I'm sorry but your query does not provide enough information for me to help you out of your apparent contradiction. By itself, the term "parallel connections" doesn't describe the precise network interface or medium in use. That said, in technologies like fiber optic or copper-based media where individual connections are switched, provided that the network interfaces and the switches are capable of operating in full duplex mode, the medium itself can handle the traffic. If you can tell me a little bit more about what kind of connections are covered in the term "parallel connections" I might be able to shed a little more light on your puzzle.
This was first published in July 2002