A Queue Model for Reliable Forecasting of Future CPU Consumption

Statistical queuing models are popular to analyze a computer systems ability to process different types requests. A common strategy is to run stress tests by sending artificial requests to the system. The rate and sizes of the requests are varied to investigate the impact on the computer system. A challenge with such an approach is that we do not know if the artificial requests processes are realistic when the system is applied in a real setting. Motivated by this challenge, we develop a method to estimate the properties of the underlying request processes to the computer system when the system is used in a real setting. In particular we look at the problem of recovering the request patterns to a CPU processor. It turns out that this is a challenging statistical estimation problem since we do not observe the request process (rate and size of the requests) to the CPU directly, but only the average CPU usage in disjoint time intervals. In this paper we demonstrate that, quite astonishingly, we are able to recover the properties of the underlying request process (rate and sizes of the requests) by using specially constructed statistics of the observed CPU data and apply a recently developed statistical framework called Approximate Bayesian Computing. Further we apply the model to forecast future CPU consumption. Our results show that the model forecast future CPU consumption with less error than both the hidden Markov model (HMM) in (Hammer et al. 2016) and an ARIMA model. Another good property of the queue model is that we can forecast the instantaneous CPU consumption at any time point in the future, while the HMM in (Hammer et al. 2016) and time series models are limited to only forecasting the average CPU consumption in disjoint time intervals.