A COMPARISON OF CONVERGENCE-RATES FOR 3 MODELS IN THE THEORY OF DAMS

This paper compares the convergence rate properties of three storage m odels (dams) driven by time-homogeneous jump process input: the infini tely high dam, the finite dam, and the infinitely deep dam. We show th at the convergence rate of the infinitely high dam depends on the mome nt properties of the input process, the finite dam always approaches i ts limiting distribution exponentially fast, and the infinitely deep d am approaches its limiting distribution exponentially fast under very general conditions. Our methods make use of rare results for regenerat ive processes and several sample path orderings.