Macroscopic parking dynamics and equitable pricing: Integrating trip-based modeling with simulation-based robust optimization

Characterizing the integrated traffic and parking dynamics in a coupled road-parking system is challenging due to the interactions between parking and non-parking vehicles and the presence of cruising-for-parking. In this paper, we propose a new trip-based macroscopic model of parking considering various sources of user heterogeneity that are key to modeling parking. The macroscopic or network fundamental diagram is used to describe the accumulation-based network speed at which vehicles are traveling. An efficient event-based simulation algorithm is proposed as the resolution scheme for the trip-based model. Numerical results reveal that after calibration, the proposed trip-based model yields similar results to those obtained using an accumulation-based approach and microscopic simulation. Taking the trip-based model as the simulation engine, we formulate a simulation-based robust optimization problem of equitable duration-based parking pricing. To solve this problem with simulation stochasticity, a new global optimizer termed NoisyDIRECT is proposed as an open-source solution algorithm. This algorithm automatically identifies the level of simulation stochasticity for each decision vector across the search space, based on which the variable number of simulation runs per point is determined. Thus, the computational resource can be better allocated so that the optimal solution can be found in a more computationally efficient and reliable manner. Numerical results demonstrate that NoisyDIRECT provides better solutions than those yielded by fixed-number sample-path optimization and non-robust optimization methods.