Dynamic differential models for studying traffic flow and density

In this paper, we propose a dynamic stochastic differential model for describing traffic flow based on the Markov chain theory. A key feature of our approach is considering vehicle arrivals and departures, which results in the total number of vehicles in the system varying over time. This makes our proposed transport system dynamic and more realistic. By theoretically and numerically analyzing a simplified model with two speed states, we show our dynamic model obtains accurate fitted values for predicting traffic flow. Analytic solutions for both speed states and the expected values of traffic flow are obtained. By using traffic flow data from the I-80 Freeway Dataset from the NGSIM program, we make predictions on traffic flow and compare our predictions with those of existing approaches. The results show that our proposed approach provides more accurate predictions of traffic flow; thus, dynamic terms are of great significance in constructing traffic flow models.