Metastability of fair bandwidth sharing under fluctuating demand and necessity of flow admission control

Introduction: A flow level Markov model of fair bandwidth sharing under fluctuating demand has been proposed in [1, 2] for a case of file transfer flows, and in [3] for a case of a mixture of file transfer and streaming flows. These Markov models assume separation of timescales: given numbers of flows in progress, the fair bandwidth sharing protocol reaches equilibrium much faster than the numbers of flows in progress change due to flow arrivals=departures. Stability under the condition that each link can accommodate its average load was established in [2, 3]. However, these Markov models and stability results do not account for bandwidth wasted on transmissions of ‘dead’ file transferring packets which will be dropped downstream and then retransmitted. This Letter proposes to account for wasted bandwidth by assuming that the file transfer rates are determined by the end-to-end goodputs rather than the corresponding throughputs as in [1–3]. The ‘goodputbased’ Markov model is unstable even under light exogenous load, when the corresponding throughput-based models [1–3] are stable. The instability, observed in [4] by simulations, is a result of demand fluctuations: increase in the number of flows in progress causes increase in packet loss, reducing goodput and further increasing the number of flows in progress. Despite instability, a desirable metastable network state with a finite number of flows in progress may still exist. The network can be stabilised in a close neighbourhood of this metastable state with appropriately designed flow admission control at the price of a small flow rejection probability. Network over provisioning without flow admission control only reduces but does not eliminate the instability region.