Bits through queues

Consider the following simple communication channel model: an error-free bit pipe leading to a buffer modeled by a single-server queue whose “packets” or “customers” are single bits. If the service rate is p bits/sec, common wisdom would indicate that the Shannon capacity of this communication link is p bits/sec. As we show in this paper, that intuition is wrong: the answer is actually higher than p bits/sec. How could we possibly transmit information at a rate faster than the service rate? After all, overdriving the queue with an arrival rate higher than p will not do, as the queue will become unstable and its output rate will not be higher than p. The capacity (revealed at the end of this summary) is higher than p because information can be encoded into the arrival epochs. Let us consider now a simpler and more fundamental problem, namely the Shannon capacity of the single-server queue. Suppose that “packets” are identical, and thus carry no information except in their arrival times. Every message is encoded by a different sequence of n arrival times to the queue. The decoder selects one of the possible messages upon observation of the corresponding n departure times. The rate of the code is equal to the logarithm of the number of messages divided by the average time it takes to receive all n packets. The sources of randomness in this channel are the service times, which are assumed to be independent and identically distributed for each packet. Despite the simplicity and canonical nature of this channel, the derivation of its capacity is far from elementary because of the various challenges it presents to the information theorist: