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首页> 外文期刊>Bulletin of the Polish Academy of Sciences. Technical Sciences >Single-server queueing system with external and internal customers
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Single-server queueing system with external and internal customers

机译：具有外部和内部客户的单服务器队列系统

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摘要

In the paper,we investigate a single-server queueing system with unlimited memory space and non-homogeneous customers(calls)of the two following types: 1)external customers that are served by the system under consideration,2)internal customers that arrive and interrupt the service process only when an external customer is being served.The external customers appear according to a stationary Poisson process.Customers of each of the above-mentioned types are characterized by some random volume.The customer service time depends arbitrarily on its volume.Two schemes of customer service organization are analyzed.The non-stationary and stationary distributions of the total volume of customers present in the system are determined in terms of Laplace and Laplace-Stieltjes transforms.The stationary first and second moments of total customers volume are also calculated.The obtained results are used to approximate loss characteristics in analogous systems with limited buffer space.Numerical examples illustrating theoretical results are attached as well.
机译：在本文中，我们研究了一个单服务器排队系统，该系统具有无限的内存空间和以下两种类型的非同质客户（调用）：1）由所考虑的系统服务的外部客户，2）只有在外部客户被服务时才到达并中断服务过程的内部客户。外部客户是按照平稳泊松过程出现的。上述每种类型的客户都具有随机数量的特征。客户服务时间任意取决于其数量。分析了两种客户服务组织方案。根据拉普拉斯变换和拉普拉斯-斯蒂尔杰斯变换，确定了系统中总客户量的非平稳和平稳分布。还计算了总客户量的平稳一阶矩和二阶矩。所得结果可用于模拟缓冲空间有限的系统的损耗特性。文中还附上了一些数值例子来说明理论结果。

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