The big thing I'd say is also needed is added beds as most A&E departments have access to way more than 30 beds.
My local which isn't a major hospital has access to around 50 to 60 beds within what's considered their ED these beds include ones in CAU, MIU, Majors and Minors plus resus basically they stuff patients in where ever they can fit them and have the bed managers hunting forna suitable ward bed for them.
Those in Resus and Majors are top of list to be moved to wheres best and are normally gone from the ED within 3 hours.
Minors are typically either discharged within 3 to 6 hours or moved to CAU if they are expected to breach 6 hours (normally any that's going to breach the 3 hour target are moved here as that gets them off the clock) or if condition worsens go to Majors
CAU are normally those minor patients that need further examination or GP referrals and would be either discharged or moved within 24 hours of admission to the ED. These patients are considered off the clock for the ED but are still technically an ED patient.
MIU are walk ins and normally never admitted to Hospital.
Now there are more emergency admissions that boycott EDs especially cardiac cases these have been known to be delivered directly to either the cath lab or the cardiac unit so would avoid the ed.
Now I do like Caolans idea on the times as that would be more suitable for the game but as he says make use of the departments more especially ones like cardiac where even if the patient goes in via ED they are moved quickly to that department and same with nurology.
Calls like child birth should not cost any patient place in the ED side as these almost always go direct to the Gynecology/Maternity units yes there are exceptions but mostly they don't see ED.
But before waiting times are introduced we need more beds for it to be realistic as some of us can easily fill all our hospitals in an hour or so just now. Today I had done a quick run through my list and 3 out of my 7 hospitals and 4 of my 8 clinics were full within the first hour or so. If I was able to keep jobs going I'd have been using alliance beds, which on a day where I get a good bit of time in the game I could fill easily too.
Once we have more beds then yes waiting times would be good.
Also adding in ambulance downtime is needed as they always go off the run after transporting for cleaning can be 10 mins or out of service return to station as needs full decontamination. Also crew welfare can have them go off the run after a call even if it's just for the crew to have a decompress from the case or just a quick head wobble and back at it.
Lots could be done with this part of the game but just now I'd rather see the medical upgrade that's due as that will bring more features to that side of the game.