We consider open multi-class queueing networks with general arrival processes, general processing time sequences and Bernoulli routing. The network is assumed to be operating under an arbitrary work-conserving scheduling policy that makes the system stable. We study the variability of flows within the network. Computable expressions for quantifying flow variability have previously been discussed in the literature. However, in this paper, we shed more light on such analysis to justify the use of these expressions in the asymptotic analysis of network flows. Toward that end, we find a simple diffusion limit for the inter-class flows and establish the relation to asymptotic (co-)variance rates.

我们考虑具有一般到达过程、一般处理时间序列和伯努利路由的开放式多类排队网络。假定网络在使系统稳定的任意工作保护调度策略下运行。我们研究网络内流量的可变性。用于量化流量可变性的可计算表达式先前已在文献中讨论过。然而，在本文中，我们对此类分析进行了更多阐述，以证明在网络流的渐近分析中使用这些表达式是合理的。为此，我们找到了类间流量的简单扩散限制，并建立了与渐近（共）方差率的关系。