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Stochastic Duels with Limited Ammunition Supply

Operations Research, 1964
In a previous paper the ground work was laid for a new theoretical model of combat called the “stochastic duel.” The principal elements of the model were fixed kill probabilities on each round fired, a random time between rounds fired, and unlimited ammunition supply.
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Stochastic duels with lethal dose

Naval Research Logistics Quarterly, 1970
This paper introduces the idea of lethal dose to achieve a kill and examines its effect on the course and final outcome of a duel. Results have been illustrated for a particular case of exponential firing rates.
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Many-Versus-Many Stochastic Duels

1984
Abstract : The free-world literature on Many-Versus-Many Stochastic models of combat firefights (excluding pre-fire-fight optimization models) has been exhaustively searched, collected and reviewed. A bibliography has been prepared. Keywords include: Stochastic, Duels, Many-Versus-Many, Bibliography.
null A. V., Gafarian C. J., Jr. Ancker
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Stochastic duels with nonrepairable weapons

Naval Research Logistics Quarterly, 1970
This paper examines the effect of limitation, regarding weapons that are likely to fail during the period of deployment, on the final outcome in a stochastic duel model. Inter-firing times as well as inter-failure times have been assumed to be exponentially distributed.
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Stochastic duels with round‐dependent hit probabilities

Naval Research Logistics Quarterly, 1975
AbstractThe effect of round dependent hit probabilities in the fundamental stochastic duel are examined. The general solution and several specific examples are derived where one side's hit probabilities are improved from round to round. For these specific cases the advantages of round to round improvement are explicitly displayed.
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Explicit modeling of detection within a stochastic duel

Naval Research Logistics, 1993
Many mathematical models have been formulated to describe combat between two weapon systems. However, until recently duel models did not explicitly represent target detection within a duel, leading to the necessity for the development of new model for each tactical situation.
Wand, K., Humble, S., Wilson, R. J. T.
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Theory of Stochastic Duels - Miscellaneous Results

1978
Abstract : This memorandum presents particular applications of various aspects of the theory of stochastic duels that the author has accumulated over a period of years.
null C. J., Jr Ancker
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The distribution of rounds fired in stochastic duels

Naval Research Logistics Quarterly, 1964
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.
Ancker, C. J. jun., Gafarian, A. V.
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The many-on-one stochastic duel

Naval Research Logistics, 1987
The general many-on-one stochastic duel conditioned on the order in which targets are attacked is investigated, and the state probabilities are derived for the first time. The results are illustrated by an example of a three-on-one stochastic duel with negative exponential interfiring times. Some aspects of the tradeoff between individual firepower and
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Some Discrete Processes in the Theory of Stochastic Duels

Operations Research, 1965
The duel in which the contestant on each side has a fixed kill probability and a random (continuous) time between firings has been previously considered. By limiting the time between rounds to a constant, certain situations in which strong interactions occur are investigated.
Ancker, C. J. jun., Williams, Trevor
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