We consider a two-node queue modeled as a two-dimensional random walk. In particular, we consider the case that one or both queues have finite buffers. We develop an approximation scheme based on the Markov reward approach to error bounds in order to bound performance measures of such random walks. The approximation scheme is developed in terms of a perturbed random walk in which the transitions along the boundaries are different from those in the original model and the invariant measure of the perturbed random walk is of product-form. We then apply this approximation scheme to a tandem queue and some variants of this model, for the case that both buffers are finite. The modified approximation scheme and the corresponding applications for a two-node queueing system in which only one of the buffers has finite capacity have also been discussed.

中文翻译：

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有限缓冲区的两节点队列的性能测量

我们考虑建模为二维随机游走的两节点队列。特别是，我们考虑一个或两个队列具有有限缓冲区的情况。我们开发了一种基于马尔可夫奖励方法的近似方案，以限制这种随机游走的性能度量。近似方案是根据扰动随机游走开发的，其中沿边界的转换与原始模型中的不同，并且扰动随机游走的不变测量是乘积形式的。然后，我们将此近似方案应用于串联队列和该模型的一些变体，以应对两个缓冲区都是有限的情况。还讨论了仅一个缓冲区具有有限容量的双节点排队系统的改进近似方案和相应应用。