Ellen Thorson

Modeling commercial vehicle empty trips with a first order trip chain model

Abstract 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 of the 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 of the benefits of including a memory function. The paper also provides empirical evidence of the importance of modeling 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.

Trip Length Distributions in Commodity-Based and Trip-Based Freight Demand Modeling: Investigation of Relationships

Commodity-based and vehicle-trip-based freight demand modeling is discussed. The characteristics of the trip length distributions (TLDs) are examined, defined in terms of tons, as required in commodity-based modeling, and in vehicle trips, as required in trip-based modeling. With data used from a major transportation study in Guatemala, the TLDs are estimated for both tons and vehicle trips. The analysis revealed that (a) the shape of the TLDs depends upon the type of movements being considered; (b) TLDs defined in terms of tonnage differ significantly from those defined in terms of vehicle trips; (c) TLDs for different types of vehicles, transporting similar commodities, reflect the range of use of each type of vehicle; (d) though tons TLDs and vehicle TLDs are different, the relationship between them seems to follow a systematic pattern that, if successfully identified, would enable transportation planners to estimate one type of TLD given the other; and (e) major freight generators affect the shape of the TLDs, so complementary models may be needed to provide meaningful depictions of freight movements.

Practical Implications of Modeling Commercial Vehicle Empty Trips

Implications of modeling commercial vehicle empty trips are discussed, a theoretical derivation for parameter estimation is provided, and insight is given into the order of magnitude of estimation errors because of the improper modeling of commercial vehicle empty trips. A set of relatively simple cases was designed to illustrate the most important implications. Also addressed are estimation errors from using naïve approaches to compensate for the lack of explicit modeling of empty trips and the errors associated with more advanced empty trip models. In the simplest simulation, directional errors for a basic complementary model were from three to six times fewer than those for the naïve models. In the more complex case, a more sophisticated complementary model performed slightly better than the basic model and both complementary models were considerably better than the naïve approaches. The directional errors for the naïve models were four to seven times greater than those for the complementary models. Moreover, an analysis of the statistical distributions of the errors indicated that the complementary models had higher probabilities of producing accurate results, whereas the naïve approaches had higher probabilities of producing very large errors. These analyses indicate that the naïve approaches translate into significant errors in directional-traffic estimates. For that reason, their use should be discontinued in favor of the more advanced models presented.

Time-Dependent Effects on Parameters of Freight Demand Models: Empirical Investigation

Seven national freight origin-destination samples collected in Colombia from 1999 to 2005 were used to conduct an empirical investigation of the temporal stability of parameters of freight demand models in the short to medium term. Freight generation, freight distribution, and empty trip models were considered. To identify time-dependent effects, models were estimated with a panel formulation with time-dependent parameters and fixed time effects and then compared with the corresponding cross-sectional models. The results indicate the presence of statistically significant time-dependent effects on all freight generation models (production and attraction), freight distribution models (based on both loaded vehicle trips and commodity flows), and empty trip models. A literature review indicates that few studies are available on the temporal stability of parameters. The results show a remarkably consistent pattern in that the components of freight demand that could change faster (i.e., freight production and attraction) are those that exhibit the largest rates of parameter change. The rates of change for these models are 18.29% and 26.37%, respectively. In contrast, the freight distribution models of loaded trips were found to change less rapidly (10.50% and 1.94%, respectively, depending on the impedance function), while the tonnage distribution model exhibited only fixed time effects. The model that changes least rapidly is the empty trip model, which has a rate of change of 0.83%.