Optimization of multi-type traffic sensor locations for estimation of multi-period origin-destination demands with covariance effects

The hourly traffic flows between various origin–destination (OD) pairs fluctuate by time of day and day of the year. These multi-period OD demands are statistically correlated with one another because of the inter-relationships of travel patterns over time. In this paper, with a focus on the covariance relationship of OD demands in multiple periods, a novel model is proposed for optimizing the allocations of multi-type traffic sensors by minimizing the uncertainty of OD demand estimates. In the proposed model, both the number and locations of multi-type traffic sensors, including point sensors and automatic vehicle identification (AVI) sensors, are optimized simultaneously with consideration of budget and associated constraints. The mathematical properties of the proposed model are studied to show the significance of multi-period OD flow covariance in the sensor location problem and to examine the trade-off between point sensors and AVI sensors. The firefly algorithm is adapted to solve the problem of multi-type traffic sensor locations for multi-period OD demand estimation. To enhance the estimation efficiency, a Kalman filter method based on the principal component analysis is adopted to extract the essential features of the OD demands and then estimate multi-period OD demand. Numerical examples are presented to demonstrate the effects of OD demand covariance in multiple periods for the multi-type sensor allocation problem.