Heavy-traffic delay insensitivity in connection-level models of data transfer with proportionally fair bandwidth sharing

Motivated by the stringent requirements on delay performance in data center networks, we study a connection-level model for bandwidth sharing among data transfer flows, where file sizes have phase-type distributions and proportionally fair bandwidth allocation is used. We analyze the expected number of files in steady-state by setting the steady-state drift of an appropriately chosen Lyapunov function equal to zero. We consider the heavy-traffic regime and obtain asymptotically tight bounds on the expected number of files in the system. Our results show that the expected number of files under proportionally fair bandwidth allocation is insensitive in heavy traffic to file size distributions, thus complementing the diusion approximation result of Vlasiou et al. [20].