Trip Length Distributions in Commodity-Based and Trip-Based Freight Demand ModelingInvestigation of Relationships

Jos Holgun-Veras and Ellen Thorson

cast methodologies have been developed for passenger trips, notfreight trips. This methodological void usually is filled by simplis-tic approaches such as assuming that freight trips follow the samebehavioral mechanisms as passenger trips, which is an implicitassumption when truck traffic is estimated as a function of passenger-car traffic. Although the error introduced by this assumption maynot have major consequences for small urban areas where the num-ber of freight trips is relatively small, it cannot be used in large met-ropolitan areas such as New York City where freight-related tripsare a major contributor to urban congestion, and freight-specifictransportation policies are warranted.

The complexity of modeling freight demand arises from a combi-nation of factors. First and foremost, multiple dimensions are to beconsidered (6). Whereas in passenger transportation there is only oneunit of demandthat is, the passenger, who for the most part happensto be the decision makerin freight transportation there are multipledimensions (volume, weight, and trips) under the control of a numberof decision makers (drivers, dispatchers, freight forwarders) whointeract in a rather dynamic environment. Also, a significant portionof freight demand is discretionary in nature. In this context, a rela-tively small number of companies have control over a significantnumber of freight movements. Integrating their behavior into plan-ning models is rather challenging because the dynamics of theirdecision-making process, marked by their commercially sensitivenature, are not part of the public domain.

The significant differences in time value, or opportunity costs,exhibited by cargoes also are cited as a major factor in determiningthe complexity of modeling freight (7). Whereas the passengers timevalue ranges within the same order of magnitude, cargo time valuedetermined by opportunity costsexhibits a much wider range.Cargoes opportunity costs are determined by a combination of theintrinsic cargo value (determined by market value and replacementcosts) and the logistic cargo value (a function of the importance ofthe cargo for the production system at a given moment in time andinventory levels). At one end, low-priority cargoes may have intrin-sic cargo values as low as $9/ton (gypsum); and at the other, high-priority cargoes have intrinsic cargo values that frequently exceed$500,000/ton (e.g., computer chips) (8). These figures wouldincrease significantly once the logistic cargo value is factored in.

The multiple dimensions that could be used for freight demandmodeling (i.e., weight, trips, and volume) have given rise to twomajor modeling platforms: commodity-based and trip-based mod-eling. Different modeling approaches can be used on each of theseplatforms. The most widely used options include (a) variants of the

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Transportation Research Record 1707 37Paper No. 00-0910

Commodity-based and vehicle-trip-based freight demand modeling isdiscussed. The characteristics of the trip length distributions (TLDs) areexamined, defined in terms of tons, as required in commodity-basedmodeling, and in vehicle trips, as required in trip-based modeling. Withdata used from a major transportation study in Guatemala, the TLDsare estimated for both tons and vehicle trips. The analysis revealed that(a) the shape of the TLDs depends upon the type of movements beingconsidered; (b) TLDs defined in terms of tonnage differ significantlyfrom those defined in terms of vehicle trips; (c) TLDs for different typesof vehicles, transporting similar commodities, reflect the range of use ofeach type of vehicle; (d ) though tons TLDs and vehicle TLDs are differ-ent, the relationship between them seems to follow a systematic patternthat, if successfully identified, would enable transportation planners toestimate one type of TLD given the other; and (e) major freight gener-ators affect the shape of the TLDs, so complementary models may beneeded to provide meaningful depictions of freight movements.

The transportation modeling process uses demand models to forecast,in combination with network models to analyze supply. For the mostpart, the evolving transportation modeling paradigms have focused onpassenger transportation while paying little or no attention to freight.This is because passenger issues traditionally have been assigned thehighest priorities, effectively reducing the amount of resources andattention allocated to freight transportation research and education.

