A Measurement-Analytic Framework for QoS Estimation Based on the Dominant Time Scale

In this paper we describe a measurement-analytic framework for estimating the overflow probability, an important measure of quality of service (QoS), at a given multiplexing point in the network. A multiplexing point in the network could be a multiplexer or an output port of a switch where resources such as bandwidth and buffers are shared. Our approach impinges on using the notion of the dominant or critical time scale, which corresponds to the time-scale relevant for describing the queueing behavior based on particular network configurations. The dominant time-scale provides us with a measurement window for the statistics of the traffic, but is unfortunately itself defined in terms of the statistics of the traffic over all time. This in essence results in a chicken and an egg type of unresolved problem. For the dominant time scale to be useful for on-line measurements, we need to be able to break this chicken and egg type of cycle. In this paper, we present a stopping criterion to successfully break this cycle through online measurements and find a bound on the dominant time scale. Thus, the result has significant implications for network measurements. Our approach is quite different from other works in the literature that require off-line measurements of the entire trace of the traffic (since in our case, we need to measure only the statistics of the traffic up to a bound on the dominant time scale.) We also investigate the characteristics of this upper bound on the dominant time scale, and provide numerical results to illustrate the utility of our measurement analytic approach. Keywords— Dominant time scale, Measurements, Gaussian processes, Stopping criterion, Overflow probability, Maximum Variance Asymptotics.