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Original Articles

The Augmented Semi-Markov System in Continuous Time

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Pages 88-107 | Received 19 Jun 2009, Accepted 10 Aug 2010, Published online: 03 Dec 2011

References

  • Barbu , V. , Limnios , N. ( 2008 ). Semi-Markov Chains and Hidden Semi-Markov Models toward Applications . LNS , Vol. 191. New York : Springer .
  • Bartholomew , D. J. ( 1982 ). Stochastic Models for Social Processes. , 3rd ed. Chichester : Wiley .
  • Bartholomew , D. J. , Forbes , A. F. , McClean , S. I. ( 1991 ). Statistical Techniques for Manpower Planning. , 2nd ed. Chichester : Wiley .
  • Blasi , A. , Janssen , J. , Manca , R. (2004). Numerical treatment of homogeneous and non-homogeneous semi-Markov reliability models. Commun. Statist. Theor. Meth. 33(3):697–714.
  • Cinlar , E. ( 1975 ). Introduction to Stochastic Processes . Englewood Cliffs , NJ : Prentice Hall .
  • De Feyter , T. ( 2006 ). Modelling heterogeneity in manpower planning: dividing the personnel system into more homogeneous subgroups . App. Stoch. Mod. Bus. Ind. 22 : 321 – 334 .
  • Dimitriou , V. A. , Tsantas , N. ( 2009 ). Prospective control in an enhanced manpower planning model . Appl. Math. Computat. 215 ( 3 ): 995 – 1014 .
  • Georgiou , A. C. , Tsantas , N. ( 2002 ). Modelling recruitment training in mathematical human resource planning . App. Stoch. Mod. Bus. Ind. 18 : 53 – 74 .
  • Gerondidis , I. ( 1991 ). Periodic strong ergodicity in non-homogeneous Markov systems . J. Appl. Probab. 28 : 58 – 73 .
  • Gilbert , G. ( 1973 ). Semi Markov processes and mobility: a note . J. Math. Sociol. 3 : 139 – 145 .
  • Ginsberg , R. B. ( 1971 ). Semi Markov processes and mobility . J. Math. Sociol. 1 : 233 – 262 .
  • Horn , R. A. , Johnson , C. R. ( 1990 ). Matrix Analysis . Cambridge : Cambridge University .
  • Howard , R. ( 1971 ). Dynamic Probabilistic Systems . Vol. II . New York : John Wiley and Sons .
  • Isaacson , D. L. , Madsen , R. W. ( 1976 ). Markov Chains Theory and Applications . New York : John Wiley and Sons .
  • Janssen , J. , Dominicis , R. D. ( 1984 ). An algorithmic approach to non-homogeneous semi-Markov processes . Insur. Math. Econ 3 : 157 – 165 .
  • Janssen , J. , Manca , R. ( 2006 ). Applied Semi Markov Processes. , 1st ed. New York : Springer .
  • Kemeny , J. , Snell , J. ( 1976 ). Finite Markov Chains. , 2nd ed. New York : Springer-Verlag .
  • Limnios , N. , Optişan , G. ( 2001 ). Semi-Markov Processes and Reliability . Boston : Birkhauser .
  • McClean , S. I. ( 1980 ). A semi-Markov model for a multigrade population with poisson recruitment . J. Appl. Probab. 17 : 846 – 852 .
  • McClean , S. I. ( 1986 ). Semi-Markov models for manpower planning . In: Janssen , J. , eds. Semi Markov Models: Theory and Applications . New York : Plenum Press .
  • McClean , S. I. , Montgomery , E. , Ugwuomo , F. ( 1998 ). Non-homogeneous continuous time Markov and semi Markov manpower models . Appl. Stoch. Mod. Data Anal. 13 : 191 – 198 .
  • McClean , S. I. , Papadopoulou , A. A. , Tsaklidis , G. ( 2004 ). Discrete time reward models for homogeneous semi-Markov systems . Commun. Statist. Theor. Meth. 33 ( 3 ): 623 – 638 .
  • Papadopoulou , A. A. ( 2004 ). Economic rewards in non-homogeneous semi-Markov systems . Commun. Statist. Theor. Meth. 33 ( 3 ): 681 – 696 .
  • Papadopoulou , A. A. , Tsaklidis , G. ( 2007 ). Semi-Markov models with stochastic selection of the transition probabilities . Methodol. Comput. Appl. Probab. 9 : 399 – 411 .
  • Papadopoulou , A. A. , Vassiliou , P.-C. G. ( 1994 ). Asymptotic behaviour of non-homogeneous semi-Markov systems . Lin. Algebra Applic. 210 : 153 – 198 .
  • Papadopoulou , A. A. , Vassiliou , P.-C. G. ( 1999 ). Continuous time non homogeneous semi-Markov systems . In: Janssen , J. , Limnios , N. , eds. Semi-Markov Models and Applications . Dordrecht , The Netherlands : Kluwer Academic Press .
  • Rudin , W. ( 1964 ). Principles of Mathematical Analysis. , 2nd ed. New York : McGraw Hill .
  • Taugels , J. L. ( 1976 ). A bibliography on semi-Markov processes . J. Computat. Appl. Math. 2 : 125 – 144 .
  • Ugwuowo , F. I. , McClean , S. I. ( 2000 ). Modelling heterogeneity in a manpower system: a review . App. Stoch. Models Bus. Ind. 16 : 99 – 110 .
  • Vassiliou , P.-C. G. ( 1982 ). Asymptotic behaviour of Markov systems . J. Appl. Probab. 19 : 815 – 857 .
  • Vassiliou , P.-C. G. , Papadopoulou , A. A. ( 1992 ). Non-homogeneous semi-Markov systems and maintainability of the state sizes . J. Appl. Probab. 29 : 519 – 534 .
  • Vassiliou , P.-C. G. , Georgiou A. C. , Tsantas N. ( 1990 ). Control of asymptotic variability in non-homogeneous Markov systems . J. Appl. Probab. 27 : 756 – 766 .
  • Yadavalli , V. S. S. , Natarajan , R. ( 2001 ). A semi Markov model of a manpower system . Stoch. Anal. Applic. 19 ( 6 ): 1077 – 1086 .

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