U.S. imports of containerized freight have been growing at about 10% per year over the past decade and now exceed 18.5 million TEUs (twenty-foot equivalent units) per year. Container traffic is highly concentrated at a small number of ports, with approximately 88% of total containerized imports (measured in TEUs) entering through the 10 largest ports. Clearly, waterborne containerized imports are of vital economic concern to the United States. Given the growth rate of imports experienced at U.S. container ports, the concentration of traffic at a small number of sea ports, and the vulnerability of some of these seaports to natural hazards, it is important to have an accurate understanding of the flow of containers from their origin country through U.S. seaports to their final destination in the United States, so that investments in port capacity and other transportation infrastructure can be made consistent with the needs generated by this traffic. This paper develops an optimization model to synthesize the PIERS international trade data, the Carload Waybill data available from the Surface Transportation Board, and economic data into an estimate of an origin-destination table for the number of containers (measured in TEUs) that are shipped from foreign countries to aggregations of Bureau of Economic Analysis (BEA) economic areas in the United States. 

These waterborne containerized imports are worth over 30 trillion dollars in value and represent commodities such as furniture, electronics, machinery, toys and games, and beverages (Waterborne Databank, 2004). Clearly, these imports are of vital economic concern to the United States. Also, several container ports are in areas threatened by natural disasters. During the 1989 Loma Prieta earthquake in the San Francisco Bay Area, the Port of Oakland sustained significant damage from earthquake induced settlement and liquefaction resulting in damage to rail lines, cranes, and cracked wharf piles. Given the growth rate of imports experienced at U.S. container ports, the concentration of traffic at a small number of sea ports, and the vulnerability of some of these seaports to natural hazards, it is important to have an accurate understanding of the flow of containers from their origin country through U.S. seaports to their final destination in the United States, so that investments in port capacity and other transportation infrastructure can be made consistent with the needs generated by this traffic. 
This paper focuses on the estimation of the number of containers (measured in TEUs) 
that are shipped from foreign countries through international and U.S. ports to aggregations of Bureau of Economic Analysis (BEA) economic areas in the United 
States. BEA areas are geographic regions, denoted by a collection of counties, which represent centers of regional economic activity. There are 177 of these regions in the United States. While there is considerable data related to containerized shipments, no origin-destination table of this nature currently exists. To estimate the origindestination table, we have developed an optimization model that synthesizes data on international trade available from PIERS Global Intelligence Solutions and the Carload Waybill Sample of domestic railcar movements available from the Surface Transportation Board (STB) with a gravity model of the demand for the transportation of international sea containers. 
The next chapter focuses on the development of an optimization model to estimate an origin-destination model for containerized traffic. The third chapter describes the insights gained from the application of that model to U.S. waterborne containerized imports for 2004. The fourth chapter discusses conclusions and opportunities for future research. 
CHAPTER 2 

MODEL FORMULATION

We formulate the origin-destination table estimation problem as a linear program 
where the origins are one of 67 foreign countries and the destinations are aggregations of BEA economic areas which form 84 regions. As mentioned previously, we integrate two types of data into the optimization: the PIERS dataset on international trade from 2004 and the Carload Waybill sample of domestic railcar movements from 2003. We also integrate a gravity model into the mathematical formulation. The goal is to synthesize an origin-destination table that matches the datasets and the gravity model as closely as possible. 
Figure 3 presents a map of the 67 countries that are considered container origins and a graphical representation of the number of containers they export to the U.S. These 67 countries represent about 98% of the containers that entered the U.S. in 2004. In Figure 3, the container volumes for China and Hong Kong have been grouped together (though not in the model) and represent more than 39% and 7% of containers imported (as measured in TEU sea containers) in 2004, respectively. From this map, it is clear that the largest export countries can be grouped into three distinct regions: Asia, The 84 regions we refer to as Transportation Analysis Zones (TAZs) are illustrated in the number of loaded containers to be moved (over some defined period of time) can be summarized by a 67 x 84 table. For this analysis, we use the 2004 PIERS international trade-data, the 2003 STB Waybill, and economic data from 2004; hence, the estimated origin-destination table is for 2004. sample of rail traffic and therefore provides a detailed picture of rail movements over the rail network each year. Wolfe and Linde (1997) provide a useful description of the Waybill Sample and explain how it can be effectively used. However, the transportation of containers from a U.S. port p to a TAZ d can be either by truck or by rail, with rail substantially more likely as the distance from the port increases. 
Therefore, the Carload Waybill Sample provides a lower bound on the flow for these links. Again, we allow deviations in these flows where inconsistencies arise. It is also important to note that the STB Waybill does not explicitly identify the number of international containers transported. Rather, the STB Waybill identifies the number of carloads for STCC 46 transported from one county to another. This designation corresponds to mixed freight, which is used for intermodal shipments. Based on the origination county of these flows, we can attempt to infer which of these flows actually originated at a seaport. and Tacoma. These have also been incorporated into the estimates of the number of containers moved by rail from each of these ports given below. For the remainder of the ports, we have no data to indicate what the share of rail might be. However, the number of TEU container originations implied by the rail carload originations in these counties is less than the number of containers handled at the ports, so it is reasonable to assume that all of the rail carloads originate at the ports themselves. Wolfe and Linde (2007). This occurs when carloads are interchanged between two railroads and therefore two separate waybills are generated, one for each segment of the movement. Since there is no mechanism to identify the follow-on movement, rebilling leads to over estimates of the traffic that terminates at interchange points such as Chicago and Memphis. To account for the practice of rebilling in the model, we assume that for ports on the east coast, observations of TEU containers into the TAZs that include Chicago and Memphis really reflect the flow of TEU containers bound for those TAZs as well as TAZs to the west. Similarly, for ports on the west coast, observations of TEU container flows for the TAZs that include Chicago and Memphis are assumed to be bound for those TAZs as well the TAZs to the east. These assumptions are reasonable given both the practice of rebilling and the fact that shippers tend to minimize their shipping distance; therefore, the follow-on movement is likely in the same general direction. Before describing the model in more detail, we present the following sets and parameters. Let (i,j) be the set of all links where i is the origin node of the link and j is the destination node of the link. As mentioned, each node is a foreign country, a foreign port, a U.S. port, or a TAZ. Let r be an index over the set of all routes. Let p be an index over the set of all U.S. ports. Let p′ be an index over the set of all foreign ports. Let p′(r) be the set of all routes that use foreign port p′. Let r ij be the set of all routes that include link (i,j). Let p(r) be the set of all routes that include U.S. port p. 
Let R od be the set of all routes connecting origin o with destination d. 
The key decision variables in this model are the number of containers on route r, r f , where each route is a path from an origin country o, through a foreign port p′, to a U.S. 
port p, to a TAZ d. These route flows can then be translated into an origin destination table by summing the route flows which have the same origin country and destination TAZ. These variables are constrained to be non-negative. 
The PIERS international trade dataset gives the number of containers (in TEUs) that travel along each link from origin o to foreign port p′, t op' . The first term on the left hand side of equation ( 1 
= + + - + = = ∈ ∑ ' , p o ∀ (1) 
The PIERS dataset also gives the total number of containers (in TEUs) that are shipped from each foreign port p′ to each U.S. port p, p p l ' . The first term on the left hand side of equation ( 2) is the sum of the route flows that use both foreign port p′ and domestic port p. The next two terms are variables that represent the amount by which the route flows are lower or greater than that implied by the PIERS data p p l ' . + ' pp g is constrained to be non-negative and - p p g ' is constrained to be non-positive. Therefore constraint (2) attempts to identify route flows that are as consistent as possible with the number of containers (in TEUs) shipped from each foreign port to each U.S. port. k is constrained to be non-negative. 
p p p p pp p j p i r r r l g g f ij ' ' ' , | ' = + + - + = = ∈ ∑ p p , ' ∀ (2 
d p d p d j p i r r r n k f ij , | ≥ + + ∈ = ∈ ∑ , d p ∀ (5) 
For all TAZs, except the ones that include Chicago and Memphis, the observations in the STB Waybill pertain to a single destination TAZ. We do not write a lower limit for the TAZ that includes Chicago or the TAZ that includes Memphis separately from each port. Rather, if the port is on the west coast, we write a lower limit constraint that pertains to all TAZs to the east of the Mississippi River. If the port is on the east coast, we write a lower limit that pertains to all TAZs west of the Mississippi River plus the TAZs that include Chicago and Memphis. We compute this lower limit by summing the flows given in the Waybill from that particular port to each of the TAZs that the constraint pertains to. This allows the model to re-distribute the containers that the Waybill associates with Memphis and Chicago to other TAZs in the appropriate group from each port. 
We can also create upper bounds on the flows from the ports to some of the 
∀ ≤ + - ∈ = ∈ ∑ γ δ , | (6) 
where γ p is an inflation factor. The inflation factor can be used to represent the amount above the values in the STB Waybill for which deviations are considered acceptable. It can also be used to compensate for the growth that has occurred between the time period of the PIERS international trade data and the STB Waybill. 
We use the growth that occurred between 2003 and 2004 at each of the ports as estimated by the U.S. Maritime Administration (U.S. Maritime Administration, 2007). Thus, constraint (6) states that for each U.S. port p, the sum of the route flows to all destinations serviced only by rail must be at most the observation value in the STB waybill, increased by some inflation factor. 
In order to give the model additional guidance as to how to determine the route flows and therefore the origin-destination table, we can incorporate a gravity model into the mathematical formulation. Constraint ( 7) is a gravity model for the movement of seaborne containerized freight imports from origin country o to TAZ d. 
λ - = od d o o od d G G K B d o, ∀ (7) 
where 
B
- ∧ = od d o od d G K B d o, ∀ (8) 
This equation implies that the number of containers that flow from origin country o to destination TAZ d is proportional to both the GDP of the destination TAZ d and the distance from country o to TAZ d. These are reasonable assumptions for two reasons. 
First, much of what is transported in waterborne containers are retail goods and the consumption of these goods is reasonably assumed to be proportional to economic activity. Second, distance has a negative impact on the demand for transportation. It is also important to realize that the PIERS international trade data provides substantial information on the total number of TEUs imported from each country. Hence, there is substantial information on the sum of the B od variables for a given o. This information is integrated into the model through equation ( 1). Ashtakala andMurthy (1988 and1993) use a similar gravity model for land-based freight transportation and find that value of λ varies from 0.25 to 1.0 depending on the commodity. Ashtakala and Murthy (1988) also observe that higher exponent values are associated with the transportation of lower value goods. They reference two other studies that draw the same conclusion (Chisholm and O'Sullivan (1973) and Black (1971)). Since this model focuses on international waterborne shipments and the associated domestic land movement, it is unclear what an effective value of the exponent will be. One strategy to address this is to use different values for the exponent and select the one that appears to fit the data best; that is, generates the least amount of discrepancies with the data in the PIERS international trade dataset, the STB Waybill, and the resultant gravity model. 
Constraint (9) allows the model to select route flows that deviate from the gravity model given in equation ( 8). This is done by attempting to match the route flows from a given country o to a TAZ d to the gravity model estimate for the sum of those route flows, B od . Again, we include error terms to allow for deviations. + od q is a variable represents the amount by which the flows, r f , are smaller than that expected based on the gravity model and - od q is a variable that represents the amount by which the flows, r f , are larger than expected. 
+ od q is constrained to be non-negative and - od q is constrained to be non-positive. 
od od od R r r B q q f od = + + - + ∈ ∑ d o, ∀ (9) 
The goal of this formulation is to identify route flows for containerized international freight traffic that enters the U.S. through seaports which is as consistent as possible We include this term to encourage the use of shorter routes, when possible, because this will produce a more reasonable solution. We use the rail distance to compute the land portion of the route distance, because if substantial travel is required on land, it is more likely to be done by rail than by truck. 
( ) ( ) ( )+ - + - + - ∑ ∑ ∑ - + - + - + ' ' ' 2 ) , ' ( ) , ' ( ' ' 1 ' ' 0 p p p p p p p p p p p op op e e g g u u α α α ( ) ( ) r r r d o od od p p d p d p p p p D f q q y k h h ∑ ∑ ∑ ∑ ∑ + - + - + - - + - + - + β α α α α ) , ( 6 5 ~4 3 (10)
α o, α 1 , α 2, α 3, α 4, α 5 and α 6 are coefficients that reflect the relative importance of deviations from each set of constraints, and β is a per container mile penalty for travel distance. We penalize separately (1) deviations from expected total port container volumes at foreign ports and U.S. ports; (2) deviations from the observations of flows from individual foreign countries to individual foreign ports; and (3) deviations from the observations of flows from individual foreign ports to individual U.S. ports, because generally it is more important to match the total volumes at each port than it is to match the flows of containers between specific ports. It is also likely that the observations of total volumes at ports are more reliable than those on individual foreign port to U.S. port movements. By setting the coefficients α 3 and α 4 higher than α 0 and α 1, this can be achieved. Since the data that supports the first four terms is derived from the PIERS international trade data, and that data is internally consistent, the trade-off in the objective is really between the first four terms, the fifth and sixth which come from the 2003 STB Waybill, and the distance term. The distance term has the lowest penalty because it is simply used to choose between alternative optimal solutions. CHAPTER 3 

