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Some two‐on‐two homogeneous stochastic combats
Author(s) -
Gafarian A. V.,
Manion K. R.
Publication year - 1989
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(198912)36:6<721::aid-nav3220360602>3.0.co;2-v
Subject(s) - mathematics , homogeneous , variance (accounting) , square (algebra) , exponential function , battle , variable (mathematics) , mean square , mathematical economics , computation , statistics , combinatorics , algorithm , mathematical analysis , economics , geometry , accounting , archaeology , history
Abstract In this article we consider two versions of two‐on‐two homogeneous stochastic combat and develop expressions, in each case, for the state probabilities. The models are natural generalizations of the exponential Lanchester square law model. In the first version, a marksman whose target is killed resumes afresh the killing process on a surviving target; in the second version, the marksman whose target is killed merely uses up his remaining time to a kill on a surviving target. Using the state probabilities we then compute such important combat measures as (1) the mean and variance of the number of survivors as they vary with time for each of the sides, (2) the win probabilities for each of the sides, and (3) the mean and variance of the battle duration time. As an application, computations were made for the specific case of a gamma (2) interfiring time random variable for each side and the above combat measures were compared with the appropriate exponential and deterministic Lanchester square law approximations. The latter two are shown to be very poor approximations in this case.