Brownian models of open queueing networks: Product-form stationary distributions

Product Form Queueing Networks

Queueing network models have been extensively applied to represent and analyze resource sharing systems such as communication and computer systems and they have proved to be a powerful and versatile tool for system performance evaluation and prediction. Product form queueing networks have a simple closed form expression of the stationary state distribution that allow to define efficient algorit...

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 ...

Product-form stationary distributions for deficiency zero chemical reaction networks.

We consider stochastically modeled chemical reaction systems with mass-action kinetics and prove that a product-form stationary distribution exists for each closed, irreducible subset of the state space if an analogous deterministically modeled system with mass-action kinetics admits a complex balanced equilibrium. Feinberg's deficiency zero theorem then implies that such a distribution exists ...

Brownian Approximations of Multiclass Open-Queueing Networks

A Characterization of Product-form Stationary Distributions for Queueing Systems in Random Environment

We consider continuous-time Markov chains representing queueing systems in random environment and we obtain necessary and sufficient conditions for having product-form stationary distributions. The related topics of partial balance and the ESTA property are also studied. As an illustration, we apply the results to study the stationary distributions of Jackson networks in random environment. For...