Optimal Timing of Control Messages for a Two-State Markov Process

The purpose of this paper is to extend the results of the analysis [9] on the optimal timing of messages.' The model and theorems [9] are applicable to a situation involving the of a single (or aggregated) decision-making unit's performance terms of a single (or aggregated) goal. This goal need not be constant over time. The model used [9] is a continuous-time finite horizon model whose formulation and optimization involved the use of a finite-state continuous-time Markov process and tools from continuous-time optimal theory. In the present paper, attention is restricted to a two-state process. This restriction decreases the generality of the results return for a more specific model and more specific theorems. A two-state process is typically chosen for analytical treatment because of expositional convenience or practical applicability. The two states of the process are defined by the usual general descriptions: in control or consistent with goal(s) and out of control or inconsistent with goal(s). This type of process has been analyzed using mathematical programming, quality-control, and Markov chain techniques.2