In this paper, a queueing system with multicast service, random resource requirements and general probability distributions of busy and idle periods is considered. Motivated by challenges from practical applications in the area of performance analysis of telecommunication systems, the model is built on the basis of well-known resource queueing systems theory. Two distinctive features of the model related to resource requirements are: the volume of a requirement, which is random with a given probability distribution function, and the resource requirements which overlap with each other. The first feature comes from the analysis of wireless networks, where the volume of resource depends on the location of the mobile equipment, type of telecommunication service, required data bitrate and radio signal path loss. The second feature relates to the multicast approach to data delivery in modern telecommunication networks. The stationary probability distribution of the number of customers in the system is derived. The main characteristics for the performance analysis of multicast telecommunication systems including the blocking probability, the mean number of customers in the system and the mean of the total amount of occupied resources are proposed. The analytical formulas for the performance calculations are obtained for the Fréchet-type distribution of a requested resources volume.

中文翻译：

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具有重叠资源需求的损失系统分析

在本文中，考虑了具有组播服务、随机资源需求和忙闲时间一般概率分布的排队系统。受电信系统性能分析领域实际应用挑战的启发，该模型建立在众所周知的资源排队系统理论的基础上。与资源需求相关的模型的两个显着特征是：需求量，它是随机的，具有给定的概率分布函数，以及相互重叠的资源需求。第一个特征来自对无线网络的分析，其中资源量取决于移动设备的位置、电信服务类型、所需的数据比特率和无线电信号路径损耗。第二个特征与现代电信网络中数据传输的多播方法有关。推导出系统中客户数量的平稳概率分布。提出了组播通信系统性能分析的主要特征，包括阻塞概率、系统平均客户数和占用资源总量的平均值。性能计算的分析公式是针对所请求资源量的 Fréchet 型分布获得的。提出了组播通信系统性能分析的主要特征，包括阻塞概率、系统平均客户数和占用资源总量的平均值。性能计算的分析公式是针对所请求资源量的 Fréchet 型分布获得的。提出了组播通信系统性能分析的主要特征，包括阻塞概率、系统平均客户数和占用资源总量的平均值。性能计算的分析公式是针对所请求资源量的 Fréchet 型分布获得的。