INSIGHTS FROM THE MODEL

This section focuses on the model results and insights that can be gained from the route flows and estimated origin-destination table. This origin-destination table is included in the appendix. When the exponent on the distance term in the gravity model (equation 8) is 1.2, the origin-destination table is consistent with both the 2004 PIERS international trade data for containerized imports and the gravity model. As mentioned previously, the STB Waybill indicates that more containers are destined for Chicago and Memphis then is likely to be correct, due to the practice of rebilling. 
A -L O N G B E A C H S E A T T L E -T A C O M A N E W Y O R K S A V A N N A H O A K L A N D N O R F O L K U.S.
We can use the model to infer the actual destinations for the containers that are labeled as destined for Chicago or Memphis in the STB Waybill. When doing this, it is important to understand that these flows are generally higher than those indicated by the 2003 STB Waybill because they include the growth that has occurred at these ports from 2003 to 2004 through Equation ( 6). Clearly, Asia is the dominant region. Perhaps the most interesting observations in this figure is how constant the balance is between the four regions of the world across the continental U.S. Certainly, there is a slight increase in the percentage from Asia in the west, Europe in the east, and Central & South America in the south and gulf coast, but these shifts are still quite minor. For example, the TAZs with the largest percentage share from Asia are in California, Seattle, Oregon, Montana, Utah and Idaho (percentages in the low eighties). Whereas the TAZs with the smallest percentage share from Asia (percentages in the low sixties and among the highest from Europe) are in Maine, Florida, Georgia, South Carolina, Massachusetts, Pennsylvania, etc. 
Imports from Central & South America are relatively larger in Florida, Georgia, South Carolina, and the Gulf Coast Region (percentages in the mid-teens). 

CHAPTER 4 CONCLUSIONS & FUTURE RESEARCH

This paper has created a method using optimization to synthesize information on U.S. international trade, the Carload Waybill from the Surface Transportation Board, and economic information to estimate an international origin-destination table for containerized imports. The estimated origin-destination table is consistent with the PIERS international trade data, a gravity model for the transportation of international sea containers based on economic data, and impedance computed from travel time, and is nearly consistent with the STB Carload Waybill. The exponent on the distance term in the gravity model was optimized to be as consistent as possible with data in the model. This yielded a value of 1.2 for that exponent, which is similar to values obtained in other studies. 
The primary limitation of the analysis described in this paper is the data quality. The PIERS international trade dataset is quite detailed and appears to be accurate, whereas the STB Carload Waybill has a few significant problems. First, there is no clear indication of which railcar flows actually originate or terminate at a port, and therefore the spatial distribution of the railcar flows from a port is unknown. We have inferred this based on the county that the waybill originated in and Leechman's estimate of rail share (2005). Second, for STCC 46, the STB Waybill does not appear to have accurate information on the number of containers; rather, it focuses on the number of railcars. We have estimated the number of containers from the number of railcars. 
Third, due to the practice of "rebilling," the STB Carload Waybill does not accurately capture true destinations of as much as 50% of the railcars we have associated with waterborne containerized imports. Finally, we have not integrated any information into the model pertaining to truck movements. There may be some opportunities to collect this data from the ports themselves. A few ports have focused on in-land transportation as part of defining their port development strategies. This research can be extended in a few different directions. First, it is possible that additional data could be developed to augment the optimization. This data could be improvements to the types of data already included, or it could be the identification of new datasets to complement the data included. Second, the gravity model could be refined. Currently, we focus on aggregate measures of economic activity, but there is the opportunity to create other gravity models that might, potentially, be more representative of the demand for the transportation of waterborne sea containers. 
Third, there are a large number of solutions to this optimization model which have very similar values for the objective function. It could be interesting and useful to understand the patterns that exist in these solutions and possibly to develop a representation for the origin-destination table that is probabilistic based on these solutions. Fourth, the PEIRS data contains substantial information about the movements of individual commodities which could be effectively used if it could be complemented with other data at the commodity level. That other data could be in the form of demand models at the commodity level or on the spatial demand for those commodities inside the U.S. Finally, it is also important to develop an origindestination table for U.S. exports through container seaports. This analysis should be readily adaptable to the development of this 

Figure 6 .

 6 Figure 1. Containers Imported from 1997 to 2006 Figure 2. Waterborne Containerized Imports from Select Countries Figure 3. Origin Countries Figure 4. Transportation Analysis Zones Figure 5. Sample Routes in the Network Figure 6. Flows from Selected Ports to TAZs based on 2003 STB Waybill Figure 7. Export Port Volumes from China Figure 8. U.S. Port Volumes from China Figure 9. Estimated Number of TEUs Imported from China to TAZs Figure 10. Flow of Containers from Key West Coast Ports to TAZs Figure 11. Flow of Containers from Key East Coast Ports to TAZs Figure 12. Inferred Flows from West Coast Ports through Chicago & Memphis Figure 13. Distribution of TEUs Across Regions of Origin for each TAZ 


Figure 4

 4 Figure 4 and cover the entire continental U.S. Each TAZ is composed of one or more BEA economic areas. The BEA economic areas are indicated by the dashed lines in the figure. For example, TAZ 152 is composed of BEA Economic areas 110 through 113. Since the countries are considered the origins and the TAZs are the destinations, 


Figure 4 .

 4 Figure 4. Transportation Analysis Zones. 


Figure 6 .

