In this paper, the concept of correlated reneging is introduced in queuing theory. The reneging considered so far is dependent on system size, but there are many real life situations where customers may renege due to exogenous factors other than the state of the system. Further, the reneging of customer may induce the other customers to renege at two successive time points. Such reneging is called correlated reneging. An M/M/1/K queuing model with correlated reneging is studied. Runge-Kutta method of fourth order is presented to obtain the transient solution of the model. Some performance measures like expected system size and expected waiting time in the system are studied. KeywordsQueuing model, Correlated reneging, Transient solution, Runge-Kutta method, Transition marks.

中文翻译：

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使用Runge-Kutta方法的具有相关重新定性的单服务器排队模型的瞬态解决方案

本文在排队理论中引入了相关重整的概念。到目前为止考虑的取消操作取决于系统大小，但是在许多现实生活中，客户可能会由于系统状态以外的外在因素而放弃。此外，客户的拒绝可能会导致其他客户在两个连续的时间点放弃。这种重新链接称为相关重新链接。研究了具有相关重新修饰的M / M / 1 / K排队模型。提出了四阶Runge-Kutta方法来获得模型的瞬态解。研究了一些性能指标，例如预期的系统大小和预期的系统等待时间。排队模型关联相关过渡解决方案Runge-Kutta方法过渡标记。