Difference Equations Approach for Multi-Server Queueing Models with Removable Servers

We consider an extended form of the MX/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.