CALIBRATION OF THE GRAVITY MODEL FOR TRUCK FREIGHT FLOW DISTRIBUTION

Research Report No. UVACTS-5-14-14 August 2002 CALIBRATION OF THE GRAVITY MODEL FOR TRUCK FREIGHT FLOW DISTRIBUTION by Shaohui Mao Dr. Michael J. Demetsky

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: sm2bk@virginia.edu Dr. Michael J. Demetsky Department of Civil Engineering Email: mjd@virginia.edu 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 http://cts.virginia.edu Center for Transportation Studies University of Virginia 351 McCormick Road, P.O. Box 400742 Charlottesville, 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 logform 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 List of Figures VII 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 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 21 st 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 socioeconomic 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 tripbased 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 trucktrip 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 fourdigit 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 socioeconomic 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: T ij P A i = n j= 1 j A j F ij F ij K K ij ij where T ij = flow from zone i to zone j P i = flow productions in zone i A j = flow attractions in zone j F ij = the friction factor relating to the spatial separation between zone i and zone j

14 K ij = 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 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). F ij b ij ct ij = at e (1) where t ij = The travel impedance, and a, b, c are coefficients. The log form of this function is a linear form. LnF ij = Lna + blnt ct (2) ij ij 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. F = T obs i+1 Fi (3) Ti where F = The friction factor for iteration i + 1 i+1 F i = The friction factor for iteration i T obs = The observed flow T i = 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 t ij is the impedance of O-D pair i j, 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 T ij 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. K ij = R ij 1 X 1 X ij ij R ij (4) where Rij = ratio of observed flows to the gravity model result for the flows from zone i to zone j. X ij = 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 1 st 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 5 th Iteration K-factor Adjusted Overall RMSE (ton) 2314 333.1 Percent RMSE 110% 16% (mile) 127.6 121.5 127.8 Difference of 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 5 th Iteration K-factor Adjusted Overall RMSE (ton) 1720.9 217.9 Percent RMSE 141% 21% (mile) 264.9 242.0 265.7 Difference of 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 5 th Iteration K-factor Adjusted Overall RMSE (ton) 28776.1 8597.1 Percent RMSE 143% 25% (mile) 426.2 547.7 420.4 Difference of Average Trip 28.5% 1.4% Length 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 5 th Iteration K-factor Adjusted Overall RMSE (ton) 124026 39577 Percent RMSE 114% 21% (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 /Difference 137.8 120.9 (12.2%) 137.5 (0.2%) (STCC3700) Chemicals or Allied Products Percent RMSE 119% 15% /Difference 131.1 120.9 (7.8%) 130.3 (0.6%) (STCC2800) Percent RMSE 129% 27% Electrical Machinery, Equipment or Supplies /Difference 102.9 102.8 (0.1%) 103.3 (0.4%) (STCC3600) Percent RMSE 114% 13% Food and /Difference 121.7 117.6 (3.3%) 119.3 (2%) Kindred Products (STCC2000) Percent RMSE 126% 18% Pulp, Paper or Allied Products /Difference 125.9 117.6 (6.6%) 126.7 (0.6%) (STCC2600) Percent RMSE 134% 18% Rubber or Miscellaneous /Difference 159 129.2 (19%) 160.4 (0.9%) Plastic Products (STCC3000) Percent RMSE 128% 9% Clay, Concrete, Glass or /Difference 131.1 128.2 (2.2%) 127.8 (2.5%) Stone Products (STCC3200) Percent RMSE 102% 20%

