It is often desirable to monitor end-to-end properties, such as loss rates
or packet delays, across an entire network. However, active end-to-end
measurement in such settings does not scale well, and so complete
network-wide measurement quickly becomes infeasible. More efficient
measurement strategies are therefore needed. Previous work, examining this
problem from a linear algebraic perspective, has shown that for exact
recovery of complete end-to-end network properties, the number of paths
that need to be monitored can be reduced to approximately the number of
links in the network. Here we argue that in fact measurement strategies
of even greater efficiency are possible.
We begin by recasting the problem as one of statistical prediction and
show that end-to-end network properties may be accurately predicted in
many cases using a significantly smaller set of carefully chosen paths
than needed for exact recovery. We formulate a general framework for the
prediction problem, propose a simple class of predictors for standard
quantities of interest (e.g., averages, totals, differences), and show
that linear algebraic methods of subset selection may be used to make
effective choice of which paths to measure. We explore the accuracy of
the resulting methods both analytically and numerically, in the context of
real network topologies of varying size. The feasibility of our methods
derives from the low effective rank of routing matrices as encountered in
practice, which appears to be a new observation of interest in its own
right. The resulting framework, which is quite general, appears to hold
promise for studying and improving the efficiency of monitoring of
end-to-end-network properties.
http://math.bu.edu/people/kolaczyk/