Optimal number and location of Bluetooth sensors considering stochastic travel time prediction

Abstract

Determining the optimal number and location of sensors is essential to effectively manage traffic on highways. Optimal solutions dealing with dynamic traffic patterns and relocation of sensors have received little attention. In this study, existing fixed sensors are used to estimate travel time prediction errors at candidate locations where we deploy portable sensors. Potential sampling error of each candidate location is also counted in selecting optimal locations. A two-stage stochastic formulation considers uncertainty of traffic conditions based on scenarios generated by principal component analysis and clustering analysis to uncover the underlying spatial correlations and temporal patterns. The first stage decision, determining the optimal number of sensors, is made before the deployment. The second stage, evaluating the expected travel time prediction errors, specifies sensor arrangements in each scenario. A dynamic model has predefined rearrangement stages. At each stage, sensor locations are modified as the pattern of travel time error changes over time, considering sensor acquisition and relocation expenses. The deterministic and stochastic solutions serve as a lower bound and an upper bound for the dynamic solution. Higher relocation expense leads to more sensors being used, while higher sensor costs leads to fewer sensors being used with more frequent relocations.