An appropriate consideration of freight transportation issues isimportant, both in modeling and policy making, because in additionto making significant contributions to the economy, truck freighttransportation generates externalitiesthat is, pollution (1). For thatreason, an increasing number of planning studies are focusing on(a) defining the role of advanced technologies to enhance system pro-ductivity and efficiency (e.g., 2,3); (b) defining traffic control strate-gies aimed at ameliorating the negative environmental impacts oftruck traffic upon local communities (e.g., 4); and/or (c) estimatingfuture freight supply and demand to estimate future needs (e.g., 5).The latter type of analysis faces significant limitations because (a) thebulk of transportation demand models have been developed for pas-senger transportation, not freight; and (b) transportation planningagencies usually do not have the specialized staff required to deal withfreight issues nor do they assign freight transportation a high priority.

The most significant hurdle to including freight transportation inthe transportation modeling process is that most of the demand fore-

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Four Steps Model, (b) direct demand models, and (c) input-outputmodels. Table 1 summarizes the major combinations, according tothe principal authors experience. As can be seen, approaches suchas developing regression models of truck traffic as a function ofpassenger-car traffic have been purposely left out of the figure becausethey have very little behavioral and economic support, regardless oftheir statistical significance.

In addition to the modeling approaches depicted in Table 1, thereare methodologies that attempt to synthesize (estimate) freight origin-destination matrices from secondary data, such as traffic counts, andscreen counts (9, 10). However promising, these methodologies areout of the scope of this paper because they do not attempt to explainthe fundamental mechanisms of freight demand, their main focusbeing on the estimation of origin-destination matrices consistent withtraffic counts or other secondary data.

This paper analyzes variants of the Four Steps Model applied toboth commodity-based and trip-based platforms. More specifically,the paper analyzes the characteristics of the trip length distributions(TLDs) used in these platforms. The paper has three major sections,in addition to the introduction. In the section on commodity-basedversus trip-based models, the major modeling platforms are brieflydescribed, discussing advantages and disadvantages and the potentialbenefits that could be derived from their integration. The case-studysection discusses the TLDs obtained from a recent origin-destinationsurvey conducted as part of a major modeling project in GuatemalaCity. This project was selected as the case study because (a) the datawere collected using state-of-the-art questionnaires; (b) the samplewas expanded with proper consideration of double counting of trips;and (c) the sample contains a mix of intercity and urban trips, whichenables the comparison of the TLDs from these different environ-ments. The findings extracted from this analysis are, for the mostpart, of general applicability and are presented in the conclusionssection. These conclusions will assist freight modelers in producingmeaningful models of freight demand.

COMMODITY-BASED MODELS VERSUS TRIP-BASED MODELS

Commodity-Based Models

Commodity-based models focus on modeling the amount of freightmeasured in tons, or any comparable unit of weight. It is widelyaccepted that the focus on the cargoes enables commodity-based

models to capture more accurately the fundamental economic mech-anisms driving freight movements, which largely are determined bythe cargoes attributes (e.g., shape, unit weight). In general terms, thecomponents of the modeling process are those depicted in Figure 1(built upon Ogden, 6).

The commodity generation models estimate the total number oftons produced and attracted by each of the individual zones com-prising the study area. The commodity distribution phase estimatesthe number of tons moving between each origin-destination pair, andit usually is undertaken with the help of gravity models (simply ordoubly constrained) or any other form of spatial interaction models,such as intervening opportunity models. The mode-split component,intended to estimate the number of tons moved by each of the avail-able modes, usually is done with discrete choice models or paneldata from a group of business representatives (as in Cross HarborFreight Movement Major Investment Study, 5), or both. Once theorigin-destination matrices for each mode have been estimated,vehicle-loading models estimate the corresponding number of vehi-cle trips. Finally, the vehicle trips estimated in the previous stepare assigned to the different networks, thus completing the demandestimation process.

The aforementioned process is believed to have the potential forcapturing the fundamental mechanisms of the freight demand process,though some issues deserve further discussion:

Empty trips. Since commodity-based models focus on the actualcargoes being transported, there is no clear way to model emptytrips, which by different estimates may represent between 15 and50 percent of the total trips in specific corridors (11). Modelingempty trips is quite challenging because they are determined by thelogistics of the freight movements in the area (something the trans-portation modelers do not have access to), and for that reason, it usu-ally is very difficult to establish a cause-effect relationship betweenempty trips and commodity flows or any other attributes of the trans-portation zones. In some cases, practitioners have opted to considerempty trips as another commodity. However pragmatic, this approachneglects the interrelationship among empty trips, commodity flows,and the logistics of freight movements, and it does not ensure com-patibility between the total number of loaded trips and the totalnumber of empties.

