Automated process for creating service areas?

Hello all,

Suppose you would like a final map that shows the service areas of a hundred hospitals, based on some sort of network cost (travel time, travel distance). Network Analysis has the service area rings option, but there is too much data for arcGIS and my computer to handle. In addition, there is the question of trimming any overlapping rings afterward. On any of the above, does anyone have any ideas how to proceed?

Thanks!