Using the theory of M/M/1 queues at stationarity, we provide criteria of stability (recurrence) for a stochastic inventory model with an observed selling rate and an optimally chosen buying rate. Optimality is based on the maximum gain under stability, where buying and selling prices, as well as shop- and stock-keeping costs are incorporated into the model. An important aspect is to achieve robustness of the stocking process by minimizing the fluctuation of the predicted gain. This robustness can be achieved by controlling intermediate transfer rates of the assumed stochastic tandem network. Stochastic simulations demonstrate the applicability of the stability criteria under several scenarios of differing intensities of perturbation. Copyright © 2010 John Wiley & Sons, Ltd.