Needed commodity flows. Another obvious disadvantage is thatcommodity-based approaches require commodity flows, estimatedthrough expensive and time-consuming origin-destination surveys,such as the commodity flow surveys conducted by the U.S. Cen-

TABLE 1 Modeling Platforms and Approaches Most Frequently Used (I-O = Input-Output)

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sus Bureau (12); although in the United States an increasing num-ber of transportation planning agencies are relying on proprietaryfreight demand databases. These databases are assembled by pri-vate companies from waybill samples and complemented withsmall origin-destination surveys.

Trip-Based Models

Trip-based models, as the name implies, focus on modeling vehicletrips. As can be seen in Figure 2, they only have three components: tripgeneration (to estimate the number of vehicle trips produced andattracted by each zone), trip distribution (to estimate the number ofvehicle trips between each origin-destination pair), and traffic assign-ment (to estimate the traffic in the network). Since the focus is onvehicle trips, which presupposes that the mode selection and thevehicle selections already were done, trip-based models do not needmode-split or vehicle-loading models.

Trip-based models have some advantages. First and foremost, theyfocus on a unit (the vehicle trip) for which there is a significantamount of data in the form of traffic counts, screen counts, and soforth. Furthermore, an increasing number of intelligent transporta-tion systems applications are able to track the movements of vehiclesthrough, at least, segments of the highway networks, thus increas-ingly becoming an important source of traffic data. Second, since thefocus is on the vehicle trip, considering empty trips does not presentany major problem.

Trip-based models have some disadvantages, however. First, theyare of questionable applicability to situations in which multiple freighttransportation modes are to be considered. Second, since the vehicletripthe focus of trip-based modelsis in itself the result of a modechoice and vehicle selection processes (which have not been takenexplicitly into account), the identification and modeling of the eco-nomic and behavioral mechanisms determining freight demandbecome more difficult, because those mechanisms are associatedwith the actual commodities being transported.

As can be seen, neither commodity-based nor trip-based modelingis able to capture the full complexity of freight movements. The for-mer is expected to capture more accurately the fundamental mecha-nisms driving freight demand, though it fails to properly considerempty trips; whereas the latter is able to use readily available data,including empty trips, but it may not be able to fully capture themechanisms driving freight demand (which are conditioned by thecommodities attributes).

This is because by focusing on either the commodities or the vehi-cle trips, the analysis takes into account only one dimension of freightdemand. In an ideal world, the ultimate freight demand model wouldbe able to properly take into account the three main dimensions:weight, volume, and vehicle trips. An enhanced representation offreight movements could be achieved if, at least, two of these dimen-sions were jointly modeled. This quest provides the rationale forthe study of the relationship between vehicle TLDs and tons TLDs.Should it be feasible to develop approximation functions to estimatevehicle TLDs from tons TLDs, or more appropriately to develop

FIGURE 1 Model components of commodity-based Four Steps approach.

FIGURE 2 Model components of trip-based Four Steps approach.

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models of empty trips as a function of commodity flows, it would bepossible to create freight demand models able to take advantage ofthe best features of both commodity-based and trip-based modeling.

ROLE OF THE TRIP LENGTH DISTRIBUTION

As indicated in Table 1, regardless of the platform being used (i.e.,commodity- or trip-based), the bulk of areawide studies rely on spa-tial interaction models, either gravity models or intervening oppor-tunity models. A fundamental input to these models is the trip lengthdistribution, or related parameters, which describe the way in whichfreight demand decreases along a given impedance variable (e.g., dis-tance, travel time, generalized cost). The negative relationship be-tween demand and the impedance variable is required by postulatesof economic rationalitythat is, the consumption of normal goodsdecreases with price.

