In the railway infrastructure, positive train control (PTC) is an automated method for controlling and monitoring train movements to ensure safe travel by enforcing safe braking distances and speed limits, even if the locomotive driver fails to act within the specified guidelines. Obviously, it is vital to assure the timely delivery of control messages to the on-board computer system that implements PTC for a locomotive. In particular, the parameters for the timely delivery of control messages must be evaluated and specified. The delivery times of the control messages are directly impacted by the locomotive speed and braking characteristics. Train braking is characterized by braking curves that express speed as a function of distance or position. This paper utilizes numerical techniques to convert braking curves into functions of time to specify safety-driven requirements for the upper bounds on message delivery delays. Message delivery time requirements are combined with the requirement that the probability of erroneously stopping a train is very small. Rules are derived for scheduling re-transmissions of train control messages to ensure timely train braking in the event of driver error.