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A Linear Formulation of The On-Time Arrival Problem in Multi-Regional Networks

This work proposes a convex formulation of the on-time arrival problem based on macroscopic traffic dynamics. The on-time arrival problem is modeled as an optimization program that jointly solves the demand management and route guidance strategies. The objective is to manage the routes (route guidance) and departure times (demand management) of all demands such that vehicles reach their destination at a desired time. The proposed problem is formulated as a nonconvex nonlinear multi-objective optimization program that is solved efficiently by relaxing the original nonlinear problem into a linear lower bound solution. Furthermore, considering that lower bound solution may result in infeasible control decisions, this work proposes a simulation-based feedback mechanism to transform the lower bound solution into a good quality upper bound feasible solution. Finally, simulation results demonstrate that the proposed solution can significantly reduce congestion and ensure that all vehicles arrive at their destination on their desired time.