Suchergebnisse

AbstractThe one‐on‐one stochastic duel is extended to the general two‐on‐one duel for the first time. The state equations, win probabilities, mean value, and variance functions are derived. The case where one side has Erlang (2) firing times and the other is negative exponential is compared with the corresponding "Stochastic Lanchester" and Lanchester models to demonstrate their nonequivalence.

AbstractThe Theory of Stochastic Duels is extended by considering the distribution of time‐to‐completion of the fundamental duel. The model has fixed kill probabilities and either random or fixed time between rounds fired. Time‐limitation is included. Special cases and examples are worked out. Clearly, the time‐duration of combat has both tactical and logistic implications for the decision‐maker.

AbstractThis paper continues the development of the theory of stochastic duels to include the distribution of the number of rounds fired. This distribution is principally of interest in estimating stock levels and resupply requirements in appropriate combat situations. Most generally, the duel between two contestants who fire at each other with constant kill probabilities per round is considered. The time between rounds fired may be either a continuous random variable or it may be constant. These two cases are treated separately. The number of rounds available to each contestant at the beginning of the duel may be limited and is a discrete random variable. Besides the distribution of rounds fired, its first two moments and right tail are obtained. In addition to general results, special cases and specific examples are worked out.

AbstractA definition of the problem of the initial transient with respect to the steady‐state mean value has been formulated. A set of criteria has been set forth by which the efficaacy of any proposed rule may be assessed. Within this framework, five heuristic rules for predicting the approximate end of transiency, four of which have been quoted extensively in the simulation literature, have been evaluated in the M/M/1 situation. All performed poorly and are not suitable for their intended use.