Analysis of the loss probability in the M/G/1+G queue
Analysis of the loss probability in the M/G/1+G queue
复制标题
M/G/1G队列丢包概率分析
DOI：
10.1007/s11134-015-9449-7
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发表时间：
2015
期刊：
影响因子：
1.2
通讯作者：
Yoshiaki Inoue and Tetsuya Takine
中科院分区：
文献类型：
--
作者：
Yoshiaki Inoue and Tetsuya Takine
我们考虑了平稳M/G/1+G排队的损失概率，即具有不耐烦顾客的平稳M/G/1排队，其不耐烦时间一般为分布。已知损失概率以虚拟等待时间的概率密度函数v(X)给出，v(X)由Volterra积分方程级数解形式给出。本文证明了V(X)的级数解可以解释为相依随机变量的随机和的概率密度函数，并通过对具有工作量相关损失的后进先服务抢先恢复M/G/1排队的分析，揭示了它的相依结构。此外，基于这一观察结果，我们还给出了丢失概率的一些性质。
We consider the loss probability in the stationary M/G/1+G queue, i.e., the stationary M/G/1 queue with impatient customers whose impatience times are generally distributed. It is known that the loss probability is given in terms of the probability density functionv(x) of the virtual waiting time and thatv(x) is given by a formal series solution of a Volterra integral equation. In this paper, we show that the series solution ofv(x) can be interpreted as the probability density function of a random sum of dependent random variables and we reveal its dependency structure through the analysis of a last-come first-served, preemptive-resume M/G/1 queue with workload-dependent loss. Furthermore, based on this observation, we show some properties of the loss probability.