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

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. (C) 2002 Elsevier Science Ltd. All rights reserved.