A new look at the 3:1 rule of combat through Markov Stochastic Lanchester models

Kress, Moshe; Talmor, Irit

doi:10.1057/palgrave.jors.2600758

Cited by 28 publications

(15 citation statements)

References 10 publications

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“…This law states that if red has N times the initial force size of blue, then blue needs a skill rate N 2 times red's skill rate in order for the deterministic model to predict a draw. We call this scenario the Parity Point scenario and use a value of N ¼ 3, as is often used in the literature (Kress andTalmor 1999, McNaught 1999). We anticipate the probability of red winning being around 0.5.…”

Section: Results and Implications For Stochastic Lanchester Modelsmentioning

confidence: 99%

“…One way SLMs can be studied is by varying the parameters to estimate the probability that one side (say, red) wins under various conditions (for an example, see Kress and Talmor (1999)). We will use IBS to assess the effect of changing the parameters within a simulation run on the probability that a certain side wins.…”

Section: Interval-based Simulation To Model Input Uncertainty In Stocmentioning

confidence: 99%

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Interval-Based Simulation to Model Input Uncertainty in Stochastic Lanchester Models

Singham

Batarseh

2013

Military Oper Res

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I nterval-based simulation (IBS) has been proposed to model input uncertainty in discrete-event simulation. The foundation of this new simulation paradigm is imprecise probability, which models systems under both aleatory and epistemic uncertainties. The statistical distribution parameters in IBS are represented by intervals instead of precise real numbers. This paper discusses how the IBS approach can be applied to stochastic Lanchester models that are used in combat simulation to better account for input parameter uncertainty. The advantages of this approach are explored in comparison with secondorder Monte Carlo simulation. Using IBS, an improved estimate of the probability of a team winning a battle is calculated by exploiting the interval structure. By resampling from intervals to determine event times, we can separate the effect of parameter uncertainty from random number generator uncertainty to estimate the probability that one team will win for a given stream of random numbers used in a single replication. Additionally, we show how our method can be used to improve the reliability of stochastic Lanchester results by accounting for different skill levels within each team, and show how the interval structure can be used to highlight the disproportionate effect of the first few encounters in the battle.

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Section: Results and Implications For Stochastic Lanchester Modelsmentioning

confidence: 99%

Section: Interval-based Simulation To Model Input Uncertainty In Stocmentioning

confidence: 99%

Interval-Based Simulation to Model Input Uncertainty in Stochastic Lanchester Models

Singham

Batarseh

2013

Military Oper Res

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“…We assume that the inter-detection and the attack times are exponentially distributed random variables with parameters λ and µ , respectively. While the former is a reasonable assumption based on the independent and memory-less nature of the search process (see Section 4 below), the latter is an approximation, which is similar to the exponential inter-firing assumption in stochastic duel or stochastic Lanchester models (e.g., Kress (1991) and Kress and Talmor (1999) …”

Section: The Basic Situationmentioning

confidence: 99%

Probability Modeling of Autonomous Unmanned Combat Aerial Vehicles (UCAVs)

Kress

Baggesen²,

Gofer³

2006

military oper res

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Unmanned Combat Aerial Vehicles (UCAVs) are advanced weapon systems that can loiter autonomously in a pack over a target area, detect and acquire the targets, and then engage them. Modeling these capabilities in a specific hostile operational setting is necessary for addressing weapons' design and operational issues. In this paper we develop several analytic probability models, which range from a simple regenerative formula to a large-scale continuous-time Markov chain, with the objective to address the aforementioned issues. While these models capture key individual aspects of the weapon such as detection, recognition, memory and survivability, special attention is given to pack related aspects such as simultaneous targeting, multiple kills due to imperfect battle damage assessment, and the effect of attack coordination. From implementing the models we gain some insights on design and operational considerations regarding the employment of a pack of UCAVs in a strike scenario.

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“…A stream of works extended the Lanchester models-which are deterministic in nature-to stochastic duel models by introducing randomness to shot outcomes, time between taking shots, etc. ; see, for instance, Brown (1963); Williams and Ancker (1963); Barfoot (1974); Kress (1992); and Kress and Talmor (1999). These stochastic duel models, however, assume homogeneous units, so there is no decision making.…”

Section: Introductionmentioning

confidence: 99%

New Results on a Stochastic Duel Game with Each Force Consisting of Heterogeneous Units

Lin¹

2013

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) AND ADDRESS(ES)Naval Postgraduate School Monterey, CA 93943 PERFORMING ORGANIZATION REPORT NUMBER SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES)U.S. Army Training and Doctrine Command (TRADOC) TRADOC Analysis Center TRAC-Monterey 700 Dyer Road, Monterey, CA 93943-0692 SPONSOR/MONITOR'S ACRONYM(S) SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION / AVAILABILITY STATEMENTApproved for public release; distribution is unlimited SUPPLEMENTARY NOTES ABSTRACTTwo forces engage in a duel, with each force initially consisting of several heterogeneous units. Each unit can be assigned to fire at any opposing unit, but the kill rate depends on the assignment. As the duel proceeds, each forceknowing which units are still alive in real time-decides dynamically how to assign its fire, in order to maximize the probability of wiping out the opposing force before getting wiped out. It has been shown in the literature that an optimal pure strategy exists for this two-person, zero-sum game, but computing the optimal strategy remained cumbersome because of the game's huge payoff matrix. This paper gives an efficient algorithm to compute the optimal strategy without enumerating the entire payoff matrix, and offers some insights into the special case, when one force has only one unit. SUBJECT TERMS ABSTRACTTwo forces engage in a duel, with each force initially consisting of several heterogeneous units. Each unit can be assigned to fire at any opposing unit, but the kill rate depends on the assignment. As the duel proceeds, each force-knowing which units are still alive in real time-decides dynamically how to assign its fire, in order to maximize the probability of wiping out the opposing force before getting wiped out. It has been shown in the literature that an optimal pure strategy exists for this two-person zero-sum game, but computing the optimal strategy remained cumbersome because of the game's huge payoff matrix. This paper gives an efficient algorithm to compute the optimal strategy without enumerating the entire payoff matrix, and offers some insights into the special case, when one force has only one unit. vi THIS PAGE INTENTIONALLY LEFT BLANK

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A new look at the 3:1 rule of combat through Markov Stochastic Lanchester models

Cited by 28 publications

References 10 publications

Interval-Based Simulation to Model Input Uncertainty in Stochastic Lanchester Models

Interval-Based Simulation to Model Input Uncertainty in Stochastic Lanchester Models

Probability Modeling of Autonomous Unmanned Combat Aerial Vehicles (UCAVs)

New Results on a Stochastic Duel Game with Each Force Consisting of Heterogeneous Units

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