Chydzinski Andrzej
Department of Computer Networks and Systems, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland.
Entropy (Basel). 2020 Jul 28;22(8):825. doi: 10.3390/e22080825.
We deal with a queueing system, in which arriving packets are being dropped with the probability depending on the queue size. Such a scheme is used in several active queue management schemes proposed for Internet routers. In this paper, we derive and analyze a selected transient characteristic of the model, i.e., the probability that in a given time interval the queue size is kept under a predefined level. As the main purpose of the discussed queueing scheme is to maintain the queue size low, this is a natural characteristic to study. In addition to that, the average time to reach a given level is derived. Theoretical results for both characteristics are accompanied by numerical examples. Among other things, they demonstrate that the transient behavior of the queue may vary significantly with the shape of the dropping function, even if the steady-state performance remains unaltered.
我们研究一个排队系统，在该系统中，到达的数据包会以取决于队列大小的概率被丢弃。这种方案被用于为互联网路由器提出的几种主动队列管理方案中。在本文中，我们推导并分析了该模型的一个选定的瞬态特性，即在给定时间间隔内队列大小保持在预定义水平以下的概率。由于所讨论的排队方案的主要目的是保持队列大小较低，这是一个自然要研究的特性。除此之外，还推导了达到给定水平的平均时间。这两个特性的理论结果都伴有数值示例。其中，它们表明即使稳态性能保持不变，队列的瞬态行为也可能随丢弃函数的形状而显著变化。
