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

Abstract

a b s t r a c tThis 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 GammaGamma distribution shows good fits to travel delay observations when compared to the (simple) Gamma and Lognormal distributions. The main advantage of the GammaGamma 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 GammaGamma 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.

Travel Time Reliability for Urban Networks: Modelling and Empirics

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Heterogeneous perimeter flow distributions and MFD-based traffic simulation

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Calculation of Urban Transportation Network Reliability Considering Correlation Among the Links Comprising a Route

“…Other researchers studied the relationship between average travel time per unit distance and standard deviation of travel time (see for example [30,[33][34][35]), and also optimal routes across a potential network (see for example [2,36]). Kim et al [37] proposed a mixed gamma distribution for modeling the variations of travel time across a road network. They found that the mixed gamma distribution is the best distribution for travel time estimation, with different dimensions of changes in relation to daily variations and vehicle type.…”