 6 Figure 6. Flows from the Port of LA/Long Beach and the Port of New York to each TAZ based on the 2003 STB Waybill 




  incorporates observations of container flows from the 2003 STB Waybill data. Each observation in the waybill applies to a group of links (i,j) starting from a U.S. port and ending at a TAZ or group of TAZs. The total freight shipped across those links must be at least as large as that implied by the 2003 STB Waybill data, d p n ~, where p is the port and d ~ is the set of TAZ destinations that the observation pertains to. The set d ~ may be composed of a single destination TAZ or a collection of destination TAZs. The observations in the STB Waybill are lower limits on the link flows for two reasons. First, the observations only include rail movements from the ports, and therefore exclude those shipped by truck. Second, we are using the 2003 STB Waybill rather than the 2004 dataset, and since containerized traffic has been growing at about 8% per year, we can expect that the 2004 values for the flows from the Waybill are generally greater than those in the 2003 (Intermodal Association of North America, 2007). The first term on the left hand side of Equation (5) is the sum of the route flows that use U.S. port p and terminate at a TAZ in the set d ~. The right hand side is the total number of TEU containers indicated by the 2003 STB Waybill that enter a port p and terminate at one of the TAZs in the set d ~. + pd k is a variable that represents the amount by which the flows, r f , are smaller than suggested by the STB Waybill. + pd 




  od is the number of containers (in TEUs) shipped from origin country o to TAZ d, G o is the GDP of origin country o (World Bank, 2007), G d is the earnings in TAZ d (U.S. Commerce, 2007), d od is the distance o to d and K o is a country specific variable (what is commonly referred to as a K-factor in the freight demand modeling literature). Equation (7) can be simplified because K o and o G can be grouped together, since they are constant for a particular origin. If we then assume that d od is the shortest route from o to d measured in travel time, and that λ is a constant, then λ od d is a constant for each origin-destination pair. The simplification is then given as equation (8) below, where o K ∧ and od B are the two decision variables, both of which are constrained to be non-negative. 




  λ 




  with: (1) observations of flows from each foreign origin country to each foreign port of export; (2) observations of flows from each foreign port to each US port; (3) the total freight leaving each foreign seaport that is destined for the U.S.; (4) the total freight entering each US port; (5) the number of containers shipped by rail from the largest U.S. seaports to each TAZ or group of TAZs; (6) for each port, the number of TEU containers destined for the TAZs that are served by rail only; (7) a gravity model between origin country o and TAZ d based on GDP for each foreign country, earnings for each TAZ and the distance between them. (1)-(4) is obtained from the 2004 PIERS international trade dataset and (5)-(6) is obtained from the 2003 STB Waybill.The objective is given in equation (10) below. The first term in the objective penalizes deviations from estimates of the number of containers that are exported from each foreign country through each foreign port. The second term penalizes deviations from the flows of containers from each foreign port to each U.S. port. The third term in the objective penalizes deviations from estimates of the number of containers that are exported from each foreign port to the U.S. The fourth term penalizes deviations from estimates of the number of containers that are imported through each U.S. port.The fifth term penalizes flows that are lower than that implied by the 2003 STB Waybill from each U.S. port to each TAZ or group of TAZs. The sixth term penalizes flows that are higher than that implied by the 2003 STB Waybill for the largest U.S. ports to each group of TAZs that are served by rail only. The seventh term penalizes deviations from the gravity model. The final term in the objective minimizes the total distance represented by all of the route flows where D r is the distance of the r th route. 




  However, there is one inconsistency with the observations in the 2003 STB Waybill that were used to generate lower bound constraints (equation 5), and one inconsistency with the observations in the 2003 STB Waybill that were used to generate upper bound constraints (equation 6). These discrepancies are given in Table 2. The only discrepancy of significant magnitude is that from the Port of Houston to Los Angeles. The estimated route flows from the model imply that about 190,000 TEU containers enter at the Port of Houston and are bound for the Los Angeles area. The 2003 STB Waybill implies there are about 347,000 TEU containers that are shipped from the Port of Houston to the Los Angeles area by rail. Hence, there is a discrepancy of about 157,000 TEU containers. The 347,000 TEU containers reported in the Waybill represents about 77% of all rail movements from the Port of Houston estimated from the 2003 STB Waybill. While there is no evidence to discount this observation in the Waybill, the magnitude of the observation is somewhat inconsistent with theTable 2. Discrepancies with the 2003 STB Waybill Constraint Error Houston -Los Angeles TAZ Lower Bound, Eqn (5) 157,000 Ports of LA & Long Beach to TAZs East of Mississippi Upper Bound, Eqn (6) -62,000 remainder of the traffic at the Port of Houston (which is more local in nature). The other discrepancy arises from a violation of the upper bound constraint. The 2003 STB Waybill and the growth rate at the ports of Los Angeles and Long Beach from 2003 to 2004 implies that about 1.8 million TEU containers travel from the ports of Los Angeles and Long Beach to all TAZ east of the Mississippi River, whereas the model estimates that this number is low by about 62,000 TEU containers. However, this represents an error of only about 3.5%. From the route flows and the estimated origin-destination table, the flow of TEU containers can be tracked through the network. If we consider the traffic originating abroad in China, about 95% of TEU containers exported from Mainland China are shipped through eight Mainland Chinese ports, the Port of Hong Kong, the Port in Busan, South Korea and through the Port of Kaohsiung, Taiwan. These ports and the TEU containers imported are illustrated in Figure 7. It is useful to notice the concentration of activity at the Shanghai and Hong Kong port areas. The region from Shanghai to Hong Kong is a special economic zone with substantial financial incentives spurring tremendous growth. Historically, Hong Kong has been the dominant port, second only to Singapore. However, with the rapid growth in this special economic zone in China, the ports of Yantian and Shanghai have attracted substantial traffic. Today Shanghai is the second largest port in the world next to Singapore (Asian Economic News, 2007), with Hong Kong third. Once TEU containers, originating in China, are exported through the collection of Asian ports mentioned above, the TEUs arrive at U.S. ports. Figure 8 gives the number of TEU containers imported from China through the six U.S. Ports with the highest volume. Together, these six ports represent about 94% of the total number of 


Figure

  Figure 7. Export Port Volumes (in TEU Containers) from China 




  Figure 8. Port Volumes (in TEU Containers) from China 


Figure 9 Figure 9 .

 99 Figure9gives an estimate of the number of TEU containers imported from China that are destined for each TAZ. Notice that the large economic areas in the U.S. attract a large number of TEUs. For example, there are almost 600,000 TEUs destined for the New York City TAZ from China. The model estimates that about 75% enters the U.S. through the Port of New York and about 25% through the Ports of Los Angeles and Long Beach. On the other hand, shipments from China headed to the TAZs near Savannah and Norfolk enter almost exclusively through these ports and are served via truck. However, these conclusions should be used with some caution. This formulation has significantly more decision variables than equations, and linear programs tend to produce solutions that have relatively small numbers of variables that take on positive values, thereby producing "lumpy solutions". Therefore, individual TAZs may be served by a larger number of ports than indicated in the solution, though there is a strong basis to believe that the ports indicated in the solution do provide significant service. 


Figure 11 Figure 10 .Figure 11 .

 111011 Figure11gives the estimated number of TEU containers (by truck and rail) destined for each TAZ from the Ports of New York, Charleston, Norfolk and Savannah. It is interesting to notice that the vast majority of the containers that enter the U.S. through these ports are destined for TAZs on the east coast. Very few containers travel west of the Mississippi River. This is in contrast to the ports on the West Coast, which service a large portion of the continental U.S. 


Figure 12 Figure 12 .Figure 13 .

 121213 Figure 12 shows the estimated TEU container flows from both the Ports of Seattle and Tacoma and the Ports of Los Angeles and Long Beach to TAZs east of the Mississippi River, and that were indicated as terminating at Chicago or Memphis in the STB Waybill. The model concludes that some of this traffic does indeed terminate at the TAZs that include Chicago and Memphis, but much of it is destined for other TAZs. For example, the 2003 STB Waybill indicates that from the Ports of Seattle and Tacoma, about 600,000 TEU containers are destined for the TAZ that includes Chicago and about 35,000 are destined for the TAZ that includes Memphis. The model indicates that much of this traffic is really destined for the Northeast U.S. with significant concentrations in New York City, Boston, and to a lesser extent, Michigan and Ohio. On the other hand, the 2003 STB Waybill indicates that from the Ports of Los Angeles and Long Beach about 1,090,000 TEUs are destined for the TAZ that includes Chicago and about 400,000 TEUs are destined for the TAZ that includes Memphis. The model indicates that, just like the Seattle ports, much of this traffic is really destined for other TAZs east of the Mississippi River. Given the larger role of Memphis, substantial traffic is estimated to be destined for TAZs in the South. 


Table 1 .

 1 Estimated Container Originations by Port 10 



Table 2 .

 2 Discrepancies in Model Results with 2003 STB Waybill United States through U.S. container ports (U.S. Maritime Administration, 2007). On average, containerized import volumes have been growing at about 10% per year over the last decade. Figure 1 gives the total number of containers (in TEUs) imported, as well as the number that entered through the 4 largest container ports from 1997 to 2006. In 2006, approximately 23% of containers entered through the port of Los 


	CHAPTER 1
	INTRODUCTION

Angeles, which has experienced a growth rate of about 14% per year over the last decade. The second largest container port is Long Beach, which handled about 20% of imported containers in 2006 and has been experiencing a growth rate of about 20% per year over the last decade. It is clear from the figure that container traffic is highly concentrated at a small number of ports. Almost 88% of total containerized imports (measured in TEUs) enter through the 10 largest ports. These ports are Los Angeles, Long Beach, New York, Charleston, Savannah, Norfolk, Oakland, Seattle, Tacoma, 


  .7 containers per railcar(Intermodal Association of North America, 2007), and that there are about 1.79 TEUs per container handled at these two ports(Pacific Maritime Association, 2007), we can infer that the total number of containers that originate in Los Angeles county is about 5.7 million TEU containers, of which about 2.7 million TEU containers originate at the ports.Table1gives estimates of the number of containers (measured in TEUs and rounded to the nearest thousand) moved by rail from 12 of the largest ports. Miami is not 


	They also estimate that another 5% of containers from these two ports are trans-loaded
	near the port into 53 foot containers for rail shipment. Therefore, we can infer that
	about 2.7 million TEU containers move by rail from the Ports of Los Angeles and
	Long Beach. Since the ports of Los Angeles and Long Beach are both in Los Angeles
	County, for the purposes of extracting flows of rail cars from the 2003 STB Waybill,

In 2003, approximately 6 million TEU containers were imported through the Ports of Los Angeles and Long Beach. Leechman (2005) estimates, based on 2004 data, that rail traffic has about a 40% share from the Ports of Los Angeles and Long Beach. these ports are considered together. According to the 2003 STB Waybill, 1,886,000 rail carloads of STCC 46 originated in Los Angeles County. Thus, if we assume that there are about 1included because the 2003 STB Waybill reports no rail carloads of STCC 46 originating in Miami-Dade County. It is not clear why this is the case, although the 2005 STB Waybill does have originations from Miami-Dade County. Leechman (2005) also provides estimates for the rail share from the Ports of Oakland, Seattle, 
Table 1 .

