A discrete-time storage process with a general release rule

Abstract

A discrete-time storage system with a general release rule and stationary nonnegative inflows is examined. A simple condition is found for the existence of a stationary storage and outflow for a general possibly non-monotone release function. It is also shown that in the Markov case (i.e. independent inflows) these distributions are unique under certain conditions. It is demonstrated that under these conditions the stationary behaviour in the Markov case varies continuously with parametric changes in the release rule. This result is used to prove convergence of a finite state space approximation for the Markov storage system.

Temporal Reasoning and Bayesian Networks

“…A storage process, like a reservoir, warehouse, or dam, is characterized by an inflow, a capacity, and release rules (Glynn 1989). If the events are additive inputs, the release rules are functions of the inputs and the storage level, and the level is the degree of belief.…”

Efficient Simulation via Coupling

“…See, for example, Glynn [10]; the class of recurrent autoregressive sequences (either scalar or vector-valued) also have this property.…”