Demand uncertainty, as manifest by the difference between expected and actual departure times, is a significant source of error for predicting times-of-arrival for aircraft at points of congestion such as airports. Assigning and controlling four-dimensional trajectories is envisioned as an important component of the U.S. next generation air traffic system, with the ability to schedule aircraft and assign delays based on predicted arrival times an important component of such four-dimensional trajectory capability. For this reason methods need to be developed to mitigate the effects of demand uncertainty on predicted times-of-arrival. This paper discusses the results of ongoing research into determining appropriate and manageable methods for mitigating such effects on a scheduling system. The results follow previous studies that examined the effect of demand uncertainty on scheduling over short distances (approximately 250 nautical miles); this study found that different methods may be needed for long distances. While no conclusive results were found, a method for identifying and testing possible solutions is presented along with the results of the analysis to date.