Chicago (IL) - Apple’s iPhone went on sale officially today - and once again, the hype machine of the Cupertino-based appears to have worked very well: Despite software problems in London, a global undersupply of the iPhone 3G, especially of the 16 GB model, people patiently waited in line to get one of the new phones. Apple is estimated to see up to $1 billion in revenues during the launch period.

Christmas is arriving a bit early for Apple this year, with what appears to be yet another successful launch of a gadget. The iPhone 3G will or already has been launched in 22 countries today and we are seeing first indications how well Apple’s supply can keep up with demand.

Australia was the first country to sell the new phone to the public. Demand is reported to have been very so far, with at least dozens people lining up in front of carrier stores and wait times of the first people in line of 60 hours or more. About 150 people were reported to have waited in line in front of Apple’s London flagship store. Shortages are reported on a global basis: Apparently, must consumers are buying the more expensive ($299) 16 GB phone, meaning that many buyers will have to be happy with a $199 8 GB version.

UK users reported activation problems during the iPhone launch. O2’s web-based activation system only allows users to register a new phone using Microsoft’s Internet Explorer and won’t work with Apple’s Safari browser. According to reports, there were even hiccups with the Internet Explorer and took the carrier some time to get the process running. However, the average purchase process seems to be in line with previous expectations and last about 10-20 minutes around the globe.

Market research firm iSuppli estimates that Apple will have to provide about 1 - 2 million phones to meet global demand. If iSuppli’s estimates are correct, then Apple may have dramatically underestimated the actual demand during launch. However, if Apple and its partner carriers are able to sell 2 million phones today, the company could see revenues of up to $1 billion - based on the general believe that AT&T will pay Apple at least $500 for each sold iPhone 3G.

If you decided not to stand in line for the iPhone 3G you always can wait for the second wave or purchase an iPhone 3G on the Internet. eBay sellers are already listing the phones and were listing the phones for "buy it now" prices of up to $1500 at the time of this writing.