Brownian models of open queueing networks

Brownian Approximations of Multiclass Open-Queueing Networks

Nonexistence of Brownian models for certain multiclass queueing networks

It has been demonstrated that Brownian models are effective for approximate analysis of queueing networks, particularly when no explicit analytical methods are available [3,4,1]. In 1988 Harrison [2] proposed Brownian models as approximations for multiclass open queueing networks. That work was expanded by Harrison and Nguyen in two recent papers [3,4] with the aim of developing a systematic me...

Dynamic routing in open queueing networks: Brownian models, cut constraints and resource pooling

We present an introductory review of recent work on the control of open queueing networks. We assume that customers of different types arrive at a network and pass through the system via one of several possible routes; the set of routes available to a customer depends on its type. A route through the network is an ordered set of service stations: a customer queues for service at each station on...

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...

Brownian Models of Feedforward Queueing Networks: Quasireversibility and Product Form Solutions

We consider a very general type of d-station open queueing network, with multiple customer classes and a more or less arbitrary service discipline at each station, but restricted by the requirement that customers always ow from lowered numbered stations to higher numbered ones. To approximate the behavior of such a queueing network under heavy traac conditions, a corresponding Brownian network ...