Regardless of how busy you are; you are never too busy to let your customers know you see them. They come here to be taken care of, so don't start out their dining experience by ignoring them. All new customers should be greeted within one minute.
If your hands are full, the customer knows automatically that you can't take their order, at that minute. You can pause, smile, and say "Hi, I'll be with you in just a minute." This will satisfy the customer so that they feel important and will be able to relax until you return.
When approaching a table your objective is to make you guests feel welcome and confident in knowing you're there to take care of them.
From a server training manual at slideshare.net