Intractability of bounded protocols for non-FIFO channels

We discuss the efficiency of data link protocols for non-FIFO physical channels. We consider three resources; the number of packets that have to be sent, the number of headers, and the amount of space required by the protocol. We prove three lower bounds. First, we show that the space required by any protocol for delivering n messages using less than n headers can not be bounded by any function of n. Second, we prove that the number of packets that have to be sent by any data link protocol using a fixed number of headers in order to deliver a message is linear in the number of packets that are delayed on the channel at the time the message is sent. Finally, we introduce the notion of a probabilistic physical channel, in which a packet is lost with probability q. We prove an exponential lower bound, with overwhelming probability, on the number of packets that have to be sent by any data link protocol using a fixed number of headers, when it is implemented over a probabilistic physical channel.