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Queueing networks are systems of theoretical interest that find widespreaduse in the performance evaluation of interconnected resources. In comparison tocounterpart models in genetics or mathematical biology, the stochastic (jump)processes induced by queueing networks have distinctive coupling andsynchronization properties. This has prevented the derivation of variationalapproximations for conditional representations of transient dynamics, whichrely on simplifying independence assumptions. Here, we present a modelaugmentation to a multivariate counting process for interactions across servicestations, and we enable the variational evaluation of mean-field measures forpartially-observed multi-class networks. We also show that our framework offersan efficient and improved alternative for inference tasks, where existingvariational or numerically intensive solutions do not work.

Variational inequalities and mean-field approximations for partially observed systems of queueing networks