Qualitative dynamical analysis of queueing networks with inhibition

Abstract

An approximate dynamical extension of queueing theory result is described and is applied to Jackson's and G's Networks. It is shown that the dynamics of these networks may be represented by non-linear compartmental systems which are cooperative for the former case and may sometimes be competitive for the latter case. The implications in term of stability are discussed and an illustrative example is provided.

Diffusion Approximation of State-Dependent G-Networks Under Heavy Traffic

“…The problem of describing the transient evolution of a queueing network with negative customers has been dealt with in some recent works using fluid approximations [4], [35]. In the former article, transient evolution of a state-dependent network with negative customers was considered using a fluid approximation together with a heavy-traffic assumption.…”