 1 Estimated Container Originations by Port 


	Port	Counties	TEU Containers
			Moved by Rail
	LA/Long Beach	Los Angeles	2,700,000
	Oakland	Alameda/Contra Costa/ San Joaquin	365,000
	Seattle/Tacoma	King/Peirce	864,000
	New York	Hudson, Union, Bergen, Essex	843,000
	Baltimore	Baltimore	101,000
	Norfolk	Norfolk, Portsmouth	296,000
	Charleston	Charleston	160,000
	Savannah	Savannah	140,000
	Port Everglades	Broward	66,000
	Houston	Harris	450,000



  TAZsfrom the 2003 STB Waybill. It is reasonable to assume that containers entering the U.S. through west coast ports would primarily move by rail if the destination TAZ is in the east. Similarly, it is reasonable to assume that containers entering the U.S. through east coast ports move primarily by rail if the destination is a TAZ is in the west. We use the Mississippi River as the geographic boundary of the East with the caveat that the TAZs that include Chicago and Memphis are assumed to be on the "rail only" side. For West Coast ports, this is consistent with the geographic boundary of the Mississippi. For East Coast ports, this assumes that the TAZs that include Chicago and Memphis are grouped with the TAZs to the West of the Mississippi River. 


	Let p x y f p p p r
	r	r ij	i	p	j	p

p δ be the set of all TAZs d that are considered to be serviced only by rail from U.S. port p. Let p x be the number of TEU containers that originate at port p and terminate at TAZs that are exclusively served by rail as given in the 2003 STB Waybill. - p y is a variable that indicates the amount by which the flows are larger than that suggested by the upper limits derived from the STB Waybill. - p y is constrained to be non-positive. 
table .

