A methodology for separation of multiple distributions in arterial travel time data
Anderson, James Miller
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Multiple distribution travel time data has been observed in signalized corridors as well as freeway corridors. This behavior is typically caused by congestion, uncoordinated signals, or routes through a coordinated corridor that are not a priority. On the SR140 corridor near the Jimmy Carter Boulevard / I-85 Interchange, it was found that the travel times recorded on the corridor contained multiple distributions and thus a methodology was sought to properly separate the distributions in order to perform more robust statistical analysis. Next, an R statistical language library was found, called “mixtools”, which contained a multiple gamma distribution fitting function called “gammamixEM”. Gamma distributions were chosen for this application as typical travel time distributions tend contain a one sided tail. This function was used in conjunction with a monte-carlo approach to find fits for one to six distributions. The accuracy of the fit was confirmed through visual inspection of the plotted distributions. Then, the Akaike Information Criteria were used to compare the fits to determine the best fit number of distributions. This thesis contains a detailed outline of the algorithm as well as results from the algorithm for the combined Tuesday dataset from this project. It was found that the approach worked well for 60 out of 70 cases. In the 10 cases that were not ideal, the distributional fits make sense on a statistical level, however, for the purposes of the before and after project the next best Akaike Information Criteria value fit may need to used. These 10 cases tended to split obvious single distributions into two distributions, which is not desirable in a before and after analysis where one is not only testing individual distributions before and after construction but also determining if distributions were created or removed as a result of the change in operation of the interchange.