Institute of Informatics, Silesian University of Technology, Gliwice, Poland.
PLoS One. 2019 Jul 17;14(7):e0219444. doi: 10.1371/journal.pone.0219444. eCollection 2019.
We present an analysis of queueing systems with the dropping function, infinite buffer and general distribution of the service time. Firstly, a stability condition, more general than the well-known ρ < 1, is proven. Secondly, the formulas for the queue size distribution, loss ratio and mean duration of the busy period, are derived. Thirdly, numerical examples are given, including optimizations of the shape of the dropping function with regard to the combined cost of the queue size and loss ratio.
我们提出了具有丢弃功能、无限缓冲区和一般服务时间分布的排队系统分析。首先，证明了一个比著名的 ρ < 1 更一般的稳定性条件。其次，导出了队列大小分布、损失比和忙期平均持续时间的公式。第三，给出了数值示例，包括针对队列大小和损失比的组合成本对丢弃函数形状的优化。
