Nonexistence of Brownian Models for Certain Multiclass Queueing Networks

We present two multiclass queueing networks where the Brownian models proposed by Harrison and Nguyen [3, 4] do not exist. If self-feedback is allowed, we can construct such an example with a twostation network. For a three-station network, we can construct such an example without self-feedback. Keywords: Brownian model, multiclass network, heavy traffic, diffusion approximation, performance analysis. Running Head: Nonexistence of Brownian Models 1 Introduction 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 method for performance analysis of open networks. The network models they consider have general routing and general service requiremen..