Singleton pattern and preserving a connection

On many home computers you can to click some desktop icon to connect to the Net via a conventional modem or a broadband modem. Some email and browser software will try and make a connection even if one exists. Trying to make a connection when a connection is already open sometimes spoils the existing connection in such a way that it's impossible to reconnect without rebooting the machine. How might your operating system use the singleton pattern to avoid this problem? Draw a UML diagram.