A Simulation-Optimization Framework for Robust Time-Dependent Toll Pricing Under Demand Uncertainty

This study presents a Distributional Robust Simulation Optimization (DRSO) framework for optimizing time-of-day toll pricing under uncertain traffic demand. Traditional pricing models often rely on deterministic assumptions, leading to suboptimal performance under real-world demand variability. To address this, our two-stage stochastic-robust approach first models demand uncertainty using data-driven stochastic processes, capturing key statistical properties of traffic fluctuations. In the second stage, we integrate Optimal Computational Budget Allocation (OCBA) to efficiently allocate computational resources, refining toll price decisions while ensuring robustness against worst-case scenarios. The proposed DRSO model is rigorously tested on both theoretical queuing systems and a real-world case study (Anaheim network), demonstrating superior performance compared to conventional stochastic and robust optimization methods. Key results show that DRSO reduces worst-case travel times by 12-18% while maintaining system efficiency under demand volatility. Additionally, our framework provides practical insights for policymakers by balancing revenue stability and congestion mitigation. These findings highlight DRSO’s potential as a scalable, data-adaptive tool for complex transportation pricing problems under uncertainty.