Asymptotic Analysis for Markovian Retrial Queues with Two Types of Nonpersistent Customers
Asymptotic Analysis for Markovian Retrial Queues with Two Types of Nonpersistent Customers
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发表时间：
2013-12
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通讯作者：
Tuan Phung-Duc
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作者：
Tuan Phung-Duc
我们考虑马尔可夫多服务器重试队列，其中阻塞的客户有两个放弃机会：阻塞时刻或离开轨道的时刻。在该排队系统中，系统（服务器和缓冲区）中的顾客数量与轨道上的顾客数量形成了一个依赖于水平的准生与死过程，其平稳分布用速率矩阵序列表示。利用简单的微扰技术和矩阵解析方法，导出了速率矩阵的非零元素关于轨道中顾客数的泰勒级数展开式。我们也得到了展开式所有系数的显式表达式。进一步，我们导出了系统中顾客数量与轨道上顾客数量联合平稳分布的尾部渐近公式。数值算例表明，具有两种非持久客户的模型的尾部概率大于具有一种非持久客户的相应模型的尾部概率。
We consider Markovian multiserver retrial queues where a blocked customer has two opportunities for abandonment: at the moment of blocking or at the departure epoch from the orbit. In this queueing system, the number of customers in the system (servers and buffer) and that in the orbit form a level-dependent quasi-birth-and-death (QBD) process whose stationary distribution is expressed in terms of a sequence of rate matrices. Using a simple perturbation technique and a matrix analytic method, we derive Taylor series expansion for nonzero elements of the rate matrices with respect to the number of customers in the orbit. We also obtain explicit expressions for all the coefficients of the expansion. Furthermore, we derive tail asymptotic formulae for the joint stationary distribution of the number of customers in the system and that in the orbit. Numerical examples reveal that the tail probability of the model with two types of nonpersistent customers is greater than that of the corresponding model with one type of nonpersistent customers.