Identification of sensor location and link flow reconstruction using turn ratio and flow sensors in an arterial network

Abstract

In this article, a quadratic programming problem is considered to identify all link flows in an arterial network when there are unmeasured link flows. A graphical method is provided to determine the minimum number of measurements and sensor locations required to obtain a fully observable model. It is shown that this method is also valid for the augmented graph with turn ratio measurements. If the minimum measurements required are met, a fully determined network can be obtained. If there is not enough measurement, a bound on the magnitude of the resulting inaccuracy in terms of vehicle kilometers traveled (VKT) can be calculated by the proposed linear programming method. The model is that of a queueing network; the parameters describe network geometry, saturation flow rates, turning ratios, timing plan and link flows. Three case studies are conducted to validate this approach. The first two cases are to calculate all missing flows by using a few numbers of measurements and minimum number of measurements required, respectively. Upper and lower bounds in terms of VKT are also calculated for these cases. Third case is to obtain a fully determined network with the minimum number of flow measurements when turn ratio sensors are included. Real measurements are collected from a network in Mugla including 55 links and 16 intersections. Vissim simulator is used to analyze the accuracy of the link flow calculations obtained from the proposed method. The results show that the proposed programming method can calculate the missing flows with a high accuracy and short computation time.