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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
II
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
Percent RMSE 141% 21%
Average Trip Length (mile) 264.9 242.0 265.7
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
Percent RMSE 143% 25%
Average Trip Length (mile) 426.2 547.7 420.4
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
Percent RMSE 114% 21%
Average Trip Length (mile) 571.2 604.1 563.5
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%)
(STCC2800) Percent RMSE 129% 27%
Electrical Machinery, Equipment or Supplies
Average Trip Length /Difference 102.9 102.8 (0.1%) 103.3 (0.4%)
(STCC3600) Percent RMSE 114% 13%
Food and Average Trip Length
/Difference 121.7 117.6 (3.3%) 119.3 (2%) Kindred Products
(STCC2000) Percent RMSE 126% 18%
Pulp, Paper or Allied Products
Average Trip Length /Difference 125.9 117.6 (6.6%) 126.7 (0.6%)
(STCC2600) Percent RMSE 134% 18%
Rubber or Miscellaneous Average Trip Length
/Difference 159 129.2 (19%) 160.4 (0.9%) Plastic Products
(STCC3000) Percent RMSE 128% 9%
Clay, Concrete, Glass or Average Trip Length
/Difference 131.1 128.2 (2.2%) 127.8 (2.5%) Stone Products
(STCC3200) Percent RMSE 102% 20%
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
Average Trip Length /Difference 138.9 130.5 (6%) 138.8 (0.1%)
(STCC2300) Percent RMSE 117% 10%
Tobacco Products, Average Trip Length
/Difference 134.9 129.7 (3.9%) 135.2 (0.2%) excluding Insecticides
(STCC2100) Percent RMSE 77% 2%
Printed Matter Average Trip Length
/Difference 81.7 87 (6.5%) 77.3 (5.4%) (STCC2700) Percent RMSE 131% 29%
Petroleum or Coal Products
Average Trip Length /Difference 110.6 123.8 (11.9%) 107.7 (2.6%)
(STCC2900) Percent RMSE 100% 34%
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
Commodity Measure Observed 5th Iteration K-factor adjusted
Transportation Equipment Average Trip Length
/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%
Electrical Machinery, Equipment or Supplies
Average Trip Length /Difference 224.3 210.8 (6%) 225.4 (0.5%)
(STCC3600) Percent RMSE 125% 22%
Food and Average Trip Length
/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%
Rubber or Miscellaneous Average Trip Length
/Difference 226.2 213.1 (5.8%) 227.3 (0.5%) Plastic Products (STCC3000) Percent RMSE 125% 13%
Clay, Concrete, Glass or Average Trip Length
/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
(STCC2400) Percent RMSE 115% 10%
Coal Average Trip Length
/Difference 196.9 185.6 (5.7%) 197.8 (0.5%) (STCC1100) Percent RMSE 35% 3%
Apparel or Other Finished Textile Products or Knits
Average Trip Length /Difference 233.2 214 (8.2%) 234.2 (0.4%)
(STCC2300) Percent RMSE 130% 27%
Tobacco Products, Average Trip Length
/Difference 248 232.8 (6.1%) 249.7 (0.7%) excluding Insecticides
(STCC2100) Percent RMSE 97% 18%
Printed Matter Average Trip Length
/Difference 230.3 217.8 (5.4%) 231.2 (0.4%) (STCC2700) Percent RMSE 138% 12%
Petroleum or Coal Products Average Trip Length
/Difference 201.6 192.5 (4.5%) 201.5 (0.05%) (STCC2900) Percent RMSE 78% 8%
Machinery, excluding 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%.
Commodity Measure Observed 5th Iteration K-factor adjusted
Transportation Equipment Average Trip Length
/Difference 429 367.1 (14.4%) 478.3 (11.5%) (STCC3700) Percent RMSE 138% 34%
Chemicals or Allied Products Average Trip Length
/Difference 348.2 333.3 (4.3%) 338.2 (2.9%) (STCC2800) Percent RMSE 135% 22%
Electrical Machinery, Equipment or Supplies
Average Trip Length /Difference 493.6 546 (10.6%) 486.2 (1.5%)
(STCC3600) Percent RMSE 140% 30%
Food and Average Trip Length
/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 273.2 274.1 (0.3%) 266.9 (2.3%) (STCC2600) Percent RMSE 152% 30%
Rubber or Miscellaneous Average Trip Length
/Difference 329.9 361.9 (9.7%) 330.9 (0.3%)
Plastic Products (STCC3000) Percent RMSE 142% 30%
Clay, Concrete, Glass or Average Trip Length
/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
(STCC2400) Percent RMSE 117% 32%
Coal Average Trip Length
/Difference 186.4 155.2 (16.7%) 192.6 (3.3%) (STCC1100) Percent RMSE 105% 37%
Apparel or Other Finished Textile Products or Knits
Average Trip Length /Difference 413.7 548.7 (32.6%) 387 (6.5%)
(STCC2300) Percent RMSE 135% 42%
Tobacco Products, Average Trip Length
/Difference 350.3 277.2 (20.9%) 348.9 (0.4%) excluding Insecticides
(STCC2100) Percent RMSE 130% 36%
35
Printed Matter Average Trip Length
/Difference 277.4 274.1 (1.2%) 282 (1.7%) (STCC2700) Percent RMSE 144% 28%
Petroleum or Coal Products Average Trip Length
/Difference 248.2 148.2 (40.3%) 246.4 (0.7%)
(STCC2900) Percent RMSE 113% 33%
Machinery, excluding Average Trip Length
/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.
