批排队、可逆性和首过渗流
Batch queues, reversibility and first-passage percolation
摘要：
我们考虑一个离散时间的排队模型，具有批服务和到达。到达和服务批次都具有伯努利分布的情况对应于离散时间M/M/1排队，并且两者都具有几何分布的情况也已被研究过。我们描述了一个共同的扩展到一个更一般的类，其中批次是产品的伯努利和几何，并使用可逆性参数来证明版本的伯克定理，这些模型。还描述了具有连续时间或连续工作负载的模型的扩展。作为一个应用程序，我们展示了如何将这些结果与Seppalainen和O 'Connell的方法相结合，为一类新的第一通道渗流问题提供精确解。
英文摘要：
We consider a model of queues in discrete time, with batch services and arrivals. The case where arrival and service batches both have Bernoulli distributions corresponds to a discrete-time M/M/1 queue, and the case where both have geometric distributions has also been previously studied. We describe a common extension to a more general class where the batches are the product of a Bernoulli and a geometric, and use reversibility arguments to prove versions of Burke's theorem for these models. Extensions to models with continuous time or continuous workload are also described. As an application, we show how these results can be combined with methods of Seppalainen and O'Connell to provide exact solutions for a new class of first-passage percolation problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
