Techniques are described for managing program execution capacity or other capacity of computing-related hardware resources used to execute software programs, such as for a group of computing nodes that is in use executing one or more programs for a user. Dynamic modifications to the program execution capacity of the group may include adding or removing computing nodes, such as in response to automated determinations that previously specified triggers are currently satisfied, and may be automatically governed at particular times based on automatically generated predictions of program execution capacity that will be used at those times by the group, such as to verify that requested dynamic execution capacity modifications at a time are within the predicted execution capacity values for that time. In some situations, the techniques are used in conjunction with a fee-based program execution service that executes multiple programs on behalf of multiple users of the service.