(I think dealership trading desks include most bonds, IRS, FX options, FX cash, CDS, OTC stock options…)
After saving the trade into database, all post-trade messages can be delegated to a task queue for a background thread (like swing event queue). These messages inform downstream systems , so they can update their GUI  and database in real time. These post-trade messages aren’t can’t really fail (if they fail we just have to resend). These are one-way messages. So they don’t need to be on the critical path.
 could be internal modules of the same trading engine or external systems owned by other teams like commissions:). Either way, such a downstream always runs in a separate process or machine.
 Note these GUI aren’t web pages, but WPF, Swing or similar auto-updating screen.
Q: Must position be updated in the critical path, before we process the next trade?
A: For a dealer, yes I think so. If Trade 1 depletes inventory, then we must reject next trader-sell.