A decomposition method with discrete abstraction for simultaneous traffic signal control and route selection problem with first-order hybrid Petri Nets

We propose a decomposition method for simultaneous traffic signal control and route selection problem with first-order hybrid Petri Nets. The traffic signal control problem is formulated as an optimal firing sequence problem for first order hybrid Petri Nets where a passage of the vehicles is represented by the real number of vehicles and discrete states represent the traffic signal states. A simultaneous traffic signal control and route selection model is developed with the selection of the route for a specific vehicle with traffic flows with the same traffic signals. A discrete abstraction model is introduced to reduce the computational expense for the Lagrangian relaxation technique. Computational results show the superiority of the discrete abstraction model over existing methods.