The TLD, as traditionally defined in passenger transportation mod-eling, is nothing more than a representation of the frequency of trips(or tons) made for various intervals of the impedance variable. Thecalibration of the trip distribution models entails ensuring that themodeled TLD resembles the observed TLD (13).

In freight demand modeling, the TLD can be defined in terms of(a) the weight of the commodities being transported, referred to astonnage (or tons) TLDs; and (b) the number of vehicle trips, referredto as vehicle TLDs. Commodity-based models use tonnage TLDs(usually by commodity group), whereas trip-based models use vehi-cle TLDs (usually by type of vehicle) in their respective trip distri-bution models. This ensures consistency with the previous step oftrip generation modeling. Should an origin-destination sample beavailable (as in this project), tons TLDs and vehicle TLDs could be estimated for various commodity groups and/or types of vehicle,enabling comparison and analysis. The distinction between vehicleTLDs and tons TLDs is important because, as shall be seen later, theyare significantly different.

The main objectives of this paper are (a) to examine the character-istics of vehicle and tonnage TLDs, (b) to identify the typical prob-lems found when dealing with TLDs, and (c) to study the relationshipsbetween commodity-based TLDs and trip-based TLDs. This analysissheds light into the nature of real-life TLDs and provides invaluablelessons for modeling purposes.

CASE STUDY

The data used in this paper were part of a freight origin-destinationsurvey conducted in the demand-modeling process for a major high-way project in Guatemala City. Roadside interviews were comple-mented by classified traffic counts to expand the sample accordingto time of day and type of vehicle. The origin-destination question-naire included questions about the time of the interview, vehicle type,origin, destination, commodity type, and shipment size, amongothers. The questionnaire was administered by the staff of IngenierosConsultores de Centro Amrica. The sample, comprised of 5,276observations, was expanded by time of day and type of vehicle andprocessed to eliminate double counting of trips. The overall expansionfactor was 6.476.

Due to the nature of the project under analysis, a bypass road on theoutskirts of Guatemala City, and the location of the survey stations,the sample includes a mix of intercity and urban freight movements.Out of a total of 34,986 trips/day, pickup trucks carried 59.47 percent;large two-axle trucks, 23.77 percent; semitrailers, 10.40 percent; andthe other truck types captured the rest. The total tonnage is distributedas follows: pickups, 9.54 percent; large two-axle trucks, 33.79 percent;semitrailers, 46.41 percent; with the other types capturing the rest.

The TLDs for the entire data set, shown in Figure 3, were analyzedfirst and found to have some interesting features: (a) the vehicle TLDfor total trips is a weighted combination of the empty-vehicles TLDand the loaded-vehicles TLD, as expected; (b) the tons TLD is sig-nificantly different from the vehicle TLDs; (c) the differences bet-

FIGURE 3 Vehicle and tonnage TLDs.

Holgun-Veras and Thorson Paper No. 00 -0910 41

ween the TLDs disappear with increasing values of distance; and(d) the TLDs are (statistically speaking) multimodal. As shown later,the first mode (around 30 km) corresponds to the mode of internaltrips, while the second mode (around 60 km) corresponds to the modeof intercity trips.

The statistical multimodality of the TLDs reflects the nature of thetrips being considered and the associated land use characteristics. To

examine this hypothesis, the TLDs were obtained for two trip types:(a) internal-internal trips, that is, origin and destination inside thestudy area, shown in Figure 4a; and (b) their complement (external-external, external-internal, and internal-external), mostly intercitytrips, shown in Figure 4b.

As can be seen, the TLDs depicted in Figure 4a (internal trips) aresignificantly different from those depicted in Figure 4b. First, the

FIGURE 4 TLDs for the entire sample: (a) internal trips; (b) intercity trips.

