A control of a biovmn storag system with two switcnoee deifts

We consider a bounded storage system whose content level is bounded between two critical levels 0 and 1. In the absence of any control, the content level process fluctuates as a Brownian motion with drift μ and reflected barriers at 0 and 1. We assume that the purpose of any control scheme of the system is to decrease the chance that the process hits the critical levels and increase the proportion of time it spends in a safe zone (a,b), 0 < a < b < 1, where a and b are chosen to minimize suitable cost functions. In this paper we consider a basic control scheme in which the controller is free to change (at any time) the drift of the Brownian motion and use two drift values. We study several variations of this control scheme and derive suitable cost functions).