Use of Probe Vehicle Data to Determine Joint Probability Distributions of Vehicle Location and Speed on an Arterial Road

Abstract

Monitoring traffic conditions over large road networks is a significant challenge for many transportation authorities. However, the rich data from probe vehicles that have become available in recent years can assist with such traffic monitoring. Hydrodynamic theory and horizontal queuing theory are used to derive the joint probability distribution function of vehicle location and speed on an arterial road for undersaturated and congested traffic conditions. Specifically considered are the effects of signal controllers (including 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) obtained from historical probe data (for location and speed) with maximum likelihood estimates. In a numerical experiment with data collected from private cars in Toyota City, Japan, for the 2011 Green Project, the Kolmogorov–Smirnov test validates the use of the proposed distributions of vehicle location and speed.