How does a double-buffered computer load a tile map?

There isn't a such thing as a double-buffered computer that has no sense in this question at all 

A multiple-buffered computer loads the tile map all the tiles at the same time, but uses the ram to load the image file to the graphics card. It can take a few seconds, but the bigger amount of RAM you have, the faster it will go. This method also applies with a multi-layered image.