Periodic dynamics in queuing networks

This paper deals with state-dependent open Markovian (or exponential) queuing networks, for which arrival and service rates, as well as routing probabilities, may depend on the queue lengths. For a network of this kind, following Mandelbaum and Pats, we provide a formal definition of its associated fluid model, and we focus on the relationships which may occur between the network stochastic dynamics and the deterministic dynamics of its corresponding fluid model, particularly focusing on queuing networks whose fluid models have global periodic attractors.