A Bayesian stochastic kriging optimization model dealing with heteroscedastic simulation noise for freeway traffic management

Since advanced traveler information and traffic management systems have become popular, it is vital to capture the joint impact of various strategies on transportation systems. Developing analytical models to incorporate traffic dynamics and travel behavior is challenging. Based on observation of the heteroscedasticity of the simulation noise in the stochastic simulator, this paper develops the Bayesian stochastic Kriging (BSK) model to adapt for the heteroscedastic noise and metamodel parameter uncertainty in a Bayesian framework, which enhances the existing surrogate-based optimization methods. This paper presents a metamodel for large scale simulation-based freeway traffic management optimization problems. Simulation-based optimization combines the advantages of simulation models and mathematical optimization methods. The parameter estimation of the BSK model is accomplished by the Bayesian inference. The proposed methodology enables the efficient use of large scale high-resolution traffic simulation models for simulation-based optimization, while accounting for travelers' behavioral responses to information provision.We demonstrate the advantages of BSK compared to other existing metamodels using a numerical example of a synthetic network and a mathematical example. In awork zone scenario on a real-world freeway/arterial corridor of I-270 and MD-355 in the State of Maryland, the BSK model is applied to the freeway traffic management via optimizing the high-occupancy/toll rate and deploying dynamic message signs. Field traffic measurements by loop/microwave detections are used to calibrate travel demand and to supply the simulation parameters. The optimization results are promising in reducing the corridor-wide travel delay and enhancing the vehicle throughput.