Arterial route travel time distribution estimation with a markov chain procedure

The introduction of Intelligent Transportation Systems (ITS) technologies and new sensing hardware promise significant progress in reducing the congestion level in cities. 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 arterial performance measurement and travel time reliability. Speed of vehicles at a given time in the network is not a deterministic quantity over space because of drivers' behaviours (conservative vs. aggressive drivers), the spatial effect of signals (near the signal line vs. further upstream) and temporal-spatial pockets, where average speed is temporarily different than the widespread average (e.g. point bottleneck in a freeway system). In this work, we will analyse the distribution of travel time for routes (expressed as series of links) for a period comparable to a signal cycle. In that way we smooth the variations of traffic for a specific link because of the time-dependent capacity of a signal and the variability in driver's behaviour as many vehicles pass over a link in that period. 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 can be set by basic travel time rules such as free flow travel time and oversaturated conditions. In addition, a heuristic grid clustering optimization method is done to determine boundaries in order to have more analogous states. By applying markov chain procedure, we relate states of 2D diagrams to the following one; compute the transition probabilities, and partial travel time distributions to obtain the arterial route travel time distribution. The procedure with various probe vehicles sample size is tested on an arterial Lincoln Blvd., Los Angeles, CA, during morning peak, which has been simulated in a microscopic simulator. 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. Keywords Grid clustering – Markov chain – Probe vehicle – Travel time distribution-Travel time variability