If you're going to run stairs- run up, not down. The only thing you can accomplish running downstairs is injury.
I've "heard" walking downstairs backwards is a nice hamstring warm up though.
Besides, if you walk downstairs you don't need a rest period, and you're effectively running a HIIT. You don't have to take your time walking, but you're not using your quads and most muscles in your leg going down, so theres no reason to risk injury.