 Compound Gamma representation for modeling travel time variability in a traffic networkJiwon Kim and Hani S. Mahmassani Transportation Research Part B: Methodological, 2015, vol. 80, issue C, 40-63 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. Keywords: Travel time reliability; Travel time variability; Compound probability distribution; Gamma–Gamma distribution; Network performance models; Network science (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:transb:v:80:y:2015:i:c:p:40-63 Ordering information: This journal article can be ordered from DOI: 10.1016/j.trb.2015.06.011 Access Statistics for this article Transportation Research Part B: Methodological is currently edited by Fred Mannering More articles in Transportation Research Part B: Methodological from Elsevier |
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