UCI's Department of Statistics was created in 2002 with an emphasis on research in statistical theory and interdisciplinary collaborations and is actively recruiting additional members.
The Department also intends to capitalize on existing statistical expertise in other Bren School departments as well as other schools at UCI.
In this paper, we propose an approach to estimating traffic matrices that incorporates lightweight Origin- Destination (OD) flow measurements coupled with a computationally lightweight algorithm for producing the OD estimates. There are two key ingredients in our method, called PamTram, for PArtial Measurement of TRAffic Matrices. The first is to actively select a small number of informative OD flows to measure in each estimation time interval. To avoid the heavy computation of an optimal selection, we use a heuristic based on intuition from game theory. Randomized selection rules are developed based on the goals of reducing errors and adapting to traffic changes. We provide an algorithm for selecting a good flow to measure that is fast because it avoids the computations, such as integrating over past intervals, that are needed for optimal selection. The second key aspect of our method is an explanation and proof that an Iterative Proportional Fitting (IPF) algorithm can be used to approximate the traffic matrix estimate when the goal is a minimum mean squared error and the optimization starts from a maximum entropy initial estimate.
In addition, we provide a one-step average error bound for PamTram when the randomized selection rule is uniform and no link counts are used. This bounds the average error for the worst case selection rule. Finally, we validate our method using data from Sprint’s European Tier-1 IP backbone network. Results show that our method generates average errors below the 10% carrier target error rate. Interestingly, we show that it suffices to measure a single OD flow in each estimation interval,which renders our partial measurement method very lightweight in terms of measurement overhead.