Diffusion Limit of a Two-Class Network - Stationary Distributions and Interchange of Limits

摘要

In [11], we have established the diffusion limit for a network with two servers (both being bottlenecks) and two job classes under a proportional fair resouce control. Here, we show that the usual traffic condition is necessary and sufficient for the existence and uniqueness of the stationary distributions of both the diffusion limit and the pre-limit processes. Furthermore, the interchange of limits is also justified, i.e., the sequence of stationary distributions of the pre-limit networks converges to that of the diffusion limit.