## Preliminary Insights into the Practical Implications of Modelling Commercial Vehicle Empty Trips

### Authors

J Holgu?n-Veras and E Thorson, The City College of New York, US

### Description

### Abstract

The latter part of the 20th Century and the beginning of the 21st is a period of profound and revolutionary transformations in the area of computer technology, communication networks, informationand production systems (most notably Just In Time). The convergence of these trends and the development and growth of the Internet have made possible ever deeper changes in the ways both businesses and consumers do their economic transactions. All of this points toward an increasing role ofthe freight transportation system as the conveyor of goods for the e-commerce systems. At the same time, there is increasing pressure from both community and environmental groups to ameliorate the negative impacts of freight activity. However, in spite of the negative externalities that freight activity produces, there is no doubt that freight transportation makes significant contributions to the economy. All of the above implies that the freight transportation systems of the 21st Century will be expected to cover a larger geographic area, be more responsive to user needs and expectations, reduce the environmental, safety and health externalities associated with truck traffic; and do all of this in a context in which the provision of additional freight infrastructure capacity will become more difficult and expensive. In other words, the freight transportation system will have to do more with less. This, in turn,puts a significant amount of pressure of Metropolitan Planning Organizations (MPOs) to enhance their freight transportation planning processes. This objective is confounded by the lack of freight-transportation-specific demand modelling methodologies. For the most part, the bulk of freight transportation modelling applications are nothing more than adaptations of modelling methodologies originally designed for passenger transportation, that tend to overlook the fundamental differences between freight movements and passenger transportation. Although the complexity of freight demand modelling has been discussed elsewhere (e.g., Holguín-Veras and Thorson, 2000; Cambridge Systematics, 1997; Ogden, 1992) it is important, for the purposes of this paper, to briefly discuss the multidimensional nature of freight demand. One of the unique features of freight transportation is that there are a number of different dimensions to be taken into account, most notably: weight, volume, number of vehicle-trips, and value of the commodities being transported. Each of these dimensions represents a different way to define and measure freight transportation demand, with important implications for freight demand modelling. The existence of these different dimensions has resulted into two major modelling platforms: commodity-based and vehicle-trip based modelling. These approaches represent, in essence, uni-dimensional views of a multi-dimensional problem with tonnage, vehicle-trips, and value as the most relevant dimensions. A recent formulation attempts to bridge the gap between commodity based and vehicle-trip based models by formulating the urban good problem as a market in economic equilibrium (Holguín-Veras, 2000). Vehicle-trip based modelling focuses on depicting the flows of commercial vehicles, e.g., truck trips. The focus on vehicle trips enables this type of models to consider both loaded and empty trips. However, they have some significant limitations. First and foremost, they are unable to take into account the economic characteristics of the cargoes that play an important role in the vehicle selection, mode choice and routing processes, as demonstrated theoretically in the context of optimal pricing in Holguín-Veras and Jara-Díaz (1999) and empirically in McFadden et al. (1986), Abdelwahab (1998), and Holguín-Veras (2002). A second limitation is that because of their focus on the vehicle trip -in itself the result of a choice process that already took place- these models are of limited applicability to multimodal freight transportation systems. Commodity-based modelling, on the other hand, focuses on the amount of commodities being transported, usually defined by its weight. The focus on commodities enables these models to depict the fundamental processes taking place and, in doing so, to take into account the economic characteristics of cargoes. Commodity based models do have a limitation, which is related to their inability to model empty trips, that are the result of logistic decisions not directly explained by the commodity flows. This limitation is usually addressed at the calibration stage by means of expanding the commodity distribution matrix so that the resulting traffic assignment resembles the calibration values.

