An optimal access strategy for managing reservation systems with Poisson arrivals is studied. In this strategy, the requests of service are accepted selectively with the aim to maximize the expected system utilization (stochastic optimization). A dynamic programming approach is used to solve the problem. Explicit decision rules are derived for the optimal selection of requests. Comparisons are made with a nonoptimized system as well as with a stronger optimum based on complete knowledge of all the requests to be made. Sensitivity of the stochastic optimization to variations in assumed parameters is also considered.