I currently have a huge problem. Two days ago my site running on one server was too much, so I purchased two more and had them clustered (rsync and load balanced).
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You would need to set up memcache to run on one of the servers and have all of the servers use that same memcache instance for the sessions. Otherwise, if they each run their own memcache instance, you'll have the same problem as before.
Other than configuring memcache accordingly and telling PHP to use it as your session handler, you shouldn't have to make any changes to your code.
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To clarify the advice I gave here, if you group all three servers into a single pool, you won't have any problems as long as every PHP instance references those servers in the same order. memcache uses client side hashing, so you will be guaranteed that the same key is read / written on the same server. Of course, if you alter that list in any way, then sessions will become invalidated.
The memcache developers actually don't even recommend that you use memcache for storing session data because it isn't persistent, and thus if you have to restart memcache (or something happens), then all of your users will be logged out.