A bi-level optimal control approach to route guidance problem considering travelers´ stochastic compliance

The problem of designing route guidance strategies for motorway networks with travelers´ stochastic compliance is considered in this paper. A generic problem formulation is presented in the format of a bi-level optimal control problem with the use of a second-order macroscopic traffic flow model. The problem in the upper level is a stochastic optimal control problem with the discrete control variable which is the states of the variable message signs, while the problem in the lower level is a deterministic optimal control problem with the continuous control variable which is the turning rates at the bifurcation. Next, the sensitivity with respect to travelers´ compliance is utilized to give a deterministic conversion. Finally, a gradient-based numerical solution algorithm is given and the approach is validated in a hypothetic network. Simulation shows that the expectation of the total time spent with the optimal route guidance improves about 23% in average. The efficiency of the optimization in the upper as well as in the lower level is discussed in a detailed example.