Strong approximations for multiclass feedforward queueing networks

Strong Approximations for Multi lass Feedforward Queueing Networks

Brownian Approximations of Multiclass Open-Queueing Networks

FLUID APPROXIMATIONS AND STABILITY OF MULTICLASS QUEUEING NETWORKS: WORK-CONSERVING DISCIPLINES Running Head: Multiclass Queueing Networks

This paper studies the uid approximation (also known as the functional strong law-of-large-numbers) and the stability (positive Harris recurrent) for a multiclass queueing network. Both of these are related to the stabilities of a linear uid model, constructed from the rst-order parameters (i.e., long-run average arrivals, services and routings) of the queueing network. It is proved that the ui...

Sample Path Large Deviations for Multiclass Feedforward Queueing Networks in Critical Loading

We consider multiclass feedforward queueing networks with first in first out and priority service disciplines at the nodes, and class dependent deterministic routing between nodes. The random behavior of the network is constructed from cumulative arrival and service time processes which are assumed to satisfy an appropriate sample path large deviation principle. We establish logarithmic asympto...

Stability conditions for multiclass uid queueing networks

We introduce a new method to investigate stability of work-conserving policies in multiclass queueing networks. The method decomposes feasible trajectories and uses linear programming to test stability. We show that this linear program is a necessary and suucient condition for the stability of all work-conserving policies for multiclass uid queueing networks with two stations. Furthermore, we n...