You can create a new exception type, e.g. JTransportHTTPNotConnectedException and have the transport class throw that instead. You can then catch this particular exception type with:

    try {
        // your code
    }
    catch (JTransportHTTPNotConnectedException $e)
    {
        // show the error message that you're not connected to the Internet blah blah
    }
    catch (Exception $e)
    {
        // generic error handling code
    }

That's another beauty of exceptions. You can throw and catch different types of exceptions.