Commodity Measure Observed 5th Iteration K-factor adjusted
Transportation Equipment Average Trip Length
/Difference 572.2 588 (2.8%) 589.3 (3%) (STCC3700) Percent RMSE 166% 16%
Chemicals or Allied Products
Average Trip Length /Difference 501.1 566.1 (13%) 502.2 (0.2%)
(STCC2800) Percent RMSE 126% 4%
Electrical Machinery, Equipment or Supplies
Average Trip Length /Difference 583.2 645.4 (10.7%) 566.3 (3%)
(STCC3600) Percent RMSE 130% 27%
36
Pulp, Paper or Allied Products
Average Trip Length /Difference 513.2 594.2 (16%) 512.8 (0.1%)
(STCC2600) Percent RMSE 123% 18%
Rubber or Miscellaneous Average Trip Length
/Difference 571.1 644.9 (12.9%) 566.4 (0.8%) Plastic Products
(STCC3000) Percent RMSE 99% 8%
Clay, Concrete, Glass or Average Trip Length
/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%
Tobacco Products, Average Trip Length
/Difference 206.6 190.9 (7.6%) 225 (8.9%) excluding Insecticides
(STCC2100) Percent RMSE 150% 17%
Printed Matter Average Trip Length
/Difference 444 517.8 (16.6%) 445.2 (0.3%) (STCC2700) Percent RMSE 129% 6%
Petroleum or Coal Products Average Trip Length
/Difference 372.2 386.7 (3.9%) 372.2 (0) (STCC2900) Percent RMSE 122% 0%
Machinery, excluding Average Trip Length
/Difference 571.2 604.1 (5.8%) 563.5 (1.3%) Electrical (STCC3500)
Percent RMSE 114% 21%
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
Methodology. M.S. Thesis. University of Virginia, 2001.
6. U.S. Department of Transportation. Quick Response Freight Manual. USDOT,
Washington, D.C., 1996.
7. Cambridge Systematics, Inc., et al. A Guidebook for Forecasting Freight
Transportation Demand. Report 388, National Cooperative Highway Research
Program. Transportation Research Board, Washington, D.C., 1997.
8. William A. Martin and Nancy A. McGuckin. Travel Estimation Techniques for
Urban Planning. Report 365, National Cooperative Highway Research Program.
Transportation Research Board, Washington, D.C., 1998.
9. Jose Holguin-Veras and Ellen Thorson. Trip Length Distribution in Commodity-
based and Trip-based Freight Demand Modeling: Investigation of Relationships.
49
Transportation Research Record 1707, TRB, National Research Council,
Washington, D.C., 2000, pp. 37-48.
10. Jose A. Sorratini and Robert L. Smith, Jr. Development of a Statewide Truck
Trip Forecasting Model Based on Commodity Flows and Input-Output
Coefficients. Transportation Research Record 1707, TRB, National Research
Council, Washington, D.C., 2000, pp. 49-55.
11. Michael Fischer, et al. External Urban Truck Trips Based on Commodity Flows:
A Model. Transportation Research Record 1707, TRB, National Research
Council, Washington, D.C., 2000, pp. 73-80.
12. Man-Bae Park and Robert L. Smith, Jr. Development of a Statewide Truck-Travel
Demand Model with Limited Origin-Destination Survey Data. Transportation
Research Record 1602, TRB, National Research Council, Washington, D.C.,
1997, pp. 14-21.
13. William R. Black. Commodity Flow Modeling. Transportation Research Circular.
Irvine, California, 1999, pp. 136-154.
14. Frederick W. Memmott. Application of Statewide Freight Demand Forecasting
Techniques. Report 260, National Cooperative Highway Research Program.
Transportation Research Board, Washington, D.C., 1983.
15. Michael D. Meyer and Eric J. Miller. Urban Transportation Planning, Second
Edition. McGraw-Hill Companies, Inc. 2001.
16. U.S. Department of Transportation, Federal Highway Administration. Calibrating
& Testing a Gravity Model for Any Size Urban Area. 1983.
50
17. Nicholas J. Garber and Lester A. Hoel. Traffic and Highway Engineering, Revised
2nd Edition. PWS Publishing, New York, 1999.
18. Radnor J. Paquette, et al. Transportation Engineering: Planning and Design. The
Ronald Press Company, New York, 1972.
19. Aruna Sivakumar and Chandra Bhat. A Fractional Split Distribution Model for
Statewide Commodity Flow Analysis. Paper #02-2142, TRB 2002 Annual
Meeting, Washington, D.C., 2002.
20. Kenneth Lawrence and Gary Kleinman. Development of a Freight Forecasting
Model to Forecast Truck Flow Between NJ Counties Themselves and Between NJ
Counties and Other States. Final Report on Contract Number NCTIP97-21. 2000
21. Earl R. Ruiter. Development of an Urban Truck Model for the Phoenix
Metropolitan Area. Final Report, Cambridge Systematics and O’ Neil Associates,
1992
22. Peter R. Stopher and Arnim H. Meyburg. Urban Transportation Modeling and
Planning. Lexington Books, D.C. Health and Company, 1975.
23. National Atlas website: http://nationalatlas.gov
24. Mapblast.com website: http://www.mapblast.com
25. Weldon-Cooper Center for Public Service: http://www.virginia.edu/coopercenter
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
STCC 3200 Impedance Matrix of Scenario 2 (Example) Unit: mile
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
STCC 3200 Impedance Matrix of Scenario 3 (Example) Unit: mile
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
STCC 3200 Impedance Matrix of Scenario 4 (Example) Unit: mile