A Mixture Density Network Approach to Predicting Response Times in Layered Systems

Layering is a common feature in modern service-based systems. The characterization of response times in a layered system is an important but challenging analysis dimension in Quality of Service (QoS) assessment. In this paper, we develop a novel approach to estimate the mean and variance of response time in systems that may be abstracted as layered queueing networks. The core step of the method is to obtain the response time distributions in the submodels that are used to analyze the layered queueing networks by means of decomposition. We model the conditional response time distribution as a mixture of Gamma density functions for which we learn the parameters by means of a Mixture Density Network (MDN). The scheme recursively propagates the MDN predictions through the layers using phase-type distributions and performs convolutions to gain the approximation of the system delay. The experimental results show an accurate match between simulations and MDN predictions and also verify the effectiveness of the approach.