This paper establishes a relationship between the concept of hedging point, first introduced in the realm of FMS flow control models, and the turnpike property, a key concept in infinite horizon control problems arising in economic planning models. To establish this link one considers a general class of piecewise deterministic control systems that encompasses FMS flow control as well as other related models. One uses the Markov renewal decision process formalism to characterize optimal policies via a discrete event dynamic programming approach. A family of control problems with a random stopping time is associated with these optimality conditions. These problems can be reformulated as infinite horizon deterministic control problems. It is then shown how the turnpike property should hold for these deterministic control problems under classical convexity assumptions. These turnpikes have the same generic properties as the hedging points, obtained via a problem specific approach, in FMS flow control models.