具有有限处理机共享规则的并行系统
Queueing Systems with Some Versions of Limited Processor Sharing Discipline
摘要：
本文考虑了一个处理机共享有限的调度系统。不能同时提供n个以上的工作。该系统可用于对无线通信系统中的带宽共享和计算机网络中的服务过程进行建模。如果在所考虑的调度系统中有n个作业，并且有一个新的作业到达，则到达的作业丢失，或者作业的服务中断，该作业丢失。我们学习两个规则来选择要失去的工作。根据这些规则之一，具有最短剩余长度的作业将丢失。得到了所考虑系统的状态概率与相应的无限处理机共享系统的状态概率之间的关系。如果无限处理器共享系统的状态概率已知，则这些关系允许计算所考虑系统的状态概率。在泊松到达过程的情况下，服务器容量耗尽的概率等于作业丢失的概率。我们得到了这种情况下定态概率和损失率的显式表达式。在工件长度平均值一定的条件下，这些概率在工件长度分布下是不变的。
英文摘要：
The paper considers a queueing system with limited processor sharing. No more than n jobs may be served simultaneously. This system may be used for modeling bandwidth sharing in wireless communication systems and processes of service in computer networks. If there are n jobs in the considered queueing system and a new job arrives, then the arriving job is lost or the service of a job is interrupted and this job is lost. We study two rules to choose the job to be lost. In accordance with one of these rules, the job with the shortest remaining length is lost. Relations are obtained between the state probabilities of considered system and the state probabilities of the corresponding unlimited processor sharing system. These relations allow to compute the state probabilities for considered system if the state probabilities for the unlimited processor sharing system are known. In the case of Poisson arrival process, the probability that the server capacity is exhausted is equal to the probability that a job is lost. We have obtained an explicit formulas for the stationary state probabilities and the loss probability for this case. These probabilities are invariant under the job length distribution under the condition that the average value of the length is fixed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
