181 848 807 786 868 824 918 833 182 1328 1684 1583 1593 1177 1273 1109 184 276 599 451 332 106 65 163 185 306 221 184 315 534 466 547 186 192 508 422 452 276 370 308 187 553 238 288 434 748 680 773 188 1422 1826 1749 1687 1314 1410 1246 189 791 923 843 928 763 857 753 190 719 1089 940 821 554 555 479 191 564 1009 860 741 389 475 314 192 570 970 825 835 486 579 460 193 388 788 639 520 214 254 139


Region Virginia 194 195 196 197 198 199 200 Virginia 90 653 680 785 1393 1370 2072 2717

194 653 327 1386 1035 1662 2081 2368 3012 195 680 1386 300 600 965 759 1639 2286 196 785 1035 600 300 633 1113 1339 1984 197 1393 1662 965 633 317 864 901 1546 198 1370 2081 759 1113 864 380 1444 1851 199 2072 2368 1639 1339 901 1444 318 635 200 2717 3012 2286 1984 1546 1851 635 318


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