A method for controlling speed of a vehicle, comprising the steps of: determining an arrival time error for a required time of arrival and a projected trajectory according to a travel plan with a current speed profile having a plurality of regions, each with a respective speed adjustment parameter and a respective SAP value relative to a nominal speed profile, wherein at least two of the regions of the travel plan have different SAPs; selecting, when the ATE is greater than a threshold, one of the regions as a selected region for modification of its SAP value based on a priority order of the regions that includes a highest priority region and a lowest priority region, wherein the selecting step includes sequentially selecting a current region from available regions of the regions for modification in accordance with a sequence from the highest priority region to the lowest priority region, as long as (i) the ATE is such that a magnitude of a respective SAP value of a selected region decreases upon modification and (ii) until the current region is the lowest priority region, evaluating a current position of the vehicle relative to a RTA proximity region, and sequentially selecting, when (i) the ATE is still greater than the threshold, (ii) the current region is the lowest priority region, and (iii) the current position of the vehicle is not within the proximity region, a region from the available regions for modification of its SAP value in accordance with a sequence from the lowest priority region to the highest priority region; modifying the current speed profile by implementing all SAP modifications and implementing the modified speed profile. determining an arrival time error for a required time of arrival and a projected trajectory according to a travel plan with a current speed profile having a plurality of regions, each with a respective speed adjustment parameter and a respective SAP value relative to a nominal speed profile, wherein at least two of the regions of the travel plan have different SAPs; selecting, when the ATE is greater than a threshold, one of the regions as a selected region for modification of its SAP value based on a priority order of the regions that includes a highest priority region and a lowest priority region, wherein the selecting step includes sequentially selecting a current region from available regions of the regions for modification in accordance with a sequence from the highest priority region to the lowest priority region, as long as (i) the ATE is such that a magnitude of a respective SAP value of a selected region decreases upon modification and (ii) until the current region is the lowest priority region, evaluating a current position of the vehicle relative to a RTA proximity region, and sequentially selecting, when (i) the ATE is still greater than the threshold, (ii) the current region is the lowest priority region, and (iii) the current position of the vehicle is not within the proximity region, a region from the available regions for modification of its SAP value in accordance with a sequence from the lowest priority region to the highest priority region; modifying the current speed profile by implementing all SAP modifications and implementing the modified speed profile.