Optimization of multi-type sensor locations for simultaneous estimation of origin-destination demands and link travel times with covariance effects

Abstract

This paper investigates the multi-type traffic sensor location problem for simultaneous estimation of origin-destination (OD) demands and link travel times while also considering the two sources of spatial covariance effects on a road network with uncertainties. The first source is the statistical correlation of the vehicular traffic demands for different OD pairs in a typical hourly period (e.g., morning peak hour) on a daily scale, as the travel demand patterns vary daily, weekly, and seasonally over the year. The second source is the stochastic nature of the link travel times on different road links during the peak hour period and their correlation with adjacent links in congested conditions. By considering these aspects, a novel model is formulated to optimize the number and locations of multi-type traffic sensors for simultaneous estimation of stochastic OD demands and link travel times during the same peak-hour period over a year. This estimation is supported by the data recorded by multi-type traffic sensors such as point sensors and automatic vehicle identification sensors, which yield the link speed/flow and path travel time information, respectively. Based on the integrated observations from multi-type traffic sensors, a novel Kullback–Leibler divergence-based model is developed to accommodate different probability distributions of OD demands and link travel times in different traffic conditions. Moreover, an improved firefly algorithm is developed to solve the multi-type sensor location problem. Specifically, the search strategy of this algorithm is enhanced by considering the mean and covariance of the OD demands and link travel times. Numerical examples of synthetic and real-world road networks are used to illustrate the applications and merits of the developed multi-type sensor location model for simultaneously estimating the OD demands and link travel times while also considering covariance effects.