To get rounds beginnings for a specified interval, use the command route/get_schedule_time:

svc=route/get_schedule_time&params={"itemId":<long>,
				    "scheduleId":<long>,
				    "timeFrom":<uint>,
				    "timeTo":<uint>}

[
	{
		"time":<uint>	/* time of round beginning */
	}
]