to minimize the impact on service areas:
^^^^What does this mean?
I use network analysis to choose the closest unit (quickest drive time) to an incident, but it sounds like you want to incorporate CAD (computer assisted dispatch) functionality into Network analysis. I bet in can be done; how much money do you have to spend on it?
For example, once Network Analyst returns the closest unit, CAD takes over and figures out what sort of response the call type needs like: engine, ladder, heavy rescue, whatever.
That should just about do it....