We consider an extended form of the M^X/M/c queue with two types of server groups: Static as well as dynamic (which turn on/off in a state-dependent manner) servers. The two server groups may have homogenous or non-homogenous service rates. The model is further extended to feature setup and delayed-off times, finite capacity, and k staffing levels. This class of queues is solved via the difference equations approach, which addresses narratives in the literature and achieves higher numerical efficiency than the direct method. While the model of this queueing system is not new, the methodology for solving it is. Comparisons between our model and classic queues are provided followed by concluding remarks, including a summary of key observations.

我们考虑带有两种类型的服务器组的M ^X / M / c队列的扩展形式：静态和动态（以状态相关的方式打开/关闭）服务器。这两个服务器组的服务费率可以相同或不同。该模型进一步扩展为功能设置和延迟时间，有限容量和k人员配备水平。此类队列通过差分方程方法解决，该方法解决了文献中的叙述问题，并且比直接方法具有更高的数值效率。尽管此排队系统的模型不是新的，但解决它的方法却是新的。提供了我们的模型队列与经典队列之间的比较，并附有总结性评论，包括主要观察结果的摘要。