If you did want to worry about concurrency, there is always the technique of serializing the requests by obtaining a row lock on a common resource.

Imagine a new table (SERIALIZER) that has one row, start a transaction and update the row as the first action in the stored procedure.  Now, other calls to the stored proc will wait on the first call to finish the transaction.

Just makes sure to commit the transaction at the end of the stored procedure (or rollback in case of an error).