Markov modeling of traffic flow in Smart Cities

Modeling and simulating the traffic flow in large urban road networks are important tasks. A mathematically rigorous stochastic model proposed in [8] is based on the synthesis of the graph and Markov chain theories. In this model, the transition probability matrix describes the traffic dynamics and its unique stationary distribution approximates the proportion of the vehicles at the segments of the road network. In this paper various Markov models are studied and a simulation method is presented for generating random traffic trajectories on a road network based on the two-dimensional stationary distribution of the models. In a case study we apply our method to the central region of the city of Debrecen by using the road network data from the OpenStreetMap project which is available publicly.