论文标题
与离散时间马尔可维亚到达过程的无限缓冲器批处理大小的服务队列：D- $ MAP/g_n^{（a，b）}/1 $
Analysis of an infinite-buffer batch-size-dependent service queue with discrete-time Markovian arrival process: D-$MAP/G_n^{(a,b)}/1$
论文作者
论文摘要
离散的时间排队模型找到了庞大的应用程序，因为它们用于建模在电信系统，计算机网络等数字平台上产生的排队系统。在本文中，我们分析了具有离散的Markovian到达过程的Infinite-Buffer排队模型。根据一般的批量服务规则，一台服务器分批提供了这些单元，而服务时间遵循一般分布，服务速率取决于所服务的批处理大小。我们使用补充变量技术来数学上制定模型，并在偏离时期获得矢量生成函数。生成功能依次用于根据特征方程的根来提取队列和服务器内容的联合分布。此外，我们发展了出发时期的分布与任意，到达前和外部观察者时期的分布之间的关系，该时期用于获得后者。我们评估了系统的一些基本性能度量，并广泛讨论计算过程，这是通过一些数值示例证明的。
Discrete-time queueing models find huge applications as they are used in modeling queueing systems arising in digital platforms like telecommunication systems, computer networks, etc. In this paper, we analyze an infinite-buffer queueing model with discrete Markovian arrival process. The units on arrival are served in batches by a single server according to the general bulk-service rule, and the service time follows general distribution with service rate depending on the size of the batch being served. We mathematically formulate the model using the supplementary variable technique and obtain the vector generating function at the departure epoch. The generating function is in turn used to extract the joint distribution of queue and server content in terms of the roots of the characteristic equation. Further, we develop the relationship between the distribution at the departure epoch and the distribution at arbitrary, pre-arrival and outside observer's epoch, which is used to obtain the latter ones. We evaluate some essential performance measures of the system and also discuss the computing process extensively which is demonstrated by a few numerical examples.