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internal TLDs are smoother than the intercity TLDs. This arisesbecause origins and destinations in the study area (predominantlyurban and suburban) are located in a continuum of distances, whereasorigins and destinations for intercity trips do not occupy the full rangeof distances because of terrain and the location of other cities. Second,intercity TLDs are more likely to be affected by the existence ofspecial land uses such as marine ports and major agricultural areas,which tend to produce spikes (modes) on the TLDs. For example, inFigure 4b, the relatively high percentage of movements taking placebetween 300 and 350 km is explained by the freight flows betweenPuerto Barrios (the main Guatemalan port) and Guatemala City. Thisphenomenon is discussed later.

The statistical multimodality of the TLDs is more than a statisti-cal curiosity. First, systematic (not random) multimodality is notconsistent with rational economic behavior because it implies thatdemand increases with cost (the exception is the ascending branchof the first mode, which usually is explained by intermodal or inter-vehicle competition, or both). Thus, when systematic multimodal-ity is identified (e.g., port flows in Figure 4b), complementarymodels should be used to represent those flows separately. Second,from the practical standpoint, unimodal impedance functions, suchas the ones in the commercial demand modeling software, are notable to adequately represent TLDs such as the ones depicted inFigure 4b. This situation poses a problem to practitioners calibratingtrip distribution models.

In the following sections, both tons TLDs and vehicle TLDs areestimated according to types of vehicle and to commodity groups.This will provide the basis for the analysis and identification of thecharacteristics associated with the corresponding TLDs.

Observed Characteristics of Vehicle TLDs and Tons TLDs by Type of Vehicle

This section analyzes the TLDs for different types of vehicles. For thesake of brevity, the analysis focuses only on two cases: pickup trucksand semitrailers, shown in Figures 5 and 6. As can be seen, the TLDsare significantly different with shapes and ranges that are conditionedby the vehicle size, reflecting various ranges of use. These resultsconfirm long-held assumptions that the TLDs depend upon the typeof vehicle and the corresponding carrying capacity. This clearly indi-cates that trucking companies perceive the different types of vehiclesas having a range of optimal use, which, in turn, is reflected in thecorresponding TLDs. This assumption is supported by Figures 7a, b,and c, which show the percentage of tons transported, at variousdistance intervals, by specific groups of vehicles.

The TLDs for semitrailers shown in Figure 6b exhibit a peakaround 330 km, which corresponds to flows to and from Puerto Bar-rios. However, the TLDs for pickup trucks do not exhibit suchbehavior (see Figure 5b), because they are not used to serve the port.This indicates that major generators produce differential impactsupon vehicle classes, the magnitude of which depends upon the typeof vehicle serving the generators.

Observed Characteristics of Vehicle TLDs and Tons TLDs by Commodity Group

This section analyzes the TLDs for the main commodity groups cap-tured in the origin-destination survey. The tonnage distribution trans-ported by the different types of vehicles includes (a) construction

materials, 30.37 percent; (b) manufactured products, 15.03 percent;(c) mineral fuels, 6.67 percent; (d) fruits and vegetables, 5.96 percent;(e) cereals, 4.79 percent; ( f ) others, 4.40 percent; (g) electrical equip-ment, 3.92 percent; (h) beverages, 3.24 percent; (i) miscellaneousmetal articles, 2.27 percent; and ( j) textiles, 2.02 percent. The analy-sis focuses on a selected number of commodity groups. Figure 8shows the TLDs for mineral fuels, and Figure 9 shows them for fruitsand vegetables. The TLDs shown correspond to the types of vehicleused to transport these cargoes (vehicles with less than 2 percent werenot considered) as well as the total tons TLD.

Interestingly, while the total tons TLD for the entire commoditygroup reflects the geographic distribution of economic activities(e.g., production, consumption), the tons TLDs for each of the vehi-cle types reflect the intervehicle competition discussed in the pre-vious section. The vehicle TLDs are similar to the total tons TLDonly in cases, such as the one depicted in Figure 8b, in which onetype of vehicle dominates the market.

As discussed before, major generators have an impact upon theTLDs. The peak in Figure 8b, taking place around 310 km, corre-sponds to the flow of fuel being transported by semitrailers betweenPuerto Barrios and Guatemala City. The uniqueness of the economicmechanisms explaining this relationship necessitates the use ofcomplementary models able to capture the fundamental elements ofthis process.

