Two-stage release rule procedure in a regenerative dam

We consider a dam model with a compound Poisson input having positive jumps in which the release rule can be dynamically controlled between two release functions, r1, and r2. The dam process has two switchover levels, a and b, 0 a b ∞,which are prescribed to switch the release rule from r2to r1 only when the dam downcrosses level.a and switch from r1 to r2only when the dam upcrosses level b. We derive integral equations whose solutions determine the stationary distribution of the dam content and demonstrate such a determination explicitly for the case of exponential jumps. We also compute an expression for the average number of switches from r1 to r2, and vice versa; consider an approximation to the general case (with b — a being sufficiently large with respect to r1 and r2and the jump sizes), which allows the use of asymptotic results from renewal theory; and study the wet period analysis for the case of exponential jumps.