A time-dependent approximation for the queue M/M(1,s)/c

A time-dependent approximation for the mean number of customers in the queue for the queueing system M/M(1,s)/c is presented, using coordinate transformation. Comparisons between the approximation and an equivalent simulation model are presented, and agreement is shown to be good. The appropriateness of utilizing the model as an upper bound for queues with smaller coefficients of variation is discussed. Possible applications of the model are presented.