The most important characteristics of the open M/GI/1 queue, as steady-state probabilities, mean queue length, waiting time distribution are limits of the corresponding characteristics in closed (n/M/GI/1) queues with homogeneous customers if the summarized arrival intensity is constant and if n increases to infinity. In all cases the convergence is monotone thus permitting estimates for the (n/M/GI/1) characteristics if n is large.