A Novelty Markov Design to Model Traffic in a Road Network

Traffic congestion in the urban areas has become an unremitting problem faced by city planners. Stochastic Methods such as Markov Chains and Monte Carlo Simulations produce fruitful results, hence, are proven to be highly effective in terms of predictions along a segment of highway, freeway etc. However, a major drawback of these methods is the lack of feasibility when applying to the road networks in whole, due to the high complexity of road network. Our work introduces a novelty concept based on Markov Models to overcome the above drawback of stochastic models when applied to traffic congestion in a road network in whole. The research focuses on striking a balance between the route capacity and total surface area of vehicles of each type. A road system with multiple junctions and lanes is considered and represented in matrix form. The counts of each vehicle type that enters a road segment are also represented in matrix form. Thereafter, the total surface area of vehicles occupying each road segment is expressed as a proportion of road capacity. We estimate the traffic state transition for each corresponding segment. Such transition matrices can be used to identify the converging traffic state in future. We initially conduct simulation runs for different initial conditions. The proposed method successfully provides transition matrices for the given road network. Future studies involve extending the proposed method by considering other factors such as the vehicles parked on either sides of the roadway, vehicle speed and weather conditions.