Although a widely used pragmatic solution, this approach is of questionable validity. First, there is no way to ensure that the resulting number of empty trips is consistent with the area wide estimates of the total number of empty trips. Second, expanding a commodity trip matrix to compensate for the missing empty trips implies that empty trips are directly correlated with the commodity flows. This assumption is very weak because the commodity flow between two zones determines the amount of loaded trips between them, not the amount of empty trips. A different way of overcoming this limitation of commodity based models is to develop complementary models to depict empty trips as a function of the routing choices that the commercial vehicle operators make, which are based on the commodity flows in the study area. This is the approach that is considered here. This paper uses probability principles to formulate a model of empty trips as a part of a commercial vehicle trip chain. In this paper, new mathematical formulations that depict the flow of empty commercial vehicles as a function of a given matrix of commodity flows were developed. These formulations are based on probability principles and spatial interaction concepts. The models are based on the concept of order of a trip chain, defined as the number of additional stops with respect to the primary trip, and provide a statistical link between the first order and higher order trip chains. Three different destination choice probability functions were hypothesized based on different assumptions about the destination choice process. One of these formulations included a memory component, that takes into account the amount of travel already done in the destination choice process. An example, based on data from an origin-destination study in Guatemala City, is included to show the practicality ofthe proposed models. The numerical results indicated a slight superiority of the formulation that takes into account the length of the previous trip. In all cases, this model outperformed the previous models which seems to be an indication of the reasonableness of its fundamental assumptions and specifically ofthe benefits of including a memory function. The paper also provides empirical evidence of the importance of modelling empty trips. The Root Mean Squared Error of the estimation increased between 57% and 83%, with respect to the best empty trip model, if empty trips are not explicitly modeled.

Holguin-Veras and Thorson (2002) developed a new set of models of commercial vehicle empty trips based on a first order model of trip chains. The models are based on the concept of order of a trip chain, defined as the number of additional stops with respect to the primary trip. The expected value of the total number of trips between an origin-destination pair has been reinterpreted as the summation of the expected values for the commercial vehicle trip chains for the different orders. This formulation enabled the authors to express the expected value of the total number of trips as a function of the expected values for a zero order and a first order trip chain and a set of parameters. On the basis of probability principles, the previous developments of Noortman and van Es' (1978) and Hautzinger (1984) were reinterpreted as zero-order trip chain models. Three different destination choice probability functions were hypothesized based on different assumptions about the destination choice process. One of these formulations included a memory component, intended to take into account the amount of travel already done in the destination choice process. In general, the models developed here depict empty trips as the summation of a zero order trip chain term and a first order trip chain term, expanded to take into account higher order terms. These formulations suggest that the number of emptytrips in a given area is determined by the probability of a zero order trip chain, p, the parameter that represents the ratio of higher order trip chains with respect to the first order term, and the probabilities of not getting loads. The parameters of the destination choice models do not determine the amount of empty trips, only the choice of destination.

An example, based on data from an origin-destination study in Guatemala City, was included in this paper. In all cases, the models developed here performed better than the Noortman and van Es' model,though by different margins, measured by the Root Mean Squared Error (RMSE). Two different variants of models were tested: unconstrained and constrained (those that replicate a given value of the percentage of empty trips). In the case in which there is a significant amount of zero-order trip chains, i.e., intercity trips, Noortman and van Es' model is outperformed by only 1.32% (unconstrained) and 4.89% (constrained). However, when tested in a situation in which zero order trip chains are less dominant, i.e., urban trips, the best model outperformed Noortman and van Es' model by 9.98% (unconstrained) and 8.63% (constrained). As expected, the unconstrained models perform better that the constrained ones, though by a small margin of less than 5%. The paper also provides evidence of the importance of explicitly modeling empty trips. The RMSEs calculated under the assumption that empty trips are not modeled are significantly higher than the ones corresponding to the best empty trip model. In the case study considered here, these percentage differences range from 57.24% (intercity movements with 31.59% empty trips) to 83.58% (suburban movements with 35.54% empty trips). The paper will focus on the assessment of the practical implications of the models developed by Holguin-Veras and Thorson (2002). Using data from different origin-destination studies, the authors assess the accuracy of the estimates, ease of application and directional implications of both using and not using the empty trip models. The knowledge gained through this examination will provide guidelines to both academicians and practitioners on the use of empty trip models.

#### Publisher

Association for European Transport