I had a show in univeristy where there was a love seat, two beds and a mattress, I would usually sleep on the love seat between scene changes. I had a really long break, and the other ASM would come wake me up, being tall the love seat wasn't the best, but it was extremely comfortable, and the only furniture on my side of the stage.
Obviously I wasn't fully asleep, in case of an emergency I was able to react quickly.