Algorithmic challenges in the theory of queueing networks

The theory of queueing systems is traditionally considered as a branch of applied probability. Hence the toolkit used in the analysis of queueing system draws heavily on the theory of stochastic processes. Many problems in the area of queueing networks, however, are of algorithmic nature, and thus require algorithmic/complexity theoretic approaches. In this tutorial we will discuss several such questions, ranging from some older results on designing optimal control of queueing networks, to more recent results on determining stability properties of queueing networks leading to the fascinating theory of algorithmic undecidability (non-computability). We will illustrate these approaches on a broad scope of models, including multiclass queueing networks, constrained random walks and Skorokhod mapping problem, the latter arising in studying queueing networks in the heavy traffic regime.