The technology described herein is directed towards executing continuous query tasks for monitoring a data storage system to obtain real-time metrics and store query results, in which the continuous query tasks are resource-demanding yet need to execute on limited system resources. A continuous query tasks scheduler levels the load produced by scheduling continuous query tasks with starting time offsets based on the period of continuous query tasks and load descriptions for the tasks. Further, a continuous query task that produces too high of a workload is divided into continuous query subtasks, which are scheduled at subtask starting time offsets.