Internet and the Erlang formula

Thomas Bonald (1, 2) , James Roberts (3)

1 LINCS - Laboratory of Information, Network and Communication Sciences
2 LTCI - Laboratoire Traitement et Communication de l'Information
3 RAP - Networks, Algorithms and Probabilities

We demonstrate that the Internet has a formula linking de- mand, 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.

Mots clés: Erlang formula; Traffic; Congestion

Domaines: Réseaux et télécommunications [cs.NI]

Thomas Bonald, James Roberts. Internet and the Erlang formula. Computer Communication Review, 2012, 42 (1), pp.23-30. ⟨hal-00941783⟩