A convex model for queue length estimation in a connected vehicle environment

Abstract

This paper presents a convex model for real-time queue length estimation in a connected vehicle environment. The proposed model is based on kinematic wave theory with the assumption of a triangular fundamental diagram. It first identifies the critical points where the traffic state changes, and then estimates the piecewise linear back of queue (BoQ) curve using a convex model. The arrival flow can also be recovered from the estimated BoQ curve. The proposed model does not require a priori information on signal timing, penetration rates or traffic flows. The algorithm is tested with NGSIM data. Results show that the mean absolute error of the algorithm is within 1 cars even for low penetration rates. It is also shown that the algorithm is robust to the measurement errors.