Freeway Sensor Spacing and Probe Vehicle Penetration

Accurate travel time prediction–estimation is important for advanced traveler information systems and advanced traffic management systems. Traffic managers and operators are interested in estimating optimal sensor density for new construction and retrofits. In addition, with the development of vehicle-tracking technologies, they may be interested in estimating optimal probe vehicle percentage. Unlike most studies focusing on data-driven models, this paper extends some limited previous work and describes a concept developed from first principles of traffic flow. The goal is to establish analytical relationships between travel time prediction–estimation accuracy and sensor spacing by means of two basic travel time prediction–estimation algorithms, as well as to probe vehicle penetration rate. The methods are based on computing the magnitude of under- and overprediction–estimation of total travel time (TTT) during shock passages in a time–space plane by using the midpoint method for online travel time prediction and the Coifman method for offline travel time estimation. Three shock wave configurations are assessed with each method so as to consider representative traffic dynamics situations. TTT prediction–estimation errors are calculated and expressed as a function of sensor spacing and probe vehicle percentage. Optimal sensor spacing is calculated with consideration of the tradeoff between TTT estimation error and sensor deployment cost. The results from this study can provide simple and effective support for detector placement and probe vehicle deployment, especially along a freeway corridor with existing detectors. Optimal sensor spacing results are analyzed and compared for various methods of travel time estimation during different types of shock waves.