In this paper we extend the one-on-one stochastic duel model with searching to the many-on-one case based on information-sharing. We have derived the probability density function of the time to kill the target in many-on-one model. It is illustrated by an example in which the firing time and the searching time are of different exponential distributions.
References
[1]
C. J. Ancker, “One-on-One Stochastic Duels,” Research Monograph, Military Applications Section, Operations Research Society of America (now INFORMS), Arlington, 1982.
[2]
A. V. Gafarian and C. J. Ancker, “The Two-on-One Stochastic Duel,” Naval Research Logistics Quarterly, Vol. 31, 1984, pp. 309-324. doi:10.1002/nav.3800310213
[3]
Y. Friedman, “Optimal Strategy for the One-againstMany Battle,” Operations Research, Vol. 25, No. 5, 1977, pp. 884-888. doi:10.1287/opre.25.5.884
[4]
K. Kikuta, “A Note on the One-against-Many Battle,” Operations Research, Vol. 31, No. 5, 1983, pp. 952-956.
doi:10.1287/opre.31.5.952
[5]
M. Kress, “The Many-on-One Stochastic Duel,” Naval Research Logistics Quarterly, Vol. 31, 1987, pp. 713720.
[6]
K. Wand, S. Humble and R. J. T. Wilson, “Explicit Modelling of Detection within a Stochastic Duel,” Naval Research Logistics Quarterly, Vol. 40, 1993, pp. 431-450.
doi:10.1002/1520-6750(199306)40:4<431::AID-NAV3220400402>3.0.CO;2-S
[7]
L.W. Liu, “Density Function of the Time for Target Killing Involving the Target Detection Time,” Acta Armamentarii, Vol. 23, No. 3, 2002, pp. 370-373.
[8]
L. W. Liu, “A Kind of Stochastic Duel Model for Guerrilla War,” European Journal of Operational Research, Vol. 171, No. 1, 2006, pp. 430-438.
doi:10.1016/j.ejor.2004.09.032
