Threshold:
Sorry your sleep was broken by the call.
Carolyn Knapp talks about drunk dialing in her book "Drinking: A Love Story" and if I recall correctly, she said she got the term from AA. Anyways, its common enough that it has a page on Wikipedia and there are even apps to prevent drunk dialing:
Drunk dialing
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Drunk dialing is a pop-culture term denoting an instance in which an intoxicated individual places phone calls that he or she would not likely place if sober. The term often refers to a lonely individual calling former or current love interests.
I have this disease late at night sometimes, involving alcohol and the telephone. I get drunk, and I drive my wife away with breath like mustard gas and roses. And then, speaking gravely and elegantly into the telephone, I ask the telephone operators to connect me with this friend or that one, from whom I have not heard in years.
—Kurt Vonnegut[1]
"Drunk texting" is a related phenomenon, and potentially yet more embarrassing for the sender as, once the message is sent, it cannot be retrieved; the message will most likely be misspelled (due to being drunk), and it might be reviewed and shared among many.
In media
The New York Post,[2] the New York Times,[3] and the Washington Post,[4] have all reported on drunk dialing. Cell phone manufacturers and carriers are helping callers prevent drunk dialing. Virgin Mobile has launched an option to help its users stop drunk dialing by initiating multi-hour bans on calling specific numbers[5] and the LG Group introduced the LP4100 mobile phone, which includes a breathalyzer.[6] Although the breathalyzer function was incorporated to help the user assess fitness to drive, rather than fitness to phone, the owner can program the LP4100 to restrict calls to specific telephone numbers on certain days or after a certain hour, a feature that might help limit drunk dialing by eliminating calls when the user is more likely to be intoxicated. Some reports indicate that this phone, or a planned future version for U.S. release, would activate the call-blocking function in tandem with the blood alcohol content results from the breathalyzer.[7][8]
My son once drunk dialed me from Antigua at 2 in the morning because he couldn't get the dinghy started to get home!!! I asked him what he wanted me to do in the wee hours of the morning 2,000 miles away??? Found out the next day he couldn't start the dinghy because it was out of gas. LOL.