It has been shown that, under some service policies, a queueing network can be unstable even if the load of every station is less than one. Although the stability of queueing systems in some special cases (e.g. under First-Buffer-First-Served policy) has been well addressed, there are still difficulties in coping with more general networks. In this paper, we study the stability problem through depicting the mutual blocking effect among different classes and generalize the concept of servers in the context of queueing networks based on the sample path analysis. We show that the general servers have similar impacts on the system stability as physical stations and a queueing network is pathwise stable if and only if the effective traffic intensity of every general server does not exceed one. Through case studies, we show that the stability of queueing networks and the structure of general servers are sensitive and depend on various factors, including the service policies. Furthermore, we prove that queueing systems operating under the Work-in-Progress-Dependent service policies are always stable if every physical station has sufficient capacity.

中文翻译：

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多类排队网络的路径稳定性

已经表明，在某些服务策略下，即使每个站点的负载小于1，排队网络也可能不稳定。尽管在一些特殊情况下（例如在First-Buffer-First-Served策略下）排队系统的稳定性已经得到很好的解决，但在应对更通用的网络方面仍然存在困难。在本文中，我们通过描述不同类之间的相互阻塞效应来研究稳定性问题，并基于样本路径分析在排队网络的背景下推广服务器的概念。我们表明，通用服务器对系统稳定性的影响与物理站点相似，并且当且仅当每个通用服务器的有效流量强度不超过 1 时，排队网络才是路径稳定的。通过案例研究，我们表明，排队网络的稳定性和通用服务器的结构是敏感的，取决于各种因素，包括服务策略。此外，我们证明，如果每个物理站都有足够的容量，则在工作中依赖服务策略下运行的排队系统总是稳定的。