论文标题
在四分之一平面中的部分均匀的最近邻居随机步行中，并在分析二维队列中的应用有限的状态依赖性
On partially homogeneous nearest-neighbour random walks in the quarter plane and their application in the analysis of two-dimensional queues with limited state-dependency
论文作者
论文摘要
这项工作涉及对二维部分均匀近距离随机步行的固定分析。这种类型的随机步行的特征是一步过渡概率是状态空间的函数。我们表明，通过求解有限的线性方程，两个矩阵功能方程式以及借助Riemann（-Hilbert）边界价值问题的函数方程来研究其固定行为。这项工作是由无线网络流量级别的新兴应用程序强烈的动机，这些应用程序在具有可扩展服务能力的排队模型以及基于队列的随机访问协议中引起了排队模型，其中网络的参数是队列长度的函数。还提供了一个简单的数字说明，以及有关数值实现的一些详细信息。
This work deals with the stationary analysis of two-dimensional partially homogeneous nearest-neighbour random walks. Such type of random walks are characterized by the fact that the one-step transition probabilities are functions of the state-space. We show that its stationary behaviour is investigated by solving a finite system of linear equations, two matrix functional equations, and a functional equation with the aid of the theory of Riemann (-Hilbert) boundary value problems. This work is strongly motivated by emerging applications in flow level performance of wireless networks that give rise in queueing models with scalable service capacity, as well as in queue-based random access protocols, where the network's parameters are functions of the queue lengths. A simple numerical illustration, along with some details on the numerical implementation are also presented.
