Markov Chain Procedure for Arterial Route Travel Time Distribution Estimation

Recent advances in the GPS technology and the probe vehicles deployment offer an innovative prospect for arterial travel time research. Specifically, we focus on estimation of arterial route travel time distribution which contains more information in regard to traffic network performance measurement. In the proposed technique, probe vehicles provide travel time of the traversing links. For each two consecutive links, a two‐dimensional (2D) diagram is established so that data points represent travel times of a probe vehicle crossing both two aforementioned links. States in the 2D diagrams (defined as rectangular clusters) consist of data with homogenous travel times. The state boundaries are set by simple travel time rules such as free flow travel time and oversaturated conditions. In addition, a heuristic biclustering optimization method is done to determine boundaries in order to have more analogous states. Applying markov chain procedure, we relate states of 2D diagrams to the following ones; compute the transition probabilities, and partial travel time distributions to obtain the arterial route travel time distribution. The procedure is tested on a five links arterial Lincoln Blvd., Los Angeles, CA, during morning peak, which has been simulated in a microscopic simulation environment. The simulated results are very close to the markov chain procedure and more accurate once compared to the convolution of links travel time distributions. The promising results capture the fundamental characteristic of field measurements.