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Steady-state behavior of interacting queues-a numerical approach

机译：交互队列的稳态行为-一种数值方法

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摘要

The M queues that interact according to a model of multiple-access transmissions over a collision channel are considered. Each queue receives messages that it attempts to transmit in a classical slotted ALOHA fashion. The steady-state behavior of such systems is unknown except in certain simple cases. A numerical approach is proposed that permits the calculation, within any desired accuracy, of the joint queue size distribution as well as of the moments. The approach uses a technique that involves auxiliary systems of queues that dominate, in a well-defined sense, the given ones. Consideration of such dominating systems in some cases permits the study of the ergodic region of the original systems. The methodology developed here is applicable to contexts more general than that of multiple-access transmissions.
机译：考虑了根据冲突信道上的多址传输模型进行交互的M个队列。每个队列都接收尝试尝试以传统时隙ALOHA方式传输的消息。除某些简单情况外，此类系统的稳态行为是未知的。提出了一种数值方法，该方法允许在任何期望的精度内计算联合队列大小分布以及弯矩。该方法使用一种技术，该技术涉及在明确定义的意义上主导给定队列的辅助队列系统。在某些情况下，考虑使用此类主导系统可以研究原始系统的遍历区域。此处开发的方法适用于比多址传输更通用的环境。

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