In this paper, properties of the time-dependent state probabilities of the Mt /G/∞ queue, when the queue is assumed to start empty are studied. Those results are compared with corresponding time-dependent results for the M/M/1 queue. Approximation to the time-dependent state probabilities of the M/G/m/m queue by means of the corresponding time-dependent state probabilities of the M/G/∞ queue are discussed. Through a decomposition formula it is shown that the main performance characteristics of the ergodic M/M/m/m + d queue are sums of the corresponding random variables for the ergodic M/M/m/m and M/M/1/1 + (d − 1) queues, respectively, weighted by the 3rd Erlang formula (stationary probability of waiting or being lost for the M/M/m/m + d queue). Successful exact and approximation extensions of this kind of decomposition formula to the M/M/m/m + d queue with retrials are presented.
