Fast Boundary Flow Prediction for Traffic Flow Models using Optimal Autoregressive Moving Average with Exogenous Inputs (ARMAX) Based Predictors

Traffic Management Centers (TMC) want to improve the performance of road networks and reduce congestion by actively managing the infrastructure of a freeway corridor. A promising avenue for proactive traffic management is the prediction of the near-future traffic conditions in real-time by employing a traffic flow model. An important set of calibration parameters of such a model are the boundary flows, i.e., the amount of traffic that is expected to enter the network during the prediction horizon. In this paper, we propose a boundary flow prediction method that combines the most recent traffic data with historical traffic data. An autoregressive moving average with exogenous input (ARMAX) is estimated on-line based on the most recent vehicle detector station (VDS) data. An optimal multiple step ahead traffic demand predictor is obtained based on the estimated ARMAX model by solving a corresponding Bezout equation for each predictor. Results obtained using empirical freeway mainline and on-ramp data show that this method outperforms methods that rely only on the historical average of the data to perform a prediction, especially during days with unusual traffic flow demands, such as a Super Bowl Sunday. Due to its simplicity and robustness, this method is useful in practical applications.