Variational inference for Markovian queueing networks

Abstract Queueing networks are stochastic systems formed by interconnected resources routing and serving jobs. They induce jump processes with distinctive properties, find widespread use in inferential tasks. Here, service rates for jobs potential bottlenecks the mechanism must be estimated from a reduced set of observations. However, this calls derivation complex conditional density representations, over both network trajectories rates, which is considered an intractable problem. Numerical simulation procedures designed purpose do not scale, because high computational costs; furthermore, variational approaches relying on approximating measures full independence assumptions unsuitable. In paper, we offer probabilistic interpretation methods applied to inference tasks queueing networks, show that measure choices routinely used yield ill-defined optimization problems. Yet demonstrate it still possible enable task, considering novel space expansion treatment analogous counting process job transitions. We present compare exemplary cases practical showing our framework offers efficient improved alternative where existing or numerically intensive solutions fail.