Short answer to your original question: no. Shortage of medical personnel is not the problem I want solved here. My problem is about expediting patients through the system more quickly and efficiently.

An imaginary example: A patient is waiting for lab results. The lab's it system doesn't flag incoming results; there's no email-style inbox that would chime when results come in, you have to manually query results for every patient. The system doesn't even give the user ETAs, even though it is a standardized process. In industry the system would know the current capacity and load and estimate times based on that.

The Doctor checks the patients results in between other patients, when s/he remembers. Meanwhile in another room a nurse is checking if the results are in yet so s/he can remind the doctor to look at them. The nurse is also calling up wards upstairs to see which ones have room and could admit the patient, calling the relatives, trying to find out which medications the patient is taking, taking vitals, taking samples, giving medications, and juggling these and several other things for several patients at the same time RELYING ON HER/HIS MEMORY TO KEEP TRACK OF ALL OF THAT. That is not good use of a human brain, so the staff is continuously stressed out.

Back to the patient who has now been waiting for three hours for the doctor to come tell what's wrong with him/her. The lab results have been ready for an hour, but nobody's remembered to check them. From the system's point of view, that patient has also taken up the ER's resources (bed, nurses' attention, etc.) for an extra hour.

Fast forward, the doctor has decided that the patient needs to be admitted. The nurse on shift is a new one and only now starts to call up the wards for vacant beds, not knowing that sometimes it can take an hour or two to arrange one if the wards are full or near full. The patient waits another hour to be transferred, and again uses the ER's resources for an extra hour.