  Stochastic network calculus is a tool for computing error bounds on the
performance of queueing systems. However, deriving accurate bounds for networks
consisting of several queues or subject to non-independent traffic inputs is
challenging. In this paper, we investigate the relevance of the tools from
analytic combinatorics, especially the kernel method, to tackle this problem.
Applying the kernel method allows us to compute the generating functions of the
queue state distributions in the stationary regime of the network. As a
consequence, error bounds with an arbitrary precision can be computed. In this
preliminary work, we focus on simple examples which are representative of the
difficulties that the kernel method allows us to overcome.
