We consider the important decay parameter issue for a Markovian bulk-arrival and bulk-service queue which stops at reaching the first m states. The results obtained in this paper are a significant generalization of the ones obtained in Chen et al. (Queueing Syst 66:275–311, 2010). The exact value of the decay parameter is obtained. Based on the results obtained in this paper, we provide a practical method for calculating the decay parameter which is very effective. In some cases, the decay parameter can even be easily expressed explicitly. Some important key lemmas which also have their own interest are provided. The interesting and clear geometric interpretation of the decay parameter is explained. A few examples are provided to illustrate the results obtained in this paper.

我们考虑马尔可夫批量到达和批量服务队列的重要衰减参数问题，该队列在到达前m个状态时停止。本文获得的结果是对 Chen 等人获得的结果的重要概括。（排队系统 66：275–311，2010 年）。获得衰减参数的准确值。基于本文获得的结果，我们提供了一种非常有效的计算衰减参数的实用方法。在某些情况下，衰减参数甚至可以很容易地明确表达。提供了一些重要的关键引理，它们也有自己的兴趣。解释了衰减参数的有趣且清晰的几何解释。提供了一些例子来说明本文获得的结果。