论文标题
在$ m^{[x]}/m/1 $处理器共享队列中的批量时间
On the sojourn time of a batch in the $M^{[X]}/M/1$ Processor Sharing Queue
论文作者
论文摘要
在本文中，我们分析了共享$ m^{[x]}/m/1 $处理器队列中整个批次的搬家，在那里，根据Poisson流程，几何分布式批次到达，工作需要指数级服务时间。通过根据系统中的作业数量和标记批处理中的作业数量进行调节，我们在条件索期时代之间建立了复发关系，随后，这使我们能够为相关的双变量生成功能得出一个部分微分方程。该方程涉及一个未知的生成函数，可以通过求解无限的下三角线性系统来计算其系数。一旦确定了此未知函数，我们就会计算系统中批处理时间的索期时间的平均值。
In this paper, we analyze the sojourn of an entire batch in a processor sharing $M^{[X]}/M/1$ processor queue, where geometrically distributed batches arrive according to a Poisson process and jobs require exponential service times. By conditioning on the number of jobs in the systems and the number of jobs in a tagged batch, we establish recurrence relations between conditional sojourn times, which subsequently allow us to derive a partial differential equation for an associated bivariate generating function. This equation involves an unknown generating function, whose coefficients can be computed by solving an infinite lower triangular linear system. Once this unknown function is determined, we compute the Laplace transform and the mean value of the sojourn time of a batch in the system.
