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Ensuring the conformance of a service system's end-to-end delay to servicelevel agreement (SLA) constraints is a challenging task that requiresstatistical measures beyond the average delay. In this paper, we study thereal-time prediction of the end-to-end delay distribution in systems withcomposite services such as service function chains. In order to have a generalframework, we use queueing theory to model service systems, while also adoptinga statistical learning approach to avoid the limitations of queueing-theoreticmethods such as stationarity assumptions or other approximations that are oftenused to make the analysis mathematically tractable. Specifically, we use deepmixture density networks (MDN) to predict the end-to-end distribution of thedelay given the network's state. As a result, our method is sufficientlygeneral to be applied in different contexts and applications. Our evaluationsshow a good match between the learned distributions and the simulations, whichsuggest that the proposed method is a good candidate for providingprobabilistic bounds on the end-to-end delay of more complex systems wheresimulations or theoretical methods are not applicable.

Probabilistic Bounds on the End-to-End Delay of Service Function Chains using Deep MDN