 . 
	VIETNAM	1,619		899			4,389	6,677	845	815	882
	O R I G I N ORIGIN ORIGIN ORIGIN ORIGIN ORIGIN ORIGIN ORIGIN ORIGIN ORIGIN	47 58 73 96 113 137 157 172		36 49 65 76 104 122 138 160 176	4	7 105 39 51 66 79 123 139 162 177	8 107 41 53 67 83 125 143 163 178	9 42 54 68 89 108 129 146 165 179	1 0 43 55 70 94 111 152 167 180	1 2 44 57 71 133 171 181
	AMER. SAMOA ORIGIN AMER. SAMOA AMER. SAMOA AMER. SAMOA AMER. SAMOA AMER. SAMOA AMER. SAMOA AMER. SAMOA AMER. SAMOA AMER. SAMOA	24 51 41 72 218 139 81 234 178		25 266 114 142 52 73 299 71 52 639	320	53 127 27 20 21 79 115 69 40 216 11	47 475 28 95 43 77 150 362 77 126 126	43 29 111 93 35 120 29 75 27 104 53	53 31 183 91 38 50 46 29 89 970	1,085 32 125 73 250 61 253 178
	ARGENTINA AMER. SAMOA ARGENTINA ARGENTINA ARGENTINA ARGENTINA ARGENTINA ARGENTINA ARGENTINA ARGENTINA ARGENTINA	21 323 261 441 1,171 850 402 1,096 583		2,468 1,789 22 756 940 318 397 1,716 385 229 2,210	397 141 82 136 513 761 603 389 200 858 39	343 672 52 282 499 2,733 876 1,962 379 456 434	305 77 784 594 222 692 164 411 131 398 191	363 61 1,343 556 238 285 264 135 303 3,610	8,274 44 882 462 1,551 285 818 671
	AUSTRALIA ARGENTINA AUSTRALIA AUSTRALIA AUSTRALIA AUSTRALIA AUSTRALIA AUSTRALIA AUSTRALIA AUSTRALIA AUSTRALIA	150 410 326 579 1,735 1,118 644 1,863 1,396		2,584 2,135 157 917 1,144 417 583 2,402 564 414 5,037	428 578 160 166 637 1,020 916 556 322 1,729 89	378 359 760 346 623 3,804 1,201 2,909 615 995 989	343 538 892 750 284 957 235 604 214 830 419	426 414 1,477 726 305 399 365 231 698 7,735	8,761 310 1,008 592 2,011 484 1,988 1,420
	AUSTRIA AUSTRALIA AUSTRIA AUSTRIA AUSTRIA AUSTRIA AUSTRIA AUSTRIA AUSTRIA AUSTRIA AUSTRIA	169 216 191 361 909 565 266 735 377		2,329 178 1,279 511 760 258 309 1,123 262 143 1,263	370 655 101 110 413 598 440 253 139 535 23	303 417 459 217 384 2,153 648 1,268 281 276 249	260 621 530 413 180 544 113 266 96 260 109	307 488 901 377 195 221 177 101 201 2,067	7,438 356 589 343 1,294 182 548 376
	BAHAMAS AUSTRIA BAHAMAS BAHAMAS BAHAMAS BAHAMAS BAHAMAS BAHAMAS BAHAMAS BAHAMAS BAHAMAS	120 109 61 81 210 266 77 179 65		119 640 261 184 67 72 449 79 38 254	483	84 459 55 27 109 164 115 91 35 131 4	70 277 314 80 117 538 188 444 65 53 51	60 405 318 155 49 132 34 91 20 53 24	73 305 564 143 50 52 59 21 37 458	1,957 229 335 107 295 56 95 85
	BANGLADESH BAHAMAS BANGLADESH BANGLADESH BANGLADESH BANGLADESH BANGLADESH BANGLADESH BANGLADESH BANGLADESH BANGLADESH	41 257 226 409 1,185 682 390 1,222 891		2,206 1,445 47 597 846 290 390 1,460 348 247 2,987	357 168 113 123 463 686 575 340 201 1,010 55	307 103 518 241 440 2,511 773 1,768 395 596 588	273 166 614 495 202 658 148 367 145 533 250	326 133 1,042 461 217 275 226 157 458 4,451	7,212 111 693 400 1,445 288 1,293 806
	BELGIUM BANGLADESH BELGIUM BELGIUM BELGIUM BELGIUM BELGIUM BELGIUM BELGIUM BELGIUM BELGIUM	128 820 732 1,376 3,421 2,145 997 2,767 1,401		8,735 130 4,883 1,960 2,932 976 1,163 4,255 992 538 4,688	1,386 492 389 425 1,563 2,261 1,653 955 526 2,004 85	1,156 306 1,753 827 1,453 8,125 2,443 4,792 1,062 1,025 926	991 449 2,018 1,569 680 2,051 426 1,005 363 969 407	1,165 343 3,465 1,442 737 833 668 379 746 7,729	28,461 254 2,241 1,295 4,899 689 2,039 1,405
	BRAZIL BELGIUM BRAZIL BRAZIL BRAZIL BRAZIL BRAZIL BRAZIL BRAZIL BRAZIL BRAZIL	2,062 1,090 463 2,584 1,915 3,016 7,882 6,683 2,762 7,191 3,191	18,734 14,488 457 6,122 6,718 2,243 2,683 12,902 2,709 1,506 12,130	3,000 1,777 1,156 974 3,596 5,429 4,139 2,842 1,343 5,464 212	2,520 1,071 5,787 2,170 3,639 18,887 6,214 14,183 2,512 2,524 2,395	2,220 1,565 6,517 4,471 1,596 4,750 1,157 2,973 838 2,412 1,082	2,629 1,177 11,236 4,161 1,664 1,923 1,901 1,345 860 1,780 20,726	64,640 885 7,237 3,387 10,752 1,809 1,972 4,650 3,780
	CAMBODIA BRAZIL CAMBODIA CAMBODIA CAMBODIA CAMBODIA CAMBODIA CAMBODIA CAMBODIA CAMBODIA CAMBODIA	1,157 121 101 186 573 328 188 595 447		841 1,239 633 270 367 134 188 702 166 120 1,483	139 4,546 48 53 205 318 276 163 97 495 27	122 2,741 225 103 197 1,202 370 849 191 295 291	110 4,182 265 229 90 315 71 177 70 262 124	137 3,269 439 216 98 133 108 76 228 2,201	2,848 2,511 299 183 645 140 649 397
	CANADA CAMBODIA CANADA CANADA CANADA CANADA CANADA CANADA CANADA CANADA CANADA	52 58 46 94 393 164 105 555 2,163		351 2,034 53 273 121 175 70 115 367 82 75	59 198 20 25 99 164 153 79 59 359 49	52 125 97 45 95 667 193 446 125 329 386	47 185 109 109 45 184 37 85 54 339 149	62 145 172 99 49 80 49 70 1,015 2,182	1,265 106 122 90 319 84 13,198 392
	CHILE CANADA CHILE CHILE CHILE CHILE CHILE CHILE CHILE CHILE CHILE	22 1,025 715 1,160 3,161 2,775 1,193 3,110 1,669		5,083 5,135 21 2,233 2,361 848 1,108 5,465 1,164 656 6,619	863 367 83 342 1,358 2,171 1,702 1,200 583 2,430 115	741 1,827 52 780 1,349 7,676 2,593 6,004 1,067 1,367 1,297	677 75 2,218 1,710 600 1,907 484 1,259 356 1,142 584	856 61 3,670 1,715 629 775 784 351 823 11,241	18,140 43 2,600 1,296 3,995 850 2,323 2,140
	CHINA MNLND CHILE CHINA MNLND CHINA MNLND CHINA MNLND CHINA MNLND CHINA MNLND CHINA MNLND CHINA MNLND CHINA MNLND CHINA MNLND	19,289 9,445 369 25,877 21,292 39,680 125,314 70,337 40,932 132,869 107,188	175,451 133,974 395 57,382 77,988 28,519 40,822 151,431 35,619 26,418 345,930	28,982 1,442 9,986 11,303 43,448 67,734 59,836 35,017 21,110 111,069 6,366	25,441 926 47,671 21,522 41,807 259,223 79,375 183,626 41,986 67,664 67,872	23,196 1,400 55,814 48,441 19,167 68,345 15,213 38,122 15,536 60,384 28,678	28,809 1,110 91,747 45,783 20,773 28,704 22,932 16,772 17,005 54,195 501,242	598,111 806 62,733 38,868 137,523 5,728 19,195 31,007 20,505 156,365 91,175
	CHINA TWN CHINA MNLND CHINA TWN CHINA TWN CHINA TWN CHINA TWN CHINA TWN CHINA TWN CHINA TWN CHINA TWN CHINA TWN	1,897 10,801 2,545 2,094 3,903 12,327 6,919 4,026 13,070 10,544	17,259 11,078 13,179 5,644 7,671 2,805 4,016 14,896 3,504 2,599 34,028	2,851 41,470 982 1,112 4,274 6,663 5,886 3,445 2,077 10,925 626	2,503 25,966 4,689 2,117 4,112 25,499 7,808 18,063 4,130 6,656 6,676	2,282 38,769 5,490 4,765 1,885 6,723 1,496 3,750 1,528 5,940 2,821	2,834 30,343 9,025 4,504 2,043 2,824 2,256 1,650 1,673 5,331 49,305	58,834 22,214 6,171 3,823 13,528 1,888 3,050 2,017 15,381 8,969
	COLOMBIA CHINA TWN COLOMBIA COLOMBIA COLOMBIA COLOMBIA COLOMBIA COLOMBIA COLOMBIA COLOMBIA COLOMBIA	1,062 575 365 506 1,323 1,504 506 1,230 461		2,901 1,090 3,304 1,396 1,121 406 453 2,780 508 262 1,885	500 4,079 275 162 656 990 714 578 237 907 32	417 2,554 1,508 448 688 3,314 1,172 2,838 419 385 369	357 3,814 1,569 888 295 819 215 595 134 371 167	432 2,985 2,746 852 301 326 364 134 264 3,265	11,243 2,185 1,694 645 1,823 372 676 635
	COSTA RICA COLOMBIA COSTA RICA COSTA RICA COSTA RICA COSTA RICA COSTA RICA COSTA RICA COSTA RICA COSTA RICA COSTA RICA	226 1,085 604 808 2,083 2,641 761 1,778 643		4,804 254 6,357 2,594 1,827 667 715 4,458 789 381 2,524	839 904 546 265 1,081 1,632 1,140 905 352 1,297 43	691 571 3,121 798 1,159 5,345 1,868 4,411 644 531 504	596 899 3,161 1,545 491 1,308 341 905 201 526 234	722 711 5,604 1,417 495 516 584 204 370 4,547	19,443 573 3,332 1,068 2,931 553 944 847
	CZECH REP COSTA RICA CZECH REP CZECH REP CZECH REP CZECH REP CZECH REP CZECH REP CZECH REP CZECH REP CZECH REP	411 91 80 152 382 237 112 309 158		464 538 215 320 108 130 472 110 60 531		979	156 1,672 42 46 174 252 185 106 59 225 10	127 1,026 193 91 162 905 273 533 118 116 105	110 1,652 223 174 76 229 48 112 40 109 46	129 1,317 379 159 82 93 74 42 84 869	3,128 1,102 248 144 544 76 231 158
