Sessions, Processes, Object Instances, Sequential and Parallel Processing Theory
The SPs will be queued and run based on available resources. Depending on the isolation level used in defining the SP and how the transactions are defined, the SPs will wait accordingly. By design, the SP will not always wait for the first SP to finish, and then move onto the second one etc...

This design make is possible for multiple unrelated users to call the SP and work concurrently.