Of Kernels and Queues: when network calculus meets analytic combinatorics

TL;DR

This paper explores how analytic combinatorics, particularly the kernel method, can improve the computation of error bounds in stochastic network calculus for queueing networks with complex traffic inputs.

Contribution

It introduces the application of the kernel method from analytic combinatorics to derive generating functions for queue state distributions, enabling precise error bounds.

Findings

Kernel method computes generating functions for queue states.

Error bounds with arbitrary precision are achievable.

Preliminary results on simple network examples.

Abstract

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.