End-to-End Traffic Analysis in Large Networked Systems

In this paper we describe a method to estimate the overflow probability at an arbitrary queue in a network. This work is motivated by the assumption that most network routers will have the capacity to multiplex a moderate to large number of network flows. We first provide our main results on the workload of a queue fed with a large number of traffic flows in a network. Under fairly general conditions, our results say that the workload at the network point at which a large number of traffic flows are multiplexed decreases to zero, almost surely. What the result also says is that the overflow probability at a downstream node can be estimated (within an error term) by only measuring the traffic at the edge of the network. We find an upper bound on this error term that decreases exponentially in the number of sources multiplexed. We provide numerical examples to illustrate the efficacy of our results under different network and traffic configurations.