Interesting, this "missed call" was used in Japan extensively in the early 2000's, mainly to ask friends in the middle of the night whether they were still awake or not (kind of like the late-night instant message to a friend who is displayed as "away").
The act was called "One-Giri" (Giri is a conjugated form of "Kiru" which means to cut or hang up, in the case of a phone call)
I believe that during that time, text messages were charged per character (and hence an alternative to the "missed call" was to send a text message with one character - or perhaps it was even zero characters). I don't think regular data plans or messages/month plans existed back then (or at the least, were not prevalent)
Now, data plans are the norm and many users have unlimited (non-internet) data plans and can text message indiscriminately. Limited data plans do exist, but because the "culture" has shifted towards proper messaging, people no longer send empty messages or use missed calls)
(For some reference, I don't think Japan had unlimited bandwidth internet of any kind in the late 90's, while U.S. users at least had the option of dial up unlimited monthly internet access; Earthlink, for one. The lack of a fixed cost cellphone message plan is thus in line with their overall telecommunication tradition)
If there are any users who lived in Japan and is more knowledgeable about the subject than I am, I will gladly be corrected.
The act was called "One-Giri" (Giri is a conjugated form of "Kiru" which means to cut or hang up, in the case of a phone call)