The discrete-time $M/M/c$ model here denotes a system where everything follows the $M/M/c$ except the customers in the queue are assigned to servers only at time $k\Delta t, k=1,2,\cdots$ (instead of immediate assignments once there is an idle server).
The real example can be found, say, at the airport security check. Passengers are normally required by staff to be pooled for some period of time before a waiting line and then are released to the security check channels.
My understanding is that for the server side, customers are a bulk arrival, and for the customer side, the service is bulk too. However, the literature I found related to bulk arrival/service didn’t base on the time but on capacity.
Any idea on how to formulate this model and thereby evaluating the system performance?