Monitoring traffic conditions over large road networks has proven a significant challenge for many transportation authorities. However, the rich probe vehicle data that has become available in recent years has great potential to assist with such traffic monitoring. In this work, hydrodynamic theory and horizontal queuing theory are used to derive the joint probability distribution function (PDF) of vehicle location and speed on an arterial road for both under-saturated and congested traffic regimes. The authors specifically consider the effects of signal controllers (including on deceleration, acceleration and queuing) on the distributions of location and speed. This probabilistic model is parameterized by link parameters (red signal time, cycle time, and critical flow density), driving behavior (average deceleration and acceleration, average speed and variation of arrival flow and dissipating flow) and traffic state (arrival flow density) that are learned from historical probe data (location and speed) by maximum likelihood estimation. In a numerical experiment using data collected from private cars in Toyota City’s Green Project of 2011, the Kolmogorov-Smirnov test validates the use of the proposed distributions of vehicle location and speed.
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