ABSTRACT

The quality control services provided to customers play an important role in increasing an organization’s economic benefit. Under the quality control process, we present a novel iterative algorithm to obtain the transient probability of the feedback M/M/1/N queue with balking and retention of reneged customers. Based on the Laplace transform, we obtain the exponential matrix corresponding to the proposed system consequently, obtaining the exact solution of the probability dynamical system of differential equations of $n$ customers in the system. Also, an efficient algorithm has been introduced. The Laplace transform and the proposed algorithm enable us to obtain the exact solutions of the transient-states of queuing systems with different capacities. Several numerical examples are given to illustrate the behavior of probabilities as functions in time, the expected number of units in the system, queue and the optimization of the model. A transient solution for some important queuing systems is driven as a special case.

摘要

为客户提供的质量控制服务在提高组织的经济效益方面发挥着重要作用。在质量控制过程中，我们提出了一种新颖的迭代算法来获得反馈 M/M/1/N 队列的瞬态概率，以及拒绝和保留叛逆客户。基于拉普拉斯变换，我们得到了所提出的系统对应的指数矩阵，从而得到了微分方程的概率动力学系统的精确解$n$系统中的客户。此外，还引入了一种有效的算法。拉普拉斯变换和所提出的算法使我们能够获得具有不同容量的排队系统的瞬态的精确解。给出了几个数值例子来说明作为时间函数的概率行为、系统中的预期单元数、队列和模型的优化。一些重要排队系统的瞬态解决方案是作为特例驱动的。