用离散时间马尔可夫链预测进入死锁的时间

A. Bondi
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引用次数: 1

摘要

当进程加入一个通用FCFS队列来获取或释放固定大小的对象池中的资源时,如果队列头部的进程希望在池为空时获取资源,即使希望放弃资源的进程排在后面,也会发生死锁。我们描述了这个问题的状态机表示。我们使用该表示来开发离散时间马尔可夫链分析,以确定最有可能发生死锁的负载条件以及可能发生死锁的时间。我们表明,无论负载如何,死锁几乎肯定会发生,并且死锁开始的时间取决于池中资源的请求率、资源的平均保持时间和池大小的组合。计算证实了这样的直觉,即在高负载或资源池较小时,死锁会更快发生。将此问题与具有单一吸收和单一反射屏障的随机漫步问题联系起来。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Predicting the Time to Migrate Into Deadlock Using a Discrete Time Markov Chain
When processes join a common FCFS queue to acquire or release resources in an object pool of fixed size, deadlock occurs if the process at the head of the queue wishes to acquire a resource when the pool is empty, even if a process wishing to relinquish a resource is queued behind. We describe a state machine representation of this problem. We use the representation to develop a discrete time Markov chain analysis to identify the load conditions under which deadlock is most likely to occur and how soon it is likely to occur. We show that deadlock occurs almost surely regardless of the load, and that the time to the onset of deadlock depends on combinations of the request rate for resources in the pool, the average holding time of the resources, and the size of the pool. Calculations corroborate the intuition that deadlock will occur sooner at heavy loads or when the resource pool is small. A connection will be made between this problem and the problem of random walks with a single absorbing and a single reflecting barrier.
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