Modelling a Markov Attrition Process

  • Sheng Lin Chang National Taiwan Institute of Technology, Taipei
  • Jau Yeu Menq National Taiwan Institute of Technology, Taipei
Keywords: Stochastic attrition model, Recursive algorithm

Abstract

This study proposes another computational approach to solve a stochastic attrition model. The initial contact forces for both sides canbe treated as a random variable. The approach is manipulated in amatrix form, and on account of the special form of its infinitesimal generator, some recursive algorithms are derived to compute the intended results. Numerical results to illustrate the differences betweenthe proposed model and the stochastic model with known initial contact forces are presented.

References

Jennings, N., The Mathematics of Battle 111 : Approximate Moment of the Distribution of States of a Simple Heterogeneous Battle, (M-7315, Defense Operational Analysis Establishment, U. K.), 1973.

Jennings, N., The Mathematics of Battle IV : Stochastic Linear Law Battles,(M-7316, Defense Operational Analysis Establishment, U.K.), 1973. Sheng-Lin Chang & lau-~euM eng

Bhat, U.N., A Markov Process Solution for Lanchester's Combat Model, Technical Report 82-OR-S, (Department of Operations Research and Engineering Management, Southern Methodist University, Dallas, Texas), 1982.

Weale, T.G. & Peryer, E., The Mathematics of Battle VII : Moment of the Distribution of States for a Battle with General Attrition Functions, (M-77105, Defense Operational Analysis Establishment, U.K.), 1977. ,P

Karmeshu & Jaiswal, N.K., Nav. Res. Logist. Q., 33 (1986), 101-110.

Jaiswal, N.K., Annals of Operations Research, 9 (1987), 561-573.

Neuts, M.F., Matrix-Geomctric Solutions in Stochastic Models, An Algorithmic Approach, (The Johns Hopkins University Press), 1981.

Neuts, M.F., Probability Distributions of Phase Type, In Eiber Amicorum Prof. Emeritus H. Florin. (Department of Mathematics, University of Louvain, Belgium), 1975.

Neuts, M.F., J. Appi. Prob., 16 (1979), 764-773.

Neuts, M.F., Nav. Res. Logist. Q., 25 (1978), 445-454.

Published
2013-07-01
How to Cite
Chang, S., & Menq, J. (2013). Modelling a Markov Attrition Process. Defence Science Journal, 39(3), 211-220. https://doi.org/10.14429/dsj.39.4767
Section
General Papers