  The estimation of travel time distribution (TTD) is critical for reliable
route guidance and provides theoretical bases and technical support for
advanced traffic management and control. The state-of-the art procedure for
estimating arterial TTD commonly assumes that the path travel time follows a
certain distribution without considering segment correlation. However, this
approach is usually unrealistic as travel times on successive segments may be
dependent. In this study, copula functions are used to model arterial TTD as
copulas are able to incorporate for segment correlation. First, segment
correlation is empirically investigated using day-to-day GPS data provided by
BMW Group for one major urban arterial in Munich, Germany. Segment TTDs are
estimated using a finite Gaussian Mixture Model (GMM). Next, several copula
models are introduced, namely Gaussian, Student-t, Clayton, and Gumbel, to
model the dependent structure between segment TTDs. The parameters of each
copula model are obtained by Maximum Log Likelihood Estimation. Then, path TTDs
comprised of consecutive segment TTDs are estimated based on the copula models.
The scalability of the model is evaluated by investigating the performance for
an increasing number of aggregated links. The best fitting copula is determined
in terms of goodness-of-fit test. The results demonstrate the advantage of the
proposed copula model for an increasing number of aggregated segments, compared
to the convolution without incorporating segment correlations.
