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There is a known performance issue when the ArcMap Buffer Wizard is used to create multiple rings around each feature, or ring buffers, together with the option to dissolve overlapping buffers. The problem is most noticeable when buffering many features.
Dissolving buffers requires that overlapping buffer polygons be clipped, which is a geoprocessing operation. With ring buffers this operation becomes even more memory intensive. As the computer runs out of RAM and starts to use swap memory, the buffering process slows down considerably.
To cut down on processing time do either or both of the following: