Evaluating performance of real inventory systems by using the conventional methods is a complex task because of disengagement of decision variables, especially for networks. Therefore, managers resort to the turnover role (TOR) as a local and aggregate tool. Analytic models of TOR seem to be scarce in the literature. This study developed several TOR models, based on stochastic continuous-review system, starting from completely structured objective functions. Two novel philosophies are highlighted to justify rushing TOR from cost and profitable views. The models include short ones that can be practically applied to abstract stochastic and sophisticated features of the system, The models are conducted to hypothetical and real data, followed by regression analyses. The results confirm that faster TOR is more profitable in a wide range. That is justified by the profitability curves with different allowable shortage probabilities and unit dynamic rates. Those curves are found skewed left to the optimum profitability. The explored statistical trends demonstrate generality for the system parameters that are merely modifying the trend coefficients. The same procedure can be followed to develop models for oilier deterministic and stochastic systems under several varieties of proceeding incidences.