Analysis of a Random Shock Model for a System and Its Optimization

Abstract

In this paper, a random shock model for a system is considered. Each shock arriving according to a Poisson process decreases the state of the system by a random amount. A repairman arriving according to another Poisson process of rate repairs the system only if the state of the system is below a threshold . After assigning various costs to the system, we calculate the long-run average cost and show that there exist a unique value of arrival rate and a unique value of threshold which minimize the long-run average cost per unit time.