	DENMARK CZECH REP DENMARK DENMARK DENMARK DENMARK DENMARK DENMARK DENMARK DENMARK DENMARK	50 195 173 327 817 508 240 667 340		2,083 1,139 50 455 688 232 278 1,018 238 130 1,141	334 193 91 100 371 538 396 227 126 482 21	272 117 412 193 345 1,935 583 1,142 254 249 225	233 170 476 369 161 489 102 239 87 235 98	275 128 810 337 175 199 158 91 181 1,867	6,656 96 529 308 1,162 165 495 339
	DOM. REP DENMARK DOM. REP DOM. REP DOM. REP DOM. REP DOM. REP DOM. REP DOM. REP DOM. REP DOM. REP	106 514 318 435 1,133 1,277 409 995 377		2,872 2,967 106 1,253 1,057 352 388 2,249 425 209 1,466	490 412 256 153 568 858 613 468 192 734 25	405 247 1,389 395 599 2,902 999 2,295 353 305 289	344 364 1,423 779 256 715 183 481 112 300 134	408 274 2,576 733 261 284 305 114 213 2,612	11,231 204 1,529 563 1,570 296 552 480
	ECUADOR DOM. REP ECUADOR ECUADOR ECUADOR ECUADOR ECUADOR ECUADOR ECUADOR ECUADOR ECUADOR	218 615 385 614 1,659 1,672 643 1,639 829		2,606 243 2,925 1,304 1,254 454 589 3,149 646 344 3,392	447 880 206 182 728 1,187 913 683 313 1,240 57	378 517 1,041 435 732 4,095 1,440 3,390 564 686 663	350 819 1,268 959 324 1,005 267 711 184 568 300	448 633 2,102 986 337 405 437 178 402 5,843	9,518 514 1,525 713 2,106 466 1,144 1,132
	EGYPT ECUADOR EGYPT EGYPT EGYPT EGYPT EGYPT EGYPT EGYPT EGYPT EGYPT	200 109 96 176 452 286 137 383 204		1,026 216 627 254 368 124 153 576 134 77 691	166 784 49 53 199 291 222 131 72 290 12	140 506 226 105 187 1,054 320 659 143 150 136	122 773 264 207 87 268 57 138 50 140 60	145 618 449 191 93 110 90 52 109 1,136	3,356 447 295 168 622 96 295 206
	EL SALVADOR EGYPT EL SALVADOR EL SALVADOR EL SALVADOR EL SALVADOR EL SALVADOR EL SALVADOR EL SALVADOR EL SALVADOR EL SALVADOR	57 290 184 290 783 789 307 781 567		1,230 1,399 57 616 592 214 278 1,507 305 193 2,462	211 220 97 86 344 560 431 322 148 882 40	180 134 498 205 345 1,954 680 1,600 266 492 480	165 197 607 453 153 479 126 335 87 395 221	211 149 992 465 159 193 206 84 267 4,440	4,492 112 720 337 994 225 771 893
	FINLAND EL SALVADOR FINLAND FINLAND FINLAND FINLAND FINLAND FINLAND FINLAND FINLAND FINLAND	94 141 125 234 594 371 178 494 257		1,452 102 817 331 491 166 202 743 174 97 868	232 370 65 71 266 387 291 168 93 361 16	190 239 295 138 248 1,396 422 844 186 189 171	165 365 344 268 116 356 75 176 64 177 75	196 292 586 247 126 145 116 67 137 1,409	4,622 211 384 223 837 122 375 257
	FRANCE FINLAND FRANCE FRANCE FRANCE FRANCE FRANCE FRANCE FRANCE FRANCE FRANCE	1,034 1,418 76 850 753 3,512 2,204 1,020 2,828 1,426	9,077 5,034 76 2,017 3,026 1,005 1,195 4,366 1,017 553 4,793	1,454 292 402 439 1,610 2,327 1,695 978 539 2,043 86	1,198 177 1,807 853 1,496 8,357 2,511 4,909 1,089 1,043 941	1,025 259 2,079 1,613 701 2,108 437 1,029 372 993 414	1,216 196 3,569 1,481 759 855 685 388 764 7,867	29,566 147 2,307 1,332 5,051 705 2,076 1,430
	GERMANY FRANCE GERMANY GERMANY GERMANY GERMANY GERMANY GERMANY GERMANY GERMANY GERMANY	2,630 1,009 479 2,164 1,916 3,622 9,120 5,667 2,670 7,376 3,783	23,375 472 12,838 5,124 7,630 2,588 3,101 11,275 2,634 1,438 12,673	3,713 1,838 1,012 1,106 4,145 6,006 4,412 2,534 1,398 5,366 229	3,043 1,106 4,606 2,173 3,859 21,610 6,506 12,729 2,818 2,768 2,502	2,614 1,615 5,316 4,147 1,804 5,459 1,138 2,669 966 2,613 1,095	3,078 1,213 9,047 3,785 1,953 2,219 1,773 1,223 1,014 2,013 20,749	74,659 913 5,910 3,443 12,990 1,558 1,823 5,504 3,771
	GREECE GERMANY GREECE GREECE GREECE GREECE GREECE GREECE GREECE GREECE GREECE	1,200 98 86 158 407 258 122 340 180		945 1,198 566 228 335 113 137 518 119 68 606	151 4,607 45 49 180 263 198 117 64 255 11	127 2,785 204 95 169 946 287 591 127 131 120	111 4,069 239 185 78 242 51 123 44 123 53	131 3,065 404 171 85 99 81 46 95 999	3,064 2,302 267 152 564 86 261 182
	GUATEMALA GREECE GUATEMALA GUATEMALA GUATEMALA GUATEMALA GUATEMALA GUATEMALA GUATEMALA GUATEMALA GUATEMALA	52 946 604 954 2,577 2,571 1,008 2,705 1,947		4,055 4,574 52 2,011 1,946 704 914 4,922 1,000 663 8,497	695 200 318 282 1,130 1,839 1,416 1,054 485 3,039 138	594 122 1,627 673 1,134 6,418 2,228 5,239 876 1,720 1,655	544 178 1,983 1,483 502 1,576 413 1,098 286 1,357 765	696 135 3,246 1,522 522 636 676 278 917 15,376	14,788 101 2,351 1,104 3,271 774 2,646 3,103
	HAITI GUATEMALA HAITI HAITI HAITI HAITI HAITI HAITI HAITI HAITI HAITI	310 88 49 66 169 214 62 144 52		335 516 211 148 54 58 362 64 31 205		390	68 1,215 44 22 88 133 93 74 29 105 4	56 784 253 65 94 434 152 358 52 43 41	48 1,196 257 125 40 106 28 73 16 43 19	59 957 455 115 40 42 47 17 30 369	1,579 692 271 87 238 45 77 69
	HONDURAS HAITI HONDURAS HONDURAS HONDURAS HONDURAS HONDURAS HONDURAS HONDURAS HONDURAS HONDURAS	33 1,043 666 1,052 2,843 2,837 1,112 2,984 2,148		4,473 5,046 38 2,218 2,147 777 1,008 5,430 1,103 732 9,374	767 136 351 311 1,246 2,029 1,562 1,163 535 3,353 152	655 1,795 83 742 1,251 7,081 2,458 5,780 966 1,898 1,825	600 134 2,188 1,636 554 1,738 456 1,212 315 1,497 844	768 107 3,581 1,679 576 702 746 306 1,011 16,963	16,314 89 2,594 1,218 3,608 854 2,919 3,423
	HONG KONG HONDURAS HONG KONG HONG KONG HONG KONG HONG KONG HONG KONG HONG KONG HONG KONG HONG KONG HONG KONG	3,668 1,783 342 4,848 4,030 7,481 23,400 13,221 7,660 24,614 19,347	33,332 25,215 369 10,833 14,734 5,371 7,646 28,419 6,700 4,913 63,018	5,503 1,340 1,892 2,136 8,209 12,765 11,220 6,579 3,949 20,533 1,160	4,830 865 8,972 4,079 7,899 48,491 14,931 34,419 7,830 12,404 12,372	4,400 1,319 10,527 9,149 3,617 12,821 2,860 7,151 2,892 11,076 5,238	5,454 1,055 17,419 8,644 3,918 5,380 4,308 3,145 3,152 9,825 91,997	113,342 764 11,892 7,338 25,945 1,072 3,619 5,736 3,752 28,181 16,714
	ICELAND HONG KONG ICELAND ICELAND ICELAND ICELAND ICELAND ICELAND ICELAND ICELAND ICELAND	2,051 19 18 35 83 49 24 65 32		237 2,105 113 45 74 24 28 97 24 12 106	38 7,874 9 11 39 56 40 21 12 45 2	31 4,933 41 20 36 201 60 110 25 23 21	26 7,329 47 38 17 50 10 23 9 22 9	30 5,754 80 34 19 20 16 9 17 169	770 4,195 52 32 123 15 46 30
	INDIA ICELAND INDIA INDIA INDIA INDIA INDIA INDIA INDIA INDIA INDIA	1,309 1,333 11 1,171 2,126 5,638 3,518 1,768 5,058 3,686	11,651 7,532 11 3,095 4,418 1,507 1,910 7,233 1,693 1,021 12,357	1,892 589 44 640 2,403 3,556 2,788 1,653 917 4,180 227	1,618 2,702 26 1,259 2,276 12,953 3,962 8,388 1,805 2,475 2,430	1,426 38 3,197 2,554 1,050 3,324 722 1,752 635 2,205 1,034	1,711 28 5,420 2,376 1,132 1,367 1,144 663 1,894 18,416	38,204 21 3,598 2,064 7,528 1,239 5,347 3,335
	INDONESIA INDIA INDONESIA INDONESIA INDONESIA INDONESIA INDONESIA INDONESIA INDONESIA INDONESIA INDONESIA	673 1,273 1,045 1,926 5,921 3,449 1,983 6,140 4,616		8,764 682 6,642 2,847 3,808 1,380 1,938 7,394 1,750 1,259 15,554	1,435 2,583 500 552 2,122 3,284 2,861 1,715 1,002 5,212 282	1,260 1,598 2,372 1,079 2,042 12,416 3,828 8,937 1,976 3,093 3,057	1,146 2,346 2,792 2,363 933 3,259 732 1,859 728 2,716 1,298	1,415 1,790 4,622 2,263 1,009 1,371 1,132 787 2,351 23,083	29,460 1,327 3,147 1,894 6,665 1,470 6,674 4,186
	IRELAND INDONESIA IRELAND IRELAND IRELAND IRELAND IRELAND IRELAND IRELAND IRELAND IRELAND	533 110 99 185 460 287 133 365 184		559 664 263 400 133 155 566 132 71 613	1,217	192 2,061 53 58 212 306 222 127 70 261 11	158 1,310 239 113 197 1,089 329 640 141 134 121	136 1,951 271 212 92 277 57 132 48 127 53	160 1,523 462 192 100 112 89 51 98 1,002	3,914 1,115 301 175 667 90 268 183
	ISRAEL IRELAND ISRAEL ISRAEL ISRAEL ISRAEL ISRAEL ISRAEL ISRAEL ISRAEL ISRAEL	63 431 377 692 1,786 1,128 541 1,520 811		4,018 2,470 62 1,002 1,449 490 606 2,291 528 306 2,756	649 244 195 210 783 1,149 877 518 284 1,151 50	548 145 890 414 736 4,161 1,264 2,608 564 596 544	478 214 1,038 816 341 1,058 226 547 196 557 240	570 160 1,767 755 368 435 357 205 432 4,526	13,143 120 1,162 663 2,464 381 1,177 821
