We consider Poisson streams of exponentially distributed jobs arriving at each edge of a hypergraph of queues. Upon arrival, an incoming job is routed to the shortest queue among the corresponding vertices. This generalizes many known models such as power-of- d load balancing and JSQ (join the shortest queue) on generic graphs. We prove that stability in this model is achieved if and only if there exists a stable static routing policy. This stability condition is equivalent to that of the JSW (join the shortest workload) policy. We show that some graph topologies lead to a loss of capacity, implying more restrictive stability conditions than in, for example, complete graphs.

中文翻译：

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JSQ 在具有一般服务器作业类兼容性的队列中的稳定性

我们考虑到达队列超图的每个边缘的指数分布作业的泊松流。到达后，传入的作业被路由到相应顶点中最短的队列。这在通用图上概括了许多已知模型，例如 power-of-d 负载平衡和 JSQ（加入最短队列）。我们证明了当且仅当存在稳定的静态路由策略时，才能实现该模型的稳定性。这种稳定性条件等同于 JSW（加入最短工作量）策略的稳定性条件。我们展示了一些图拓扑会导致容量损失，这意味着比完整图更具限制性的稳定性条件。