Analytical modeling of performance indices under epistemic uncertainty applied to cloud computing systems

The extent of epistemic uncertainty in modeling and analysis of complex systems is ever growing, mainly due to increasing levels of the openness, heterogeneity and versatility in cloud-based applications that are being adopted in critical sectors, like banking and finance. State-of-the-art approaches for model-based performance assessment do not embed such uncertainty in analytic models, hence the predicted results do not account for the parametric uncertainty. In this paper, we develop a method for incorporating epistemic uncertainty of the input parameters (i.e., the arrival rate λ and the service rate μ) to the M/M/1 queueing models, that are commonly used to analyze system performance. We consider two steady state and average output measures: the number of entities in the system and the response time. We start with closed-form solutions for these measures that enable us to study the propagation of epistemic uncertainty in input parameters to these output measures. We demonstrate the suitability of our method for the performance analysis of a cloud-based system, where the epistemic uncertainty comes from continuous re-deployment of applications across servers of different computational capabilities. System simulation results validate the ability of our models to produce satisfactorily accurate predictions of system performance indices under epistemic uncertainty.