A distribution-fitting-free approach to calculating travel time reliability ratio

A closed-form estimation of the travel time percentile function for characterizing travel time reliability

“…It was used to derive theoretical route choice and network assessment models, such as travel time risk model (Lu et al, 2005(Lu et al, , 2006Di et al, 2008), perceived mean-excess travel time model (Chen et al, 2011;Xu et al, 2013), and mean-excess total travel time model (Xu et al, 2014). Although Zang et al (2018) When travel time datasets cannot satisfy the validity domain after logarithm transformation, rearrangement is further integrated to make the estimated percentile function to be monotone. We rigorously prove that the rearrangement can strictly reduce the estimation error of the Cornish-Fisher expansion.…”

“…Pichler and Selitsch (2000) recommended up to the sixth-order Cornish-Fisher expansion after comparing with Johnson transformation, Delta-Normal, and the fourth-order Cornish-Fisher expansion. However, previous studies (Lu et al, 2005(Lu et al, , 2006Di et al, 2008;Chen et al, 2011;Xu et al, 2013Xu et al, , 2014Zang et al, 2018) in transportation domain only used up to the fourth-order Cornish-Fisher expansion (i.e., the first four moments). The difference between the fourth-order, fifth-order and sixth-order Cornish-Fisher expansion lies in the term of 𝜑 𝑝 in Eq.…”

“…High-quality estimation and monotonicity of the travel time percentile function are critical for characterizing TTR. Besides, this paper focuses on a more fundamental subject-the whole percentile function of TTDs; whileZang et al (2018) calculates a particular metric -TTRR, which only involves the distribution tail of the inverse CDF. Therefore,Zang et al (2018) emphasizes the accuracy of estimating TTRR, while this paper emphasizes the monotonicity required to be a percentile function in mathematical sense and the adaptability/flexibility for capturing heterogeneous TTDs.In this paper, instead of a simple and straightforward adoption, we propose and integrate two important methodological improvements with theoretically proven foundation into the Cornish-Fisher expansion for estimating the travel time percentile function of diverse TTDs.…”

“…Besides, this paper focuses on a more fundamental subject-the whole percentile function of TTDs; whileZang et al (2018) calculates a particular metric -TTRR, which only involves the distribution tail of the inverse CDF. Therefore,Zang et al (2018) emphasizes the accuracy of estimating TTRR, while this paper emphasizes the monotonicity required to be a percentile function in mathematical sense and the adaptability/flexibility for capturing heterogeneous TTDs.In this paper, instead of a simple and straightforward adoption, we propose and integrate two important methodological improvements with theoretically proven foundation into the Cornish-Fisher expansion for estimating the travel time percentile function of diverse TTDs. These two methodological improvements, i.e., logarithm transformation and rearrangement, can greatly improve the estimation accuracy of the Cornish-Fisher expansion while guaranteeing a closed-form expression of travel time percentile function.…”

On the shortest $$\alpha$$-reliable path problem

“…In our case, balancing the tradeoff between computational effort and precision, we fit distributions with three and five phases for each arc. For the fitting process of the time-travel distributions we used Lognormal, Gamma, and Weibull distributions, as they are often used in the literature (Zang et al 2018). Then, we chose the distribution that minimized the 2 estimator of the goodness-of-fit test.…”