The stability of open queueing networks

Stability of Open Multiclass Queueing Networks via Fluid Models

This paper surveys recent work on the stability of open multiclass queueing networks via fluid models. We recapitulate the stability result of Dai [8]. To facilitate study of the converse of the stability result, we distinguish between the notion of fluid limit and that of fluid solution. We define the stability region of a service discipline and the global stability region of a network. Exampl...

Stability of queueing networks

2 The classical networks 186 2.1 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 2.2 Stationarity and reversibility . . . . . . . . . . . . . . . . . . . . 191 2.3 Homogeneous nodes of Kelly type . . . . . . . . . . . . . . . . . . 195 2.4 Symmetric nodes . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 2.5 Quasi-reversibility . . . . . . . . . . . . . . . ...

Stochastic Stability of Queueing Networks*

This paper investigates geometric stability and L p-stability of discrete-time Markov chains associated with closed and open queueing networks with Markovian routing. By geometric stability (resp. L p-stability) we mean that the chain is re-generative in the Harris-recurrent sense and that the times between the successive regeneration points have a bounded moment generating function (resp. a bo...

Brownian Approximations of Multiclass Open-Queueing Networks

Stability and Optimization of Queueing Networks

We describe some approaches to the synthesis of optimal policies for multiclass queueing network models based upon the close connection between stability of queueing networks and their associated uid limit models. It is found that there is also a close connection between optimization of the network and optimal control of the far simpler uid network model. This observation leads to a new class o...