Systematic comparison of trip distribution laws and models

Maxime Lenormand1, Aleix Bassolas1 and José J. Ramasco1

1Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), 07122 Palma de Mallorca, Spain.

(June 2015)

Trip distribution laws are basic for the travel demand characterization needed in transport and urban planning. Several approaches have been considered in the last years. One of them is the so-called gravity law, in which the number of trips is assumed to be related to the population at origin and destination and to decrease with the distance. The mathematical expression of this law resembles Newton's law of gravity, which explains its name. Another popular approach is inspired by the theory of intervening opportunities and it has been concreted into the so-called radiation models. Individuals are supposed to travel until they find a job opportunity, so the population and jobs spatial distributions naturally lead to a trip flow network. In this paper, we perform a thorough comparison between the gravity and the radiation approaches in their ability at estimating commuting flows. We test the gravity and the radiation laws against empirical trip data at different scales and coming from different countries. Different versions of the gravity and the radiation laws are used to estimate the probability that an individual has to commute from one unit to another, called trip distribution law. Based on these probability distribution the commuting networks are simulated with different trip distribution models. We show that the gravity law performs better than the radiation law to estimate the commuting flows, to preserve the structure of the network and to fit the commuting distance distribution although it fails at predicting commuting flows at large distances. Finally, we show that both approaches can be used in absence of detailed data for calibration since the only parameter of both the gravity and the radiation laws depends only on the scale of the geographic unit.