A square root formula for the rate of non-persistent TCP flows

In this paper, we derive a closed form formula for the average rate attained by a non persistent TCP source which alternates between idle periods and download periods subject to a fixed packet loss probability. We also derive closed form expressions for the mean time to transfer a file and for the distribution of the transmission rate. Several distributions for the file sizes and idle times are considered including heavy tailed distributions. The formula for mean transmission rate is shown to boil down to the classical square root mean value formula for persistent flows when the average file size tends to infinity. The formulae are applied to predict bandwidth sharing among competing flows subject to active queue management.