Internet and the Erlang Formula

We demonstrate that the Internet has a formula linking demand, capacity and performance that in many ways is the analogue of the Erlang loss formula of telephony. Surprisingly, this formula is none other than the Erlang delay formula. It provides an upper bound on the probability a flow of given peak rate suffers degradation when bandwidth sharing is max-min fair. Apart from the flow rate, the only relevant parameters are link capacity and overall demand. We explain why this result is valid under a very general and realistic traffic model and discuss its significance for network engineering.