Fluid approximations and stability of multiclass queueing networks: Work-conserving disciplines
Fluid approximations, i.e. deterministic approximations, for general networks of queues have found considerable interest recently. Especially for the case of non product form networks these approximations provide under suitable conditions at the same time information about the stability (positive Harris recurrence) of the network. Compared with diffusion approximations (concerning functional central limit theorems) the fluid approximations are functional strong laws of large numbers. The fluid approximations considered here are linear fluid models constructed by using the data obtained from the long-run averages of the network's driving sequences: arrival streams, service times, routing decisions, i.e., the fluid approximations of the driving sequences. The class of linear fluid models is investigated, criteria for stability (zero-level is reached in finite time for any initial buffer content) and weak stability (empty systems remain empty) are obtained. It is proved that these properties imply the existence of the fluid approximation and guarantee positive Harris recurrence for the state process of the network. The networks considered allow for multiple customer classes, non exponential service times, and non Poisson arrivals, thus generalizing previous results from the literature.
scientific article; zbMATH DE number 854859