Estimation of Urban Link Travel Time Distribution Using Markov Chains and Bayesian Approaches

Abstract

Despite the wide application of Floating Car Data (FCD) in urban link travel time and congestion estimation, the sparsity of observations from a low penetration rate of GPS-equipped floating cars make it difficult to estimate travel time distribution (TTD), especially when the travel times may have multimodal distributions that are associated with the underlying traffic states. In this case, the study develops a Bayesian approach based on particle filter framework for link TTD estimation using real-time and historical travel time observations from FCD. First, link travel times are classified by different traffic states according to the levels of vehicle delays. Then, a state-transition function is represented as a Transition Probability Matrix of the Markov chain between upstream and current links with historical observations. Using the state-transition function, an importance distribution is constructed as the summation of historical link TTDs conditional on states weighted by the current link state probabilities. Further, a sampling strategy is developed to address the sparsity problem of observations by selecting the particles with larger weights in terms of the importance distribution and a Gaussian likelihood function. Finally, the current link TTD can be reconstructed by a generic Markov Chain Monte Carlo algorithm incorporating high weighted particles. The proposed approach is evaluated using real-world FCD. The results indicate that the proposed approach provides good accurate estimations, which are very close to the empirical distributions. In addition, the approach with different percentage of floating cars is tested. The results are encouraging, even when multimodal distributions and very few or no observations exist.

Period Division-Based Markov Models for Short-Term Traffic Flow Prediction

“…Similarly, other researchers also divided traffic flow data into two parts. But then, they adopted two of the ARIMA model, the support vector machine, the generalized autoregressive conditional heteroscedasticity (GARCH) model and the Markov model to predict the two parts of traffic flow data [25][26][27][28][29][30]. To accurately capture the change rules of short-term traffic flow, Zhang et al [31] and Yang et al [32] divided traffic flow data into three parts, including the periodic trend, the deterministic part and the volatility part, and they pointed out that the volatility part is extremely important for short-term traffic flow prediction.…”

Minimum Sampling Size of Floating Cars for Urban Link Travel Time Distribution Estimation

“…It is clear from the determination results that, of all 52 periods, only 19 can yield the minimum sample size ranges from 5 to 14. However, it can still be observed that more samples in the range of [7,14] during peak periods are needed than those in the range of [5,10] during off-peak periods.…”

“…Probability distributions contain more information, such as percentiles, skewness and multimodality, that enable the monitoring of the varying characteristics of travel times on links ( 7 ). Recently, several attempts have been made to investigate the sample size necessary to ensure that the travel time observations generated from FCD can represent the link between TTDs and statistical reliability.…”

“…Compared with uninterrupted traffic flow on freeways, the travel times of urban road links are heavily affected by traffic lights, pedestrian crossings, bus stops, roadside parking, interactions among vehicles, and conflicting traffic from cross streets ( 4 – 6 ). The interrupted nature of traffic flow on urban roads would lead to different clusters of travel times, reflecting how vehicles experienced traffic states on a given link ( 7 ). Therefore, rather than provide the average travel times that is generally used in planning applications, a probability distribution, which fully characterizes different components of travel times containing maximum traffic state information, is preferred ( 8 , 9 ).…”

Short-Term Traffic Forecasting Using Deep Learning

“…Traffic forecasting based on knowledge-driven methods mainly use queuing theory to simulate user behaviour [2] while data-driven approach for traffic congestion prediction are centred on time series-based models. Traditional time series methods as Auto-Regressive Integrated Moving Average (ARIMA) [3], Kalman filtering [4,5], principal component analysis [6], mixture models and Markov chain [7,8] may be applicable to predicting recurrent congestion as a process that is repetitive and periodic. Non-stationary effect however may not be easily captured through time series methods as well as spatial effects of congestion and they cannot mine the deep relationships between data.…”