Queue Estimation in a Connected Vehicle Environment: A Convex Approach

This paper proposes a convex optimization based algorithm for queue profile estimation in a connected vehicle environment, which can also be used for trajectory reconstruction, delay evaluation, etc. This algorithm generalizes the widely-adopted assumption of a linear back of queue (BoQ) curve to a piecewise linear BoQ curve to consider more practical scenarios. The piecewise linear BoQ curve is estimated via a convex optimization model, ensuring efficient computation. Moreover, this paper explicitly handles cases with low penetration rates and low sampling rates, as well as measurement noises. In addition, the proposed methodology is extended to an urban arterial, reusing the estimated departure information from the upstream intersections to further improve the estimation accuracy. Finally, two online implementation approaches are presented to perform real-time queue estimation. The proposed methodology is tested with two datasets: the Lankershim data set in the NGSIM project and the simulated dataset of Wehntalerstrasse, Zürich, Switzerland. Results show that the error is less than 1.5 cars in undersaturated scenarios and 5.2 cars in oversaturated scenarios if the penetration rates are larger than 0.1 and sampling rates are higher than 0.05 s^-1. It is demonstrated that by considering a piecewise linear BoQ curve, the estimation accuracy can be improved by up to 16%. Incorporating flow successfully can also reduce the estimation error by up to 16%. Results further show that the proposed methodology is robust to measurement errors. It is finally shown that the proposed framework can be solved within a reasonable time (0.8 s), which is sufficient for most real-time applications.