Concurrent usage of rdbms, write 4K rows without lockdown
I'm not sure you understand.


PostgreSQL has max_connections. If that number is hit people won't be able to connect to the database. If your server is waiting you may get a "server busy" message or the like. As @a_horse_with_no_name suggests connection pooling may solve this problem.
You can speed up writes by batching them. When you convert from your "excel format" to SQL are you doing one insert, or one insert per row? Consider inserting into an unlogged table if you're inserting one row at a time, and then running a single INSERT INTO SELECT to UPSERT into the master.
You should also check out the non-durability settings for faster writes