What I would do (pseudo code).
//timepast since last loop in ms
timepast = 0
fpslimit = 60
finished = true;
//while the game is running
while(runnning)
{
timepast += timeSinceLastrun
if(timepast > 1second/fpslimit && finished)
{
finished = false
dostuff(timepast)
}
//sleep for the time of 1second/fpslimit - timepassed to avoid cpu blocking
Thread.sleep((1second/fpslimit) - timepast )
}
dostuff(deltatime)
{
//do stuff in the end after it finished set
//finished to true so dostuff can be called again
finished = true
timepast=0
}
In this way you can easily limit the fps with a variable and dont need to block other threads.
as OldCurmudgeon said thread.sleep dosnt block other threads in java and make processor time available.
Thread.sleep causes the current thread to suspend execution for a
specified period. This is an efficient means of making processor time
available to the other threads of an application or other applications
that might be running on a computer system
Also you can pass timepast to the dostuff method as a deltatime so the game runs the same on all devices (same speed).