A Communications Satellite Replenishment Policy

This paper considers a model for the replenishment of communications satellites which may fail at random when in orbit. It is assumed that when the satellite level reaches a value N, launchings are made until the level reaches M, at which time launchings are terminated. We calculate the probability that n or fewer satellites are functional under this regime. Although the terminology here refers only to satellite systems, the application of the present theory has a wider range. It can be used to calculate the relevant parameters for any (s, S) inventory system when orders are placed singly and the time between the order and filling of the order has a negative exponential distribution.