Limiting results for multiprocessor systems with breakdowns and repairs
Limiting results for multiprocessor systems with breakdowns and repairs
复制标题
具有故障和维修的多处理器系统的限制结果
DOI：
10.1007/bf01158870
复制
发表时间：
1993
期刊：
影响因子：
1.2
通讯作者：
A. Puhalskii
中科院分区：
文献类型：
--
作者：
I. Mitrani;A. Puhalskii
M/M/N 队列中的每个处理器都受到独立的随机故障和修复，在两种限制机制下的稳定状态下进行分析。第一个是通常的大流量限制，其中提供的负载接近可用处理能力。 （适当标准化的）队列大小显示为渐近指数分布并且独立于操作处理器的数量。第二个限制方案涉及增加手术期和非手术期的平均长度，同时保持其比率恒定。再次确定适当归一化的队列大小的渐近分布。这次结果是具有简单极点的有理拉普拉斯变换。在这两种情况下，相关参数都很容易计算。
An M/M/N queue, where each of the processors is subject to independent random breakdowns and repairs, is analyzed in the steady state under two limiting regimes. The first is the usual heavy traffic limit where the offered load approaches the available processing capacity. The (suitably normalized) queue size is shown to be asymptotically exponentially distributed and independent of the number of operative processors. The second limiting regime involves increasing the average lengths of the operative and inoperative periods, while keeping their ratio constant. Again the asymptotic distribution of an appropriately normalized queue size is determined. This time it turns out to have a rational Laplace transform with simple poles. In both cases, the relevant parameters are easily computable.