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…