The Measurement Paradox in Valiant Network Design

In recent years the difficulties in measurement and prediction of Internet traffic matrices have prompted a number of routing and network design strategies broadly termed “oblivious” [1–3]. They are oblivious in the sense that they guarantee performance under any possible traffic matrix. This appealing property has a cost: extra capacity is needed to ensure that performance is maintained under all possible inputs, though several papers have shown reasonable bounds to this additional cost. In this paper we examine Valiant network design (sometimes called load balancing) a strategy extended from switch design to the design of a whole network [2, 3]. The basic principle is to build a completely connected network—a clique—and use load balancing to share all traffic across all two hop paths. The remarkable property of this network is that with only twice the capacity of an optimal network, it can carry any allowable traffic matrix, without congestion! The irony of Valiant network design is that it is predicated on the assumption that traffic matrices are hard to measure, and yet in this paper we show that such a design creates a network in which it is actually possible to measure the traffic matrix. However, this fact is of little use, because if we redesign the network based on this improved information, we then lose the ability to make ongoing measurements, leading to a paradoxical situation. It is a classic case where “you cannot have your cake, and eat it too!” Where we have the capability to make good measurements (courtesy of Valiant design) we cannot make use of them, and where we do not have such a design, the measurements are much harder to obtain. As a result, we suggest an alternative, which takes advantage of the properties of Valiant network design in addition to the ability to measure traffic matrices. We should note that there are other reasons for using Valiant network design, for instance resilience to network failures, or errors in traffic predictions, and these may outweigh the issue of difficulties in traffic matrix estimation. However, the problem of measuring traffic matrices has been found interesting in a number of contexts, and so here we examine the measurement aspect of a Valiant network.