Abstract
This paper proposes a compound probability distribution approach for capturing both vehicle-to-vehicle and day-to-day variability in modeling travel time reliability in a network. Starting from the observation that standard deviation and mean of distance-normalized travel time in a network are highly positively correlated and their relationship is well characterized by a linear function, this study assumes multiplicative error structures to describe data with such characteristics and derives a compound distribution to model travel delay per unit distance as a surrogate for travel time. The proposed Gamma-Gamma model arises when (within-day) vehicle-to-vehicle travel delay per unit distance is distributed according to a Gamma distribution, with mean that itself fluctuates from day to day following another Gamma distribution. The study calibrates the model parameters and validates the underlying assumptions using both simulated and actual vehicle trajectory data. The Gamma-Gamma distribution shows good fits to travel delay observations when compared to the (simple) Gamma and Lognormal distributions. The main advantage of the Gamma-Gamma model is its ability to recognize different variability dimensions reflected in travel time data and clear physical meanings of its parameters in connection with vehicle-to-vehicle and day-to-day variability. Based on the linearity assumption for the relationship between mean and standard deviation, two shape parameters of the Gamma-Gamma model are linked to the coefficient of variation of travel delay in vehicle-to-vehicle and day-to-day distributions, respectively, and can be directly estimated from the slope of the associated mean-standard deviation plots. An extension of the basic model form was also introduced to address potential deviations from this linearity assumption. The extended Gamma-Gamma model can account for time-of-day variations in mean-standard deviation relationships-such as hysteresis patterns observed in mean and day-to-day variation in travel time-and incorporate such dynamics in travel time distribution modeling. In summary, the model provides a systematic way of quantifying, comparing, and assessing different types of variability, which is important in understanding travel time characteristics and evaluating various transportation measures that affect reliability.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 40-63 |
| Number of pages | 24 |
| Journal | Transportation Research Part B: Methodological |
| Volume | 80 |
| DOIs | |
| State | Published - Oct 1 2015 |
Funding
This paper is based on research conducted under the Strategic Highway Research Program SHRP-2 project L04 “Incorporating Reliability Performance Measures in Operations and Planning Modeling Tools”, as well as under National Science Foundation Grant No. CMS 0928577 “Toward More Reliable Mobility: Improved Decision Support Tools for Transportation Systems”. The authors would like to acknowledge the support of the Northwestern University Transportation Center. The work presented here reflects valuable comments obtained from the SHRP-2 project Technical Expert Task Group, as well as various collaborators at Northwestern. The authors are especially grateful to William (Bill) Hyman, SHRP-2 reliability program manager and Stephen Andrle, SHRP-2 capacity program manager, for their continued support and encouragement throughout this effort. The paper has greatly benefited from the comments and suggestions of two anonymous reviewers, particularly in the analysis conducted as part of the validation section, and in the extension to consider time-varying conditions. The authors of course remain solely responsible for the content of this paper.
Keywords
- Compound probability distribution
- Gamma-Gamma distribution
- Network performance models
- Network science
- Travel time reliability
- Travel time variability
ASJC Scopus subject areas
- Civil and Structural Engineering
- Transportation