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

Empirical studies have revealed that travel time variability (TTV) can significantly affect travelers' behaviors and planners' cost-benefit assessment of transportation projects. It is therefore important to systematically quantify the value of TTV (VTTV) and its impact. Recently, Fosgerau's valuation method makes this quantification possible by converting the value of travel time (VTT) and the VTTV into monetary unit. Travel time reliability ratio (TTRR), defined as a ratio of the VTTV to the VTT, is a key parameter in Fosgerau's valuation method. Calculating TTRR involves an integral of the inverse cumulative distribution function (CDF) of the standardized travel time distribution (STTD), i.e., the mean lateness factor. Using a well-fitted STTD is a straightforward way to calculate TTRR. However, it will encounter the following challenges: (1) determination of a well-fitted STTD; (2) non-existence of an algebraic expression for the CDF and its inverse CDF; and (3) lack of a closed-form expression to efficiently calculate TTRR. To circumvent the above issues, this paper proposes a distribution-fitting-free analytical approach based on the Cornish-Fisher expansion as an alternative way to calculate TTRR without the need to fit the whole CDF. The validity domain is rigorously derived for guaranteeing the accuracy of the proposed method. Realistic travel time datasets that cover 17 links are used to systematically explore the feature and accuracy of the proposed method in estimating TTRR. The comparative results demonstrate that the proposed method can efficiently and effectively estimate TTRR. When travel time datasets satisfy the validity domain, the proposed method outperforms the distribution fitting method in estimating TTRR.