Short-term traffic flow forecasting based on Markov chain model

In this paper, the traffic flow is modeled as a high order Markov chain. And the transition probability from one state to the other state describes, given the current and recent values of the traffic flow, what the future value will be. Under the criteria of minimum mean square error, the optimal prediction is given as the conditional expectation according to the transition probability. However, in general, the transition probability is not known beforehand and we even don´t know its form exactly. Gaussian Mixture Model (GMM), whose parameters are estimated with Expectation Maximum (EM) algorithm, is applied to approximate the transition probability. Then the representation of the optimal forecasting is given in terms of the parameters in GMM. A case study with real traffic data obtained from UTC/SCOOT system in Beijing shows the applicability and effectiveness of our proposed model.