Brownian Models of Closed Queueing Networks: Explicit Solutions for Balanced Three-Station Systems

Explicit Solutions for Queueing Problems

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...

Using ODEs from PEPA models to derive asymptotic solutions for a class of closed queueing networks

In this paper a class of closed queueing network is modelled in the Markovian process algebra PEPA. It is shown that a fluid flow approximation using ordinary differential equations (ODEs) gives rise to well known asymptotic results. This result gives context to the use of a fluid flow approximation and is potentially useful in cases where the model is not obviously a closed queueing network. T...

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 ...

Load Dependent Single Chain Models of Multichain Closed Queueing Networks

Often a multichain product form queueing network is used to model a complex computer system. In many cases, the multichain demands are unavailable or are diicult to obtain. In contrast, load dependent demands are often directly measurable. This paper investigates the use of a load dependent single chain model as an approximate model of an actual multichain system. In restricted cases, it is sho...