Effective information horizon length in measuring off-line performance of stochastic dynamic systems

In stochastic problems, several sources of complete (deterministic) and incomplete (stochastic) information become available in the course of time. In this paper we introduce a ‘pseudo-stochastic’ approach, which allows modeling a specific distribution of the event's occurrence time. This model shows the possible impact of future information that is expected beyond the planning horizon, on the off-line evaluation of a dynamic system performance. By not considering the expected information beyond the planning horizon, one obtains a non-accurate performance measure of the system. Since the computational time for performance evaluation increases with the increase of the amount of future information, and since long-range forecasts are usually not accurate, we develop an analytic procedure to reduce the amount of required information. In this paper we introduce a new concept – the effective information horizon (EIH) – that measures the segment of time on which future stochastic information is relevant for evaluating the system's performance. The EIH length is found by mathematical analysis of the influence of future information on a system's dynamics under a given control strategy. Although real-life examples show that the EIH is larger than the planning horizon, it is quite limited.