An explicit solution for a tandem queue with retrials and losses
An explicit solution for a tandem queue with retrials and losses
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DOI：
10.1007/s12351-011-0113-7
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发表时间：
2011-04
影响因子：
2.7
通讯作者：
Tuan Phung-Duc
中科院分区：
文献类型：
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作者：
Tuan Phung-Duc
研究了服务时间服从两个指数分布的两服务台重试串联排队系统。有两种类型的客户：类型一和类型二。类型1的客户根据泊松过程到达第一个服务器。类型一的到达客户发现第一个服务器忙碌，加入轨道，并在一段时间后重试进入服务器。我们假设顾客从轨道到达的速率是重试顾客数的线性函数。在第一服务器处被服务之后，类型一的客户移动到第二服务器。第二类客户直接到达第二个服务器根据另一个泊松过程。如果第二个服务器在到达时忙碌，则类型一和类型二的客户都将丢失。对于这个模型，我们推导出明确的表达式的联合平稳分布之间的客户数量的轨道和服务器的状态。我们证明了平稳分布计算的数值稳定的算法。数值例子显示参数对系统性能的影响。
We consider a retrial tandem queueing system with two servers whose service times follow two exponential distributions. There are two types of customers: type one and type two. Customers of type one arrive at the first server according to a Poisson process. An arriving customer of type one that finds the first server busy joins an orbit and retries to enter the server after some time. We assume that the arrival rate of customers from the orbit is a linear function of the number of retrial customers. After being served at the first server, a customer of type one moves to the second server. Customers of type two directly arrive at the second server according to another Poisson process. Customers of both types one and two are lost if the second server is busy upon arrival. For this model, we derive explicit expressions of the joint stationary distribution between the number of customers in the orbit and the states of the servers. We prove that the stationary distribution is computed by a numerically stable algorithm. Numerical examples are provided to show the influence of parameters on the performance of the system.