Transient solution of a multiserver Poisson queue with NN-policy

We consider an M/M/cM/M/c queueing system, where the server idles until a fixed number NN of customers accumulates in a queue and following the arrival of the NN-th customer, the server serves exhaustively the queue. We obtain the exact transient solution for the state probabilities of this NN-policy queue by a direct approach. Further we obtain the time-dependent mean, variance of this system and its busy period distribution.