论文标题
带有某些版本的有限处理器共享纪律的排队系统
Queueing Systems with Some Versions of Limited Processor Sharing Discipline
论文作者
论文摘要
该论文考虑了一个有限的处理器共享的排队系统。不超过n个工作可以同时提供。该系统可用于在计算机网络中的无线通信系统和服务过程中建模带宽共享。如果在考虑的排队系统中有n个工作，并且有新的工作到来，那么到达工作就会丢失，或者工作的服务被中断，并且丢失了这一工作。我们研究两个规则以选择要丢失的工作。根据这些规则之一，剩余长度最短的工作丢失了。在考虑系统的状态概率与相应无限处理器共享系统的状态概率之间获得了关系。如果已知无限的处理器共享系统的状态概率，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丢失作业的概率。我们已经获得了固定状态概率的明确公式和此案的损失概率。这些概率在工作时间长度分布的情况下是不变的，即长度的平均值是固定的。
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.
