A Markova-Chain Approach to Model Vehicles Traffic Behavior

The ability to accurately predict freeway traffic conditions in the near future has recently gained prominence as it plays a crucial role in the fundamental traffic management functions and trip decision making processes. This study proposes a stochastic approach, the Markov chain Model, for short-term freeway traffic prediction during 24 hours, taking into account the dynamic and stochastic nature of traffic flow by means of the Markov chain process’s transition matrix. The research utilized data collected by real-time traffic monitoring devices on the clockwise M25 highway in the United Kingdom between junction 13 and junction 14 for a full 24 hours. For the first method, a first order Markov chain transition probability matrix is used to characterize the subsequent traffic flow value based on the current and previous values. To estimate the unknown transition probabilities from the observed transition counts in a time series of the vehicles’ flow over time, a Discrete Time Markov Model was calibrated using the maximum likelihood estimate method. The method’s ability to preserve the expected flow’s statistical properties is evaluated by comparing the two sets of data. Mean, standard deviation, maximum, minimum, percentiles, and autocorrelations of traffic flow values are the most popular statistical properties used for this purpose. The modeled autocorrelation coefficients for a first order Markov chain are very close to the measured autocorrelations, with a root mean square error (RMSE) of (0.0065) for the first five autocorrelations’ coefficients. When actual traffic levels are compared to expects, it is clear that statistical characteristics have been maintained satisfactorily.