Parallel Function calls using multiple processes

Problem: Function call typically takes 2-3 millisecond but at times exceeding 2-3 Minutes.
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>From the DB logs it seems when multiple processes are trying to execute the function ,
execution takes sequentially rather than parallel, which means Nth thread will have to wait for (N-1)*ExecutionTime before getting its turn

Is my observation correct? If yes then what is the solution for this? If not where/how to find the exact cause of the above problem?
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DB Version: 8.2
Function Details:
--returns numeric, takes 10 parameters
--select query to validate data
--row level lock for select and validate
--bare minimum business logic
--update data
--couple of inserts for transaction logs/account management
--also note that few of the tables have audit triggers causing the row to be inserted in audit table with the action (only Update/Insert/Delete)