This is network analyst forum so you may not get enough response as you are trying to do spatial analysis with euclidean distances.
But you may look at the GP tool called PointDistance that will compute euclidean distances between two sets of points with a specified search distance. I would suggest that you compute the distances between your ambulances and service points within some response distance, say 3 miles and then sum up the distances per ambulance site. Now you can rank them from low to high. Sites with lowest sum have the maximum accessability to service sites.
Regards,
Jay Sandhu
