An application of Bayesian Hidden Markov Models to explore traffic flow conditions in an urban area

Abstract: This study employs Bayesian Hidden Markov Models as method to explore vehicle traffic flow conditions in an urban area in Stockholm, based on sensor data from separate road positions. Inter-arrival times are used as the observed sequences. These sequences of inter-arrival times are assumed to be generated from the distributions of four different (and hidden) traffic flow states; nightly free flow, free flow, mixture and congestion. The filtered and smoothed probability distributions of the hidden states and the most probable state sequences are obtained by using the forward, forward-backward and Viterbi algorithms. The No-U-Turn sampler is used to sample from the posterior distributions of all unknown parameters. The obtained results show in a satisfactory way that the Hidden Markov Models can detect different traffic flow conditions. Some of the models have problems with divergence, but the obtained results from those models still show satisfactory results. In fact, two of the models that converged seemed to overestimate the presence of congested traffic and all the models that not converged seem to do adequate estimations of the probability of being in a congested state. Since the interest of this study lies in estimating the current traffic flow condition, and not in doing parameter inference, the model choice of Bayesian Hidden Markov Models is satisfactory. Due to the unsupervised nature of the problematization of this study, it is difficult to evaluate the accuracy of the results. However, a model with simulated data and known states was also implemented, which resulted in a high classification accuracy. This indicates that the choice of Hidden Markov Models is a good model choice for estimating traffic flow conditions.