Performance Issue

Everytime (which is at least once or twice a day) we will take 30,000+ hits per minute…

When that does happen, my MySQL starts spawning “sleeper” sessions and then the site craches.

I have another site on the same dedicated server that is static html that stays active but really slow since, my backbon usage shoots up to 100%

What are the correct settings for php and MySQL to avoid these conflicts? I mean this site must take that many hits all the time and stays stable.

I am using ZEND CE and MySQL 5. something any help?