Elementary methods for an occupancy problem of storage

Summary This paper considers the probabilities of first emptiness in two storage systems. The first, an infinite dam in discrete time, is fed by inputs whose distribution is geometric in unit time-intervals; at the end of each of these, there occurs a unit release. The second is an infinite dam in continuous time with Poisson inputs, for which the release occurs at constant unit rate except when the dam is empty.First emptiness in both dams may be formulated as a special type of classical occupancy problem. The probabilities of emptiness are derived by direct elementary methods, and their generating functions found. These are shown to define proper distributions only if the mean input per unit time does not exceed the corresponding release.