On the estimation of arterial route travel time distribution with Markov chains

Abstract

a b s t r a c tRecent advances in the probe vehicle deployment offer an innovative prospect for research in arterial travel time estimation. Specifically, we focus on the estimation of probability distribution of arterial route travel time, which contains more information regarding arterial performance measurements and travel time reliability. One of the fundamental contributions of this work is the integration of travel time correlation of route's successive links within the methodology. In the proposed technique, given probe vehicles travel times of the traversing links, a two-dimensional (2D) diagram is established with data points representing travel times of a probe vehicle crossing two consecutive links. A heuristic grid clustering method is developed to cluster each 2D diagram to rectangular sub spaces (states) with regard to travel time homogeneity. By applying a Markov chain procedure, we integrate the correlation between states of 2D diagrams for successive links. We then compute the transition probabilities and link partial travel time distributions to obtain the arterial route travel time distribution. The procedure with various probe vehicle sample sizes is tested on two study sites with time dependent conditions, with field measurements and simulated data. The results are very close to the Markov chain procedure and more accurate once compared to the convolution of links travel time distributions for different levels of congestion, even for small penetration rates of probe vehicles.

Probabilistic travel time progression and its application to automatic vehicle identification data

“…In fact, the problem of estimating road travel time distributions from link data has previously been tackled by Ramezani and Geroliminis (2012) through the ordinary (non-progressive) sum of independent random variables. In order to account for the dependency between data from across adjacent links, the authors identify regions of homogeneous density within such data.…”

“…Moreover, as we will show, the travel time distribution may exhibit multi-modal structures that cannot be completely defined through statistics like mean, median and standard deviation. Some cluster-based approaches have been proposed to address these issues by treating travel time as a random variable and, simultaneously, dealing with the problem of small samples (Jenelius andKoutsopoulos, 2013, Ramezani andGeroliminis, 2012). However, these approaches are computationally expensive and their accuracy depends on the way the AVI data is clustered (Ramezani and Geroliminis, 2012).…”

“…Some cluster-based approaches have been proposed to address these issues by treating travel time as a random variable and, simultaneously, dealing with the problem of small samples (Jenelius andKoutsopoulos, 2013, Ramezani andGeroliminis, 2012). However, these approaches are computationally expensive and their accuracy depends on the way the AVI data is clustered (Ramezani and Geroliminis, 2012). Furthermore, it is not clear how the length of the road and the number of scanned links within it affects the estimation, when real data is used (Jenelius and Koutsopoulos, 2013).…”

Vehicle Driving Risk Prediction Based on Markov Chain Model

“…Markov chains have been widely used in the engineering field and have already been applied to the area of transportation, such as traffic flow and travel speed forecasting [11][12][13], but have not been extensively researched in driving risk prediction. To solve the problem of driving risk prediction for vehicle collision avoidance, the paper aims to explore a Markov chain driving risk state forecasting model that considers the dynamic changes of real-time driver behavior, road, and environmental characteristics.…”

Modelling reliability and distribution of travel times in transit

“…Correlations across links have been captured by using a Markov chain methodology (Timothy Ramezani and Geroliminis, 2012;Woodard et al, 2015) and a dynamic Bayesian network model (Hofleitner,Herring,Abbeel, et al, 2012;. Ramezani and Geroliminis (2012) used a Markov chain approach to estimate arterial trip TTDs by capturing the spatial correlations using a Transition Probability Matrix (TPM) calibrated from historical data, and assuming that the travel times are independent conditional on link states. Similar to the Markov chain approach, Hofleitner et al (2012a,b) assumed that each link can be in a congested or uncongested state with its own independent and normal TTDs.…”