There is a need for a fuel-optimal required time of arrival (RTA) mode for aircraft flight management systems capable of enabling controlled time of arrival functionality in the presence of wind speed forecast uncertainty. A computationally tractable two-stage stochastic algorithm utilizing a data-driven, location-specific forecast uncertainty model to generate forecast uncertainty scenarios is proposed as a solution. Three years of Aircraft Communications Addressing and Reporting Systems (ACARS) wind speed reports are used in conjunction with corresponding wind speed forecasts from the Rapid Update Cycle (RUC) forecast product to construct an inhomogeneous Markov model quantifying forecast uncertainty characteristics along specific route through the national airspace system. The forecast uncertainty modeling methodology addresses previously unanswered questions regarding the regional uncertainty characteristics of the RUC model, and realizations of the model demonstrate a clear tendency of the RUC product to be positively biased along routes following the normal contours of the jet stream. A two-stage stochastic algorithm is then developed to calculate the fuel optimal stage one cruise speed given a required time of arrival at a destination waypoint and wind forecast uncertainty scenarios generated using the inhomogeneous Markov model. The algorithm utilizes a quadratic approximation of aircraft fuel flow rate as a function of cruising Mach number to quickly search for the fuel-minimum stage one cruise speed while keeping computational footprint small and ensuring RTA adherence. Compared to standard approaches to the problem utilizing large scale linear programming approximations, the algorithm performs significantly better from a computational complexity standpoint, providing solutions in fractional power time while maintaining computational tractability in on-board systems.