	ITALY ISRAEL ITALY ITALY ITALY ITALY ITALY ITALY ITALY ITALY ITALY	2,423 2,181 224 1,904 3,524 8,981 5,723 2,665 7,395 3,858	21,570 12,651 226 5,116 7,499 2,516 3,030 11,444 2,613 1,483 12,971	3,442 865 1,003 1,087 4,024 5,859 4,361 2,581 1,393 5,524 235	2,873 526 4,570 2,122 3,761 20,990 6,386 12,980 2,794 2,822 2,561	2,503 776 5,334 4,102 1,751 5,353 1,127 2,704 963 2,653 1,136	2,957 588 9,012 3,781 1,894 2,181 1,780 1,240 1,010 2,051 21,481	69,810 439 5,943 3,368 12,600 1,578 1,869 5,607 3,921
	IVORY COAST ITALY IVORY COAST IVORY COAST IVORY COAST IVORY COAST IVORY COAST IVORY COAST IVORY COAST IVORY COAST IVORY COAST	1,171 43 35 62 161 113 52 140 71		372 1,165 242 101 134 45 54 227 50 29 255	59 4,498 19 19 72 104 79 51 26 109 5	51 2,732 91 39 69 376 114 255 50 53 50	44 3,996 105 79 31 96 21 54 17 50 22	52 3,018 181 73 34 39 34 18 38 425	1,225 2,260 118 61 223 37 103 77
	JAMAICA IVORY COAST JAMAICA JAMAICA JAMAICA JAMAICA JAMAICA JAMAICA JAMAICA JAMAICA JAMAICA	21 81 45 61 156 198 57 134 48		22 477 195 137 50 54 335 59 29 190		361	63 123 83 41 20 81 86 68 26 97 3	52 234 50 60 87 401 140 331 48 40 38	45 75 237 116 37 98 26 68 15 39 18	54 57 421 106 37 39 44 15 28 341	1,460 43 250 80 220 42 71 64
	JAPAN JAMAICA JAPAN JAPAN JAPAN JAPAN JAPAN JAPAN JAPAN JAPAN JAPAN	2,392 1,179 31 3,276 2,665 5,005 16,115 8,926 5,241 17,371 14,822	21,798 16,817 35 7,218 9,796 3,605 5,218 19,277 4,513 3,426 46,872	3,605 126 1,248 1,420 5,457 8,550 7,630 4,447 2,705 14,584 861	3,165 5,984 77 2,687 5,251 32,921 10,057 23,433 5,414 9,044 9,183	2,891 124 6,978 6,089 2,413 8,707 1,931 4,857 2,011 8,061 3,864	3,623 99 11,413 5,759 2,618 3,663 2,889 2,120 2,235 7,421 66,827	74,680 83 7,828 4,889 17,323 2,421 4,025 2,751 21,696 12,187
	MALAYSIA JAPAN MALAYSIA MALAYSIA MALAYSIA MALAYSIA MALAYSIA MALAYSIA MALAYSIA MALAYSIA MALAYSIA	1,344 1,134 949 1,748 5,366 3,071 1,764 5,557 4,161		8,684 1,376 5,947 2,539 3,458 1,252 1,764 6,581 1,565 1,122 13,846	1,412 5,158 446 501 1,927 2,981 2,594 1,533 909 4,617 254	1,214 3,226 2,116 966 1,854 11,306 3,474 7,982 1,791 2,745 2,722	1,074 4,825 2,493 2,146 847 2,967 664 1,655 659 2,454 1,151	1,290 3,784 4,130 2,026 916 1,243 1,013 712 2,130 20,494	28,497 2,770 2,810 1,720 6,072 1,310 6,044 3,715
	MEXICO MALAYSIA MEXICO MEXICO MEXICO MEXICO MEXICO MEXICO MEXICO MEXICO MEXICO	505 303 122 177 465 848 258 553 173		722 515 1,163 560 365 136 181 1,957 259 120 702	128 1,938 84 53 220 384 326 358 114 395 12	105 1,203 456 151 229 1,271 493 1,637 192 146 139	93 1,773 548 342 99 293 96 355 55 146 66	125 1,361 847 392 101 115 183 49 101 1,313	2,862 1,003 693 236 599 196 254 243
	NETHERLANDS MEXICO NETHERLANDS NETHERLANDS NETHERLANDS NETHERLANDS NETHERLANDS NETHERLANDS NETHERLANDS NETHERLANDS NETHERLANDS	1,247 1,046 66 934 1,739 4,367 2,736 1,274 3,516 1,797	11,086 6,221 75 2,478 3,734 1,243 1,473 5,434 1,259 689 6,013	1,760 265 495 541 1,991 2,882 2,111 1,220 668 2,552 108	1,455 167 2,233 1,054 1,852 10,280 3,118 6,124 1,347 1,314 1,187	1,260 265 2,573 2,002 867 2,616 544 1,284 461 1,242 522	1,482 215 4,379 1,826 939 1,063 854 484 956 9,853	35,756 170 2,858 1,651 6,242 875 2,614 1,801
	NEW ZEALAND NETHERLANDS NEW ZEALAND NEW ZEALAND NEW ZEALAND NEW ZEALAND NEW ZEALAND NEW ZEALAND NEW ZEALAND NEW ZEALAND NEW ZEALAND	583 346 271 483 1,413 946 548 1,577 1,168		2,135 1,792 582 771 952 349 488 2,037 479 356 4,331	354 2,261 134 138 530 854 774 471 273 1,496 76	313 1,351 638 289 519 3,190 1,009 2,470 514 850 850	284 1,992 747 628 237 796 198 513 174 713 359	354 1,499 1,233 613 254 326 307 190 581 6,757	7,261 1,117 843 495 1,676 415 1,652 1,244
	NICARAGUA NEW ZEALAND NICARAGUA NICARAGUA NICARAGUA NICARAGUA NICARAGUA NICARAGUA NICARAGUA NICARAGUA NICARAGUA	141 170 106 165 446 462 176 441 290		698 1,232 149 812 358 338 122 159 876 176 98	120 548 56 49 197 322 246 186 84 442 20	102 347 289 118 198 1,118 391 936 152 250 243	94 521 352 261 88 274 72 194 49 202 110	122 408 575 270 91 110 120 48 138 2,200	2,559 297 419 196 567 126 392 439
	NORWAY NICARAGUA NORWAY NORWAY NORWAY NORWAY NORWAY NORWAY NORWAY NORWAY NORWAY	54 90 81 153 379 236 111 307 155		59 532 212 322 108 129 468 110 59 523		990	159 212 42 47 173 251 183 105 58 220 9	128 137 193 90 161 901 271 528 118 114 103	110 210 222 171 75 227 47 111 40 108 45	130 168 378 157 82 92 73 42 83 852	3,156 123 246 144 543 75 226 155
	OMAN NORWAY OMAN OMAN OMAN OMAN OMAN OMAN OMAN OMAN OMAN	50 21 18 34 89 56 28 78 45		50 119 49 70 24 30 114 27 16 153		186	30 193 9 10 38 56 44 26 14 60 3	26 116 43 20 36 205 63 132 29 32 30	23 170 50 40 17 52 11 28 10 29 13	27 128 86 37 18 22 18 10 23 242	609 96 57 33 119 19 66 44
	PAKISTAN OMAN PAKISTAN PAKISTAN PAKISTAN PAKISTAN PAKISTAN PAKISTAN PAKISTAN PAKISTAN PAKISTAN	11 422 370 672 1,788 1,116 558 1,575 972		3,705 2,382 11 982 1,397 478 606 2,286 535 320 3,279	599 186 41 203 763 1,129 881 524 290 1,218 60	514 858 25 398 722 4,110 1,257 2,650 570 660 645	453 37 1,011 807 332 1,051 229 556 201 594 275	541 28 1,714 751 358 432 361 210 501 4,915	12,146 21 1,138 655 2,380 391 1,409 889
	PANAMA PAKISTAN PANAMA PANAMA PANAMA PANAMA PANAMA PANAMA PANAMA PANAMA PANAMA	213 118 64 92 245 308 101 244 91		216 558 236 194 71 89 564 100 52 377	493	86 817 47 28 115 188 140 117 47 179 6	71 505 248 77 120 630 235 571 83 76 74	62 742 276 159 52 151 42 120 26 73 33	75 566 469 172 53 60 72 25 52 656	1,879 420 349 114 322 74 132 128
	PERU PANAMA PERU PERU PERU PERU PERU PERU PERU PERU PERU	39 234 154 250 677 634 258 668 351		1,077 1,137 43 503 504 183 239 1,217 256 140 1,415	184 155 81 73 294 474 365 267 125 514 24	156 405 98 172 294 1,651 571 1,331 227 290 277	143 153 492 378 130 408 105 279 76 242 125	183 121 810 379 136 165 173 74 173 2,412	3,887 97 587 284 858 184 490 463
	PHILIPPINES PERU PHILIPPINES PHILIPPINES PHILIPPINES PHILIPPINES PHILIPPINES PHILIPPINES PHILIPPINES PHILIPPINES PHILIPPINES	80 628 513 952 2,972 1,704 986 3,135 2,437		4,251 3,265 86 1,397 1,877 686 972 3,661 863 632 8,044	704 314 244 272 1,045 1,625 1,426 848 502 2,640 147	618 200 1,162 526 1,010 6,195 1,900 4,434 994 1,585 1,579	561 307 1,363 1,165 461 1,630 364 921 367 1,401 669	698 245 2,247 1,110 501 684 558 401 1,239 11,820	14,446 177 1,534 938 3,303 742 3,548 2,147
	POLAND PHILIPPINES POLAND POLAND POLAND POLAND POLAND POLAND POLAND POLAND POLAND	261 168 149 280 709 440 209 578 299		1,778 1,002 272 983 394 588 200 241 878 205 113	283 1,004 77 85 320 465 343 198 109 422 18	233 637 356 166 298 1,674 505 993 220 218 198	201 949 411 320 139 423 89 208 75 206 86	237 742 700 292 151 172 137 79 159 1,637	5,689 543 458 267 1,002 143 434 297
	PORTUGAL POLAND PORTUGAL PORTUGAL PORTUGAL PORTUGAL PORTUGAL PORTUGAL PORTUGAL PORTUGAL PORTUGAL	91 151 131 248 614 393 177 485 244		92 897 355 535 177 209 774 176 96 813	1,635	258 351 71 78 284 409 295 173 93 353 15	214 213 322 151 263 1,467 440 866 188 178 161	182 311 373 282 124 369 76 180 64 169 71	214 235 635 257 134 150 119 67 130 1,354	5,319 176 413 234 891 123 355 248
	RUSSIA PORTUGAL RUSSIA RUSSIA RUSSIA RUSSIA RUSSIA RUSSIA RUSSIA RUSSIA RUSSIA	84 152 135 254 640 397 189 528 273		84 884 357 532 180 217 799 187 103 922	1,579	254 323 70 77 288 418 313 179 100 385 17	208 194 319 149 269 1,509 455 906 200 201 182	179 286 373 288 125 382 80 189 69 189 79	214 212 630 266 135 157 124 72 146 1,498	5,060 160 415 240 901 130 397 272