32 Lumber or Wood Products, /Difference 158.5 128.6 (19%) 160.5 (1.3%) excluding Furniture (STCC2400) Percent RMSE 115% 19% Coal /Difference 302.4 287.7 (4.9%) 303.2 (0.3%) (STCC1100) Percent RMSE 62% 27% Apparel or Other Finished Textile Products or Knits /Difference 138.9 130.5 (6%) 138.8 (0.1%) (STCC2300) Percent RMSE 117% 10% Tobacco Products, /Difference 134.9 129.7 (3.9%) 135.2 (0.2%) excluding Insecticides (STCC2100) Percent RMSE 77% 2% Printed Matter /Difference 81.7 87 (6.5%) 77.3 (5.4%) (STCC2700) Percent RMSE 131% 29% Petroleum or Coal Products /Difference 110.6 123.8 (11.9%) 107.7 (2.6%) (STCC2900) Percent RMSE 100% 34% Machinery, excluding /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 /Difference 257.1 244.6 (5.1%) 264 (2.7%) (STCC3700) Percent RMSE 129% 13% Chemicals or Allied Products /Difference 218.9 188.7 (13.8%) 224.1(2.3%) (STCC2800) Percent RMSE 126% 17% Electrical Machinery, Equipment or Supplies /Difference 224.3 210.8 (6%) 225.4 (0.5%) (STCC3600) Percent RMSE 125% 22% Food and /Difference 224.3 211.2 (5.8%) 225.7 (0.6%) Kindred Products (STCC2000) Percent RMSE 125% 12% Pulp, Paper or Allied Products /Difference 219.8 184.3 (16%) 230.2 (4.7%) (STCC2600) Percent RMSE 125% 26% Rubber or Miscellaneous /Difference 226.2 213.1 (5.8%) 227.3 (0.5%) Plastic Products (STCC3000) Percent RMSE 125% 13% Clay, Concrete, Glass or /Difference 218.2 189.7 (13%) 223.8(2.6%) Stone Products (STCC3200) Percent RMSE 131% 28% Lumber or Wood Products, /Difference 214.4 196.2 (8.5%) 215.2 (0.4%) excluding Furniture (STCC2400) Percent RMSE 115% 10% Coal /Difference 196.9 185.6 (5.7%) 197.8 (0.5%) (STCC1100) Percent RMSE 35% 3% Apparel or Other Finished Textile Products or Knits /Difference 233.2 214 (8.2%) 234.2 (0.4%) (STCC2300) Percent RMSE 130% 27% Tobacco Products, /Difference 248 232.8 (6.1%) 249.7 (0.7%) excluding Insecticides (STCC2100) Percent RMSE 97% 18% Printed Matter /Difference 230.3 217.8 (5.4%) 231.2 (0.4%) (STCC2700) Percent RMSE 138% 12% Petroleum or Coal Products /Difference 201.6 192.5 (4.5%) 201.5 (0.05%) (STCC2900) Percent RMSE 78% 8% Machinery, excluding /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 /Difference 429 367.1 (14.4%) 478.3 (11.5%) (STCC3700) Percent RMSE 138% 34% Chemicals or Allied Products /Difference 348.2 333.3 (4.3%) 338.2 (2.9%) (STCC2800) Percent RMSE 135% 22% Electrical Machinery, Equipment or Supplies /Difference 493.6 546 (10.6%) 486.2 (1.5%) (STCC3600) Percent RMSE 140% 30% Food and /Difference 198.3 166.3 (16%) 207.8 (4.8%) Kindred Products (STCC2000) Percent RMSE 138% 29% Pulp, Paper or Allied Products /Difference 273.2 274.1 (0.3%) 266.9 (2.3%) (STCC2600) Percent RMSE 152% 30% Rubber or Miscellaneous /Difference 329.9 361.9 (9.7%) 330.9 (0.3%) Plastic Products (STCC3000) Clay, Concrete, Glass or Percent RMSE 142% 30% /Difference 174.5 143 (18%) 176.2 (1%) Stone Products (STCC3200) Percent RMSE 131% 17% Lumber or Wood Products, /Difference 194.3 169.9 (12.6%) 197.9 (1.9%) excluding Furniture (STCC2400) Percent RMSE 117% 32% Coal /Difference 186.4 155.2 (16.7%) 192.6 (3.3%) (STCC1100) Percent RMSE 105% 37% Apparel or Other Finished Textile Products or Knits /Difference 413.7 548.7 (32.6%) 387 (6.5%) (STCC2300) Percent RMSE 135% 42% Tobacco Products, /Difference 350.3 277.2 (20.9%) 348.9 (0.4%) excluding Insecticides (STCC2100) Percent RMSE 130% 36%

35 Printed Matter /Difference 277.4 274.1 (1.2%) 282 (1.7%) (STCC2700) Percent RMSE 144% 28% Petroleum or Coal Products /Difference 248.2 148.2 (40.3%) 246.4 (0.7%) (STCC2900) Percent RMSE 113% 33% Machinery, excluding /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 /Difference 572.2 588 (2.8%) 589.3 (3%) (STCC3700) Percent RMSE 166% 16% Chemicals or Allied Products /Difference 501.1 566.1 (13%) 502.2 (0.2%) (STCC2800) Percent RMSE 126% 4% Electrical Machinery, Equipment or Supplies (STCC3600) /Difference 583.2 645.4 (10.7%) 566.3 (3%) Percent RMSE 130% 27%

36 Pulp, Paper or Allied Products /Difference 513.2 594.2 (16%) 512.8 (0.1%) (STCC2600) Percent RMSE 123% 18% Rubber or Miscellaneous /Difference 571.1 644.9 (12.9%) 566.4 (0.8%) Plastic Products (STCC3000) Percent RMSE 99% 8% Clay, Concrete, Glass or /Difference 330.4 363.5 (10%) 330.4 (0) Stone Products (STCC3200) Percent RMSE 163% 46% Apparel or Other Finished Textile /Difference 516 585.8 (13.5%) 510 (1.2%) Products or Knits (STCC2300) Percent RMSE 103% 15% Tobacco Products, /Difference 206.6 190.9 (7.6%) 225 (8.9%) excluding Insecticides (STCC2100) Percent RMSE 150% 17% Printed Matter /Difference 444 517.8 (16.6%) 445.2 (0.3%) (STCC2700) Percent RMSE 129% 6% Petroleum or Coal Products /Difference 372.2 386.7 (3.9%) 372.2 (0) (STCC2900) Percent RMSE 122% 0% Machinery, excluding /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) STCC STCC STCC STCC STCC Region County Name 3700 2800 3600 3500 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