On a supplementary time variable approach to battle analysis

A supplementary time variable approach is used to analyze a battle where attackers search for defended logistical targets and the future actions of an attacker depend on its activities in the whole time interval since arrival at the operating area. As compared with the method discussed in this paper a corresponding Markov chain analysis of the problem requires a considerably greater number of mathematical relations for state transition probabilities with less possibilities in obtaining numerical solutions effectively and with less para‐metrical insight. A supplementary time variable is introduced to describe the arrival instants of attackers at the operating area, and is then used to express the probability generating functions of the losses at an arbitrarily selected time instant in terms of a general description of the capabilities of an individual attacker in the time interval since arrival. These capabilities are then related to a selected set of lower level parameters describing a specific battle situation by using a small set of integral relations of the multiple convolution type with solutions expressed as Laplace transforms.