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Sizing Backbone Internet Links

101 Lindy Lane, Lincroft, New Jersey 07738
danheyman{at}yahoo.com

One of the distinguishing features of a backbone link is that it is designed to carry traffic from a large number of end users. This results in a Normal distribution for the number of bytes or packets that arrive in a fixed-length time interval. Based on this observation, which is substantiated by data analysis, we present a simple model for the steady-state loss probability that can be solved in closed form. This model assumes that there is no buffer, so that issues raised by the correlation of counts that is characteristic of packet traffic are bypassed.

The longest interval that captures the relevant statistical fluctuations of backbone traffic is one second. Data collection on live commercial networks is costly, so byte and packet counts are usually collected over much longer time intervals; five minutes is a lower bound. This creates no problem in estimating the mean of the Normal distribution, but it makes direct estimation of the variance for one-second counts infeasible. Routers collect flow data; flows are analogous to "calls" in telephony. By modeling the number of active flows as an M/G/ queue and assuming that packets in a flow are spread uniformly in time, an equation for the variance of (say) one-second counts in terms of measured quantities is derived. The efficacy of this formula is demonstrated by applying it to data.

Subject classifications: queues:applications; approximations; statistics:data analysis; time series.
History: Received April 2003; revision received December 2003; accepted April 2004.