On Time-Dependent Trip Distance Distribution with For-Hire Vehicle Trips in Chicago

Abstract

For transportation system analysis in a new space dimension with respect to individual trips’ remaining distances, vehicle trips demand has two main components: the departure time and the trip distance. In particular, the trip distance distribution (TDD) is a direct input to the bathtub model in the new space dimension, and is a very important variable to consider in many applications, such as the development of distance-based congestion pricing strategies or mileage tax. For a good understanding of the demand pattern, both the distribution of trip initiation and trip distance should be calibrated from real data. In this paper, it is assumed that the demand pattern can be described by the joint distribution of trip distance and departure time. In other words, TDD is assumed to be time-dependent, and a calibration and validation methodology of the joint probability is proposed, based on log-likelihood maximization and the Kolmogorov–Smirnov test. The calibration method is applied to empirical for-hire vehicle trips in Chicago, and it is concluded that TDD varies more within a day than across weekdays. The hypothesis that TDD follows a negative exponential, log-normal, or Gamma distribution is rejected. However, the best fit is systematically observed for the time-dependent log-normal probability density function. In the future, other trip distributions should be considered and also non-parametric probability density estimation should be explored for a better understanding of the demand pattern.

Effect of the trip-length distribution on network-level traffic dynamics: Exact and statistical results

“…In addition, the empirical trip length distributions from American and European cities reported in Martínez and Jin (2021), Thomas and Tutert (2013) strongly suggest that the exponential distribution exhibits the correct overall trend of the data. Adding the main result of this paper that the statistical properties of congestion are largely independent of the distribution choice, which only affects the transient behavior of the system, makes a compelling argument in favor of the exponential assumption.…”

Effect of the Trip-Length Distribution on Network-Level Traffic Dynamics: Exact and Statistical Results

“…Finally, the empirical trip length distributions from American and European cities (Martínez andJin, 2021, Thomas andTutert, 2013) strongly suggest to the author that the exponential distribution exhibits the correct overall trend of the data, except for very short trips < 1.5mi, which explains why the lognormal distribution was proposed as a good candidate by the authors in Martínez and Jin (2021). (Notice that this empirical data applies for a singlereservoir scenario, but not for a multi-reservoir context .)…”

“…Notice that for the exponential distribution, (28) gives f X = f , as expected given the memoryless property of this distribution 3 This means that the expected remaining trip length is E {X} = E {L}, as can be verified in (29) with C 2 L = 1. For other distributions this is not the case, however, where E {X} < E {L} for distributions with light tails, as it appears to be the case in practice (Martínez andJin, 2021, Thomas andTutert, 2013). However, it would not be surprising to find cases where the trip length distribution is heavy tailed, such as the power-law distribution which is so prevalent in complex systems (Mori et al, 2020), where E {X} > E {L}.…”

“…He points out that extracting dynamic behavior from the model is possible for slow-varying demands, providing the foundations for the macroscopic modeling of cities. Despite some confusion in the literature (Jin, 2020, Johari et al, 2021, Batista et al, 2021b, Martínez and Jin, 2021, Johari et al, 2022, the role played by the exponential distribution in this model surfaced in the literature not until Arnott (2013) who considers it an unrealistic assumption. As it turns out, this important observation that (3) follows from assuming exponentially distributed trip lengths, appears to have its origins in Vickrey (1991) although it was not published until Vickrey (2020) as described in Jin (2020).…”

A Big Data Analysis on Urban Mobility: Case of Bangkok

“…Nonetheless, a statistical test is not employed in these studies. In [13], the statistical distribution of taxi trip distance in Chicago is investigated. A Kolmogorov-Smirnov (K-S) test is used to evaluate the goodness-of-fit.…”