Applying Finite Mixture Models to New York City Travel Times

Abstract

The distribution of travel times in high density urban environments is observed to be multimodal as a result of random demand fluctuations, nonrecurrent incidents, and other interruptions. Conventional travel time measures that use indices from unimodal distributions, such as average speed, cannot accurately reflect true traffic conditions in the network. Finite mixture models (FMMs) are a natural choice to represent the distribution of travel times in such settings. In this study, travel times in Midtown Manhattan collected from radio frequency identification device (RFID) transponders are used to test and validate three FMMs. The three models are the Poisson mixture, the Gaussian mixture, and the Gamma mixture. The first two are fitted using the expectation-maximization algorithm and the third using sparse approximation techniques. The Gaussian and Gamma mixture models are demonstrated as capturing the clustering in the travel time data. The Gamma mixture is demonstrated as being slightly superior in terms of generalizability to out-of-sample test data. This case study indicates the potential for a feasible performance measure of the status of urban traffic that is frequently interrupted by signal controls.