On performance bounds for balanced fairness

While Erlang’s formula has helped engineers to dimension telephone networks for over 80 years, such a three-way “performance–demand–capacity” relationship is still lacking for data networks. It may be argued that the enduring success of Erlang’s formula is essentially due to its simplicity: the call blocking rate does not depend on the distribution of call duration but on overall demand only. In this paper, we consider data networks and characterize those capacity allocations which have the same insensitivity property, in the sense that performance of data transfers does not depend on precise traffic characteristics such as the distribution of data volume but on overall demand only. We introduce the notion of “balanced fairness” and prove some key properties satisfied by this insensitive allocation. It is shown notably that the performance of balanced fairness is always better than that obtained if flows are transmitted in a “store and forward” fashion, allowing simple formula applying to the latter to be used as a conservative evaluation for network design and provisioning purposes.