Input-Output System: Reflected Compound Poisson Process. LetX(t) denote the value of a system (e.g., monetary account or storage area in acomputer) at time t that takes values in S = {i ∈ Z : a ≤ i ≤...

Input-Output System: Reflected Compound Poisson Process. LetX(t) denote the value of a system (e.g., monetary account or storage area in acomputer) at time t that takes values in S = {i ∈ Z : a ≤ i ≤ b}, where aThe value increases “potentially” by a compound Poisson process X1(t) withrate λ1 and nonnegative jump-sizes with density f1, but part or all of an inputis rejected (or disregarded) to the extent that it would force X(t) to exceed b.Also, the value decreases “potentially” by a compound Poisson process X2(t)with rate λ2 and nonnegative jump-sizes with density g, but part or all of adecrease is disregarded to the extent that it would force X(t) to fall below a.That is, letting Z(t) = X1(t) − X2(t) and ΔX(t) = X(t) − X(t−),