Major Freight Generators

As indicated before, the existence of major freight generatorsinthis case, a major porthas an impact upon both tons TLDs andvehicle TLDs. In order to illustrate the nature of this impact, gammafunctions were estimated for two different cases: with port flows (allflows) and without port flows. Gamma functions were selectedbecause they frequently are used in trip distribution modeling. Theoriginal tons TLDs and the corresponding gamma functions aredepicted in Figure 10. As can be seen, the inclusion of the port flowsin the tons TLD skews the gamma function to the right, shifting itsmode from 100 km to 180 km.

CONCLUSIONS

This research conducted an in-depth review of the major modelingplatforms for freight movements: commodity-based and vehicle-trip-based modeling. It is found that these platforms represent unidimen-sional views of a phenomenon that, in essence, is multidimensionalin naturea full depiction of freight flows entails joint considerationof cargoes weight and volume as well as vehicle trips.

Both commodity-based and vehicle-trip-based models encounterchallenges that are difficult to overcome. Commodity-based model-ing is not able to adequately model empty trips, although it hasthe potential to capture the mechanisms driving freight demand.Trip-based modeling, though able to consider empty trips, is limited inits ability to fully capture the fundamental mechanisms conditioningfreight demand, which are determined by the cargoes attributes(which are not explicitly modeled). This situation suggests thatintegrating both commodity-based and trip-based modeling wouldprovide an enhanced understanding of freight movements. Suchintegration, at the trip distribution stage, requires an understand-ing of the relationship between tons TLDs and vehicle TLDs. Thisquest provided the rationale for this paper.

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FIGURE 5 TLDs for pickup trucks: (a) internal trips; (b) intercity trips.

This paper focused on the relationship between tons TLDs andvehicle TLDs. It was found that the shape of the TLDs is condi-tioned, to a great extent, by the environment in which the freightmovements take place. Freight movements taking place in urbanand suburban areas, as a consequence of the relatively homoge-neous land use (from the standpoint of freight demand), lead toTLDs that are smooth and relatively unimodal. At the other end ofthe spectrum, freight movements in intercity travel lead to TLDsthat are (statistically) multimodal and conditioned by major freight

generators, such as ports. These major generators have the potentialto significantly alter the shape of the TLDs, and they may requirecomplementary models to fully represent their fundamental economicrelationships.

The TLDs of different vehicles reflect the range of use of each typeof vehicle. This means that each type of vehicle tends to dominate therange of distance at which its relative performance is better.

The TLDs, regardless of being defined in terms of tons or vehicletrips, are significantly different. Nevertheless, the tons TLDs and

FIGURE 6 TLDs for semitrailers: (a) internal trips; (b) intercity trips.

FIGURE 7 Vehicle shares by distance intervals: (a) pickups and small trucks; (b) large two- and three-axle trucks; (c) semitrailers.

FIGURE 8 Tons TLDs for mineral fuels: (a) internal trips; (b) intercity trips.

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FIGURE 9 Tons TLDs for fruits and vegetables: (a) internal trips; (b) intercity trips.

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vehicle TLDs tend to exhibit a fairly consistent behavior with respectto each other. In all cases, the difference between them tends to in-crease with distance up to a point, and then it consistently decreasesuntil becoming indistinguishable in the upper range of distances. Thisfeature may be exploited by developing approximation functionsbetween vehicle TLDs and tons TLDs. If such approximation func-tions are successfully calibrated, this will enable the practitionerto exploit the best features of commodity-based and truck tripmodeling.

ACKNOWLEDGMENTS

The authors acknowledge the cooperation and assistance of Inge-nieros Consultores de Centro Amrica and its president, Jorge Erdg-menger, during the data collection component of this research. Thisresearch was partially supported by the University TransportationResearch Center and its director, Robert Paaswell. This support isboth acknowledged and appreciated.

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Publication of this paper sponsored by Committee on Freight TransportationPlanning and Logistics.

FIGURE 10 Tons TLDs with and without port flows.