Your main problem is going to be with race conditions. What if two different processes are started at the exact same time? Simply telling each one to sleep, as others have suggested, will not help. They will both sleep the same amount of time, then both execute at the same time.

You need a way to implement some sort of mutual exclusion lock (or semaphore). Each process would attempt to get the lock. Once a process obtains the lock, it would be the responsibility of that process to make sure it held the lock for at least one second. Each process is only allowed to execute requests while it is holding the lock.