Asymptotically accurate flow completion time distributions under Fair Queueing

Fair queueing (FQ) is a very important queue discipline because it is sometimes viewed as a satisfactory model of the way Internet routers share their time between flows at present, and sometimes viewed as an ideal to which Internet router queueing algorithms aspire. The really important performance measure for flows is flow completion time (FCT), however no formula for the distribution of FCT is known at present under realistic assumptions for flow size distribution. In this paper, we discover that the distribution of the number of active flows under FQ when flows have a Pareto distribution (a realistic model for flow lengths) is approximately geometric, where the approximation is asymptotically accurate as the flow distributions become more heavy tailed. This then provides an estimate for the FCT distribution.