

On the Nonstationarity of Internet Traffic

Authors

Jin Cao <cao@belllabs.com>
William S. Cleveland <wsc@belllabs.com>
Dong Lin <dong@belllabs.com>
Don X. Sun <dxsun@belllabs.com>
Statistics, Statistics, Networked Computing, Statistics Research,
Bell Labs, Murray Hill

Abstract

Traffic variables on an uncongested Internet wire exhibit a pervasive
nonstationarity. As the rate of new TCP connections increases,
arrival processes (packet and connection) tend locally toward Poisson,
and time series variables (packet sizes, transferred file sizes, and
connection roundtrip times) tend locally toward independent. The cause
of the nonstationarity is superposition: the intermingling of sequences
of connections between different sourcedestination pairs, and the
intermingling of sequences of packets from different connections. We
show this empirically by extensive study of packet traces for nine
links coming from four packet header databases. We show it theoretically by
invoking the mathematical theory of point processes and time series. If
the connection rate on a link gets sufficiently high, the variables can
be quite close to Poisson and independent; if major congestion occurs on
the wire before the rate gets sufficiently high, then the progression
toward Poisson and independent can be arrested for some variables.

