This work proposes a novel formulation for the joint route guidance and demand management the problem, taking into account the uncertainty in traffic demand. Previous attempts to address this problem aimed to minimize the total time spent by all vehicles in the network by determining the optimal routes and departure times, assuming perfect knowledge of traffic demand. In contrast to prior approaches, this work introduces a more realistic model that incorporates uncertain demand. Doing so results to a stochastic model predictive control model with nonconvex nonlinear constraints. To address the stochastic nature of the problem, a scenario-based formulation is introduced, which uses a Gaussian Processes framework to generate multiple scenarios. In addition, an efficient solution methodology over the scenario-based formulation is proposed that relaxes the original nonlinear problem into a linear problem, significantly enhancing its computational tractability. Moreover, in the proposed solution methodology a quadratic reformulation is derived that ensures feasibility over the original problem space. Simulation results demonstrate the superiority of the proposed scenario-based methodology over the worst-case and simplistic averaging approaches.

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