Estimating Freeway Travel Time Reliability for Traffic Operations and Planning

Abstract

Travel time reliability (TTR) has attracted increasing attention in recent years, and is often listed as one of the major roadway performance and service quality measures for both traffic engineers and travelers. Measuring travel time reliability is the first step towards improving travel time reliability, ensuring on-time arrivals, and reducing travel costs. Four components may be primarily considered, including travel time estimation/collection, quantity of travel time selection, probability distribution selection, and TTR measure selection. Travel time is a key transportation performance measure because of its diverse applications and it also serves the foundation of estimating travel time reliability. Various modelling approaches to estimating freeway travel time have been well developed due to widespread installation of intelligent transportation system sensors. However, estimating accurate travel time using existing freeway travel time models is still challenging under congested conditions. Therefore, this study aimed to develop an innovative freeway travel time estimation model based on the General Motors (GM) car-following model. Since the GM model is usually used in a micro-simulation environment, the concepts of virtual leading and virtual following vehicles are proposed to allow the GM model to be used in macro-scale environments using aggregated traffic sensor data. Travel time data collected from three study corridors on I-270 in St. Louis, Missouri was used to verify the estimated travel times produced by the proposed General Motors Travel Time Estimation (GMTTE) model and two existing models, the instantaneous model and the time-slice model. The results showed that the GMTTE model outperformed the two existing models due to lower mean average percentage errors of 1.62% in free-flow conditions and 6.66% in two congested conditions. Overall, the GMTTE model demonstrated its robustness and accuracy for estimating freeway travel times. Most travel time reliability measures are derived directly from continuous probability distributions and applied to the traffic data directly. However, little previous research shows a consensus of probability distribution family selection for travel time reliability. Different probability distribution families could yield different values for the same travel time reliability measure (e.g. standard deviation). It is believe that the specific selection of probability distribution families has few effects on measuring travel time reliability. Therefore, two hypotheses are proposed in hope of accurately measuring travel time reliability. An experiment is designed to prove the two hypotheses. The first hypothesis is proven by conducting the Kolmogorov–Smirnov test and checking log-likelihoods, and Akaike information criterion with a correction for finite sample sizes (AICc) and Bayesian information criterion (BIC) convergences; and the second hypothesis is proven by examining both moment-based and percentile-based travel time reliability measures. The results from the two hypotheses testing suggest that 1) underfitting may cause disagreement in distribution selection, 2) travel time can be precisely fitted using mixture models with higher value of the number of mixture distributions (K), regardless of the distribution family, and 3) the travel time reliability measures are insensitive to the selection of distribution family. Findings of this research allows researchers and practitioners to avoid the work of testing various distributions, and travel time reliability can be more accurately measured using mixture models due to higher value of log-likelihoods. As with travel time collection, the accuracy of the observed travel time and the optimal travel time data quantity should be determined before using the TTR data. The statistical accuracy of TTR measures should be evaluated so that the statistical behavior and belief can be fully understood. More specifically, this issue can be formulated as a question: using a certain amount of travel time data, how accurate is the travel time reliability for a specific freeway corridor, time of day (TOD), and day of week (DOW)? A framework for answering this question has not been proposed in the past. Our study proposes a framework based on bootstrapping to evaluate the accuracy of TTR measures and answer the question. Bootstrapping is a computer-based method for assigning measures of accuracy to multiple types of statistical estimators without requiring a specific probability distribution. Three scenarios representing three traffic flow conditions (free-flow, congestion, and transition) were used to fully understand the accuracy of TTR measures under different traffic conditions. The results of the accuracy measurements primarily showed that: 1) the proposed framework can facilitate assessment of the accuracy of TTR, and 2) stabilization of the TTR measures did not necessarily correspond to statistical accuracy. The findings in our study also suggested that moment-based TTR measures may not be statistically sufficient for measuring freeway TTR. Additionally, our study suggested that 4 or 5 weeks of travel time data is enough for measuring freeway TTR under free-flow conditions, 40 weeks for congested conditions, and 35 weeks for transition conditions. A considerable number of studies have contributed to measuring travel time reliability. Travel time distribution estimation is considered as an important starting input of measuring travel time reliability. Kernel density estimation (KDE) is used to estimate travel time distribution, instead of parametric probability distributions, e.g. Lognormal distribution, the two state models. The Hasofer Lind - Rackwitz Fiessler (HL-RF) algorithm, widely used in the field of reliability engineering, is applied to this work. It is used to compute the reliability index of a system based on its previous performance. The computing procedure for travel time reliability of corridors on a freeway is first introduced. Network travel time reliability is developed afterwards. Given probability distributions estimated by the KDE technique, and an anticipated travel time from travelers, the two equations of the corridor and network travel time reliability can be used to address the question, "How reliable is my perceived travel time?" The definition of travel time reliability is in the sense of "on time performance", and it is conducted inherently from the perspective of travelers. Further, the major advantages of the proposed method are: 1) The proposed method demonstrates an alternative way to estimate travel time distributions when the choice of probability distribution family is still uncertain; 2) the proposed method shows its flexibility for being applied onto different levels of roadways (e.g. individual roadway segment or network). A user-defined anticipated travel time can be input, and travelers can utilize the computed travel time reliability information to plan their trips in advance, in order to better manage trip time, reduce cost, and avoid frustration.