The Many-on-Many General Renewal Lanchester Combat Model

Abstract

Abstract : The principal motivation for this work is the development of more realistic small-to-moderate size firefight models than the extant deterministic and exponential Lanchester square law models. It is important to note here that what we call exponential model has been called stochastic Lanchester in the literature to date. We believe substituting the adjective exponential for stochastic is a more accurate description because the classical stochastic Lanchester model merely assumes that the interkilling time is an exponential random variable. On the other hand, the models we define allow an arbitrary interkilling time random variable. Obviously the deterministic and exponential Lanchester models are greatly simplified descriptions of the firefight. Common sense and field experiments dictate that: (1) the real firefight is stochastic, and (2) the exponential assumption is a gross simplification of the actual interkilling time and is only used because its no memory property greatly simplifies the analysis. Both the deterministic and exponential lanchester models have been studied in great detail.