	SINGAPORE RUSSIA SINGAPORE SINGAPORE SINGAPORE SINGAPORE SINGAPORE SINGAPORE SINGAPORE SINGAPORE SINGAPORE	83 339 283 522 1,608 918 528 1,670 1,256		2,388 1,774 82 758 1,032 374 528 1,968 466 337 4,167	388 317 133 150 575 890 776 458 272 1,389 77	341 192 631 287 553 3,367 1,038 2,388 537 828 819	310 281 743 640 253 884 199 495 198 740 348	383 213 1,230 604 273 372 302 214 642 6,180	7,975 159 837 513 1,806 393 1,834 1,116
	SOUTH AFRICA SINGAPORE SOUTH AFRICA SOUTH AFRICA SOUTH AFRICA SOUTH AFRICA SOUTH AFRICA SOUTH AFRICA SOUTH AFRICA SOUTH AFRICA SOUTH AFRICA	145 331 270 467 1,244 869 422 1,154 601		2,607 149 1,819 768 989 334 420 1,773 402 242 2,201	418 556 143 143 538 794 630 402 211 912 39	360 349 678 290 515 2,858 908 2,031 398 460 435	321 519 794 614 233 733 171 426 138 426 192	379 405 1,366 575 251 301 275 145 326 3,610	8,630 297 895 477 1,656 299 871 654
	SOUTH KOREA SOUTH AFRICA SOUTH KOREA SOUTH KOREA SOUTH KOREA SOUTH KOREA SOUTH KOREA SOUTH KOREA SOUTH KOREA SOUTH KOREA SOUTH KOREA	1,624 2,188 155 1,800 3,367 10,724 5,953 3,477 11,454 9,398	14,784 161 11,287 4,839 6,572 2,422 3,466 12,833 3,028 2,269 30,293	2,443 596 844 953 3,679 5,749 5,074 2,980 1,804 9,535 553	2,145 369 4,016 1,818 3,540 21,947 6,748 15,660 3,577 5,852 5,940	1,957 555 4,694 4,103 1,625 5,794 1,294 3,232 1,333 5,219 2,488	2,435 424 7,735 3,879 1,762 2,448 1,935 1,417 1,465 4,733 43,584	50,512 317 5,272 3,293 11,603 1,629 2,649 1,788 13,729 7,885
	SPAIN SOUTH KOREA SPAIN SPAIN SPAIN SPAIN SPAIN SPAIN SPAIN SPAIN SPAIN	906 694 609 1,152 2,852 1,810 820 2,253 1,131		7,625 4,133 933 1,634 2,492 824 971 3,567 815 442 3,770	1,204 3,496 327 361 1,321 1,902 1,373 797 431 1,638 68	998 2,188 1,500 695 1,224 6,820 2,044 3,993 873 827 744	850 3,255 1,718 1,301 575 1,717 353 837 297 785 330	996 2,561 2,952 1,193 624 695 549 312 603 6,278	24,808 1,866 1,902 1,087 4,147 571 1,647 1,142
	SRI LANKA SPAIN SRI LANKA SRI LANKA SRI LANKA SRI LANKA SRI LANKA SRI LANKA SRI LANKA SRI LANKA SRI LANKA	392 186 163 296 787 490 247 754 550		1,617 385 1,047 431 614 210 266 1,009 237 152 1,842	262 1,506 82 89 335 495 389 231 128 625 34	224 903 375 175 317 1,804 552 1,172 252 369 362	199 1,318 445 356 146 463 101 245 90 329 154	237 988 754 331 157 191 160 97 282 2,746	5,280 745 501 289 1,046 178 797 497
	SWEDEN SRI LANKA SWEDEN SWEDEN SWEDEN SWEDEN SWEDEN SWEDEN SWEDEN SWEDEN SWEDEN	93 326 288 545 1,361 846 399 1,109 566		3,480 1,899 95 765 1,148 386 463 1,696 396 216 1,906	558 358 151 166 618 896 664 379 210 802 34	453 222 687 321 576 3,225 971 1,914 424 416 376	390 326 799 614 269 815 170 399 145 393 164	463 249 1,361 565 291 334 263 152 303 3,104	11,116 184 889 514 1,954 274 823 564
	SWITZERLAND SWEDEN SWITZERLAND SWITZERLAND SWITZERLAND SWITZERLAND SWITZERLAND SWITZERLAND SWITZERLAND SWITZERLAND SWITZERLAND	179 88 78 146 369 229 108 298 153		945 177 519 207 309 105 125 456 107 58 513	150 687 41 45 168 243 178 103 57 217 9	123 415 186 88 156 874 263 515 114 112 101	106 607 215 168 73 221 46 108 39 106 44	124 457 366 153 79 90 72 41 81 839	3,020 343 239 139 525 74 223 152
	THAILAND SWITZERLAND THAILAND THAILAND THAILAND THAILAND THAILAND THAILAND THAILAND THAILAND THAILAND	1,388 1,810 49 1,512 2,779 8,585 4,904 2,820 8,911 6,686	12,595 9,482 48 4,049 5,494 1,999 2,808 10,515 2,489 1,797 22,202	2,077 186 711 796 3,072 4,757 4,130 2,439 1,453 7,408 407	1,823 113 3,374 1,540 2,956 17,989 5,546 12,709 2,855 4,415 4,364	1,652 165 3,972 3,422 1,351 4,722 1,061 2,644 1,055 3,928 1,853	2,048 124 6,575 3,231 1,462 1,987 1,615 1,176 1,142 3,419 32,950	42,640 93 4,476 2,743 9,651 1,354 2,098 1,331 9,714 5,948
	TRINIDAD THAILAND TRINIDAD TRINIDAD TRINIDAD TRINIDAD TRINIDAD TRINIDAD TRINIDAD TRINIDAD TRINIDAD	771 34 22 33 86 85 31 76 31		798 190 80 76 26 29 158 31 16 118	211	35 2,962 16 11 42 63 46 33 15 57 2	29 1,864 82 27 43 213 72 164 27 25 23	25 2,776 89 55 19 53 13 34 9 24 11	30 2,167 157 51 19 21 22 9 17 207	772 1,587 97 40 117 22 45 38
	TURKEY TRINIDAD TURKEY TURKEY TURKEY TURKEY TURKEY TURKEY TURKEY TURKEY TURKEY	14 597 522 961 2,482 1,562 748 2,085 1,109		5,685 3,436 16 1,389 2,030 681 837 3,165 728 420 3,746	911 271 57 294 1,095 1,593 1,210 714 390 1,573 68	767 1,238 35 576 1,028 5,764 1,748 3,614 778 811 740	671 54 1,452 1,129 477 1,473 313 753 270 759 327	796 43 2,455 1,044 515 602 495 283 589 6,166	18,453 33 1,622 924 3,425 524 1,611 1,119
	UNITED ARAB TURKEY UNITED ARAB UNITED ARAB UNITED ARAB UNITED ARAB UNITED ARAB UNITED ARAB UNITED ARAB UNITED ARAB UNITED ARAB	315 97 85 155 412 257 129 363 211		315 548 226 322 110 139 526 123 74 712		852	138 1,208 43 47 176 260 203 121 67 281 13	118 738 197 92 166 943 289 610 131 148 140	104 1,080 233 186 76 242 53 127 46 137 60	125 819 395 173 82 99 83 48 109 1,121	2,783 611 262 151 548 90 305 204
	UK UNITED ARAB UK UK UK UK UK UK UK UK UK	49 910 812 1 ,520 3 ,779 2 ,375 1 ,091 3 ,001 1 ,513	,122	9,961 5,451 50 2,160 3,251 1,078 1,275 4,691 1,083 586 5,050	1,576 188 436 471 1,743 2,491 1,821 1,049 573 2,160 91	1,294 116 1,958 925 1,617 8,939 2,682 5,263 1,159 1,107 997	1,116 171 2,247 1,738 759 2,272 469 1,095 395 1,049 439	1,309 130 3,825 1,580 822 921 735 415 806 8,299	32,048 97 2,491 1,437 5,469 748 2,204 1,519
	US VIRGIN IS UK US VIRGIN IS US VIRGIN IS US VIRGIN IS US VIRGIN IS US VIRGIN IS US VIRGIN IS US VIRGIN IS US VIRGIN IS US VIRGIN IS	516 45 25 34 87 111 32 74 27		512 266 109 76 28 30 187 33 16 106		201	35 1,980 23 11 45 68 48 38 15 54 2	29 1,189 131 33 49 224 78 185 27 22 21	25 1,753 132 65 21 55 14 38 8 22 10	30 1,303 235 59 21 22 24 9 15 190	814 982 139 45 123 23 39 35
	VENEZUELA US VIRGIN IS VENEZUELA VENEZUELA VENEZUELA VENEZUELA VENEZUELA VENEZUELA VENEZUELA VENEZUELA VENEZUELA	17 327 206 293 767 801 275 678 263		1,758 1,830 19 773 647 234 262 1,469 279 144 1,020	293 155 70 94 378 571 407 309 130 503 18	244 822 43 251 389 1,915 653 1,520 237 214 201	213 69 886 509 170 474 120 319 76 208 93	253 55 1,549 470 174 189 202 78 149 1,806	6,570 46 936 364 1,054 202 385 331
	VIETNAM VENEZUELA VIETNAM VIETNAM VIETNAM VIETNAM VIETNAM VIETNAM VIETNAM VIETNAM VIETNAM	129 755 628 1,162 3,596 2,046 1,180 3,750 2,869		5,220 145 3,943 1,685 2,293 833 1,179 4,409 1,038 755 9,433	861 516 296 332 1,278 1,981 1,732 1,018 608 3,122 174	756 326 1,403 639 1,229 7,505 2,313 5,311 1,201 1,869 1,853	688 512 1,650 1,423 562 1,980 443 1,109 443 1,670 786	851 405 2,736 1,344 609 830 672 480 1,463 13,946	17,701 325 1,858 1,141 4,032 881 4,172 2,531
	VIETNAM	321		331			1,232	773	1,151	903	658

ACKNOWLEDGMENTS

I would like to acknowledge the continued support of my committee chair and advisor, Linda K. Nozick. Her dedication to students never goes unnoticed. I would also like to thank all of my other professors at Cornell University for their teaching and guidance over the years. 


Brian Levine was born and raised in Brooklyn, NY. He attended Stuyvesant High School in New York City and then enrolled in Cornell University for his undergraduate studies. In 2005, he received his bachelor's degree in Civil & Environmental Engineering and graduated magna cum laude with honors. His research interests include using mathematical models to understand the behavior of transportation systems, specifically related to airlines. Currently, he is supported by a Department of Energy Computational Science Graduate Fellowship and plans to continue at Cornell University for his Ph.D. and pursue further research in this field. v TABLE OF CONTENTS BIOGRAPHICAL SKETCH iii ACKNOWLEDGEMENTS iv LIST OF FIGURES vi LIST OF TABLES vii LIST OF ABBREVIATIONS viii CHAPTER 1: INTRODUCTION 1 CHAPTER 2: MODEL FORMULATION 5 CHAPTER 3: INSIGHTS FROM THE MODEL 22 CHAPTER 4: CONCLUSIONS AND FUTURE RESEARCH 32
Brian Seth