Compound Gamma representation for modeling travel time variability in a traffic network

Kim, Jiwon and Mahmassani, Hani S. (2015) Compound Gamma representation for modeling travel time variability in a traffic network. Transportation Research Part B: Methodological, 80 40-63. doi:10.1016/j.trb.2015.06.011

Author Kim, Jiwon
Mahmassani, Hani S.
Title Compound Gamma representation for modeling travel time variability in a traffic network
Journal name Transportation Research Part B: Methodological   Check publisher's open access policy
ISSN 0191-2615
Publication date 2015-10
Year available 2015
Sub-type Article (original research)
DOI 10.1016/j.trb.2015.06.011
Volume 80
Start page 40
End page 63
Total pages 24
Place of publication Doetinchem, The Netherlands
Publisher Elsevier
Collection year 2016
Language eng
Formatted 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
Keyword Travel time reliability
Travel time variability
Compound probability distribution
Gamma Gamma distribution
Network performance models
Network science
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Civil Engineering Publications
Official 2016 Collection
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Citation counts: TR Web of Science Citation Count  Cited 1 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 1 times in Scopus Article | Citations
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Created: Thu, 16 Jul 2015, 04:45:53 EST by Jiwon Kim on behalf of School of Civil Engineering