A multivariate reward process defined on a semi-Markov process and its first-passage-time distributions

A multivariate reward process defined on a semi-Markov process is studied. Transform results for the distributions of the multivariate reward and related processes are derived through the method of supplementary variables and the Markov renewal equations. These transform results enable the asymptotic behavior to be analyzed. A class of first-passage time distributions of the multivariate reward processes is also investigated.

[1]  Erhan Cinlar,et al.  Markov Renewal Theory: A Survey , 1973 .

[2]  木島 正明.  The bivariate Laguerre transform and its applications , 1985 .

[3]  J. Keilson,et al.  A central limit theorem for processes defined on a finite Markov chain , 1964, Mathematical Proceedings of the Cambridge Philosophical Society.

[4]  E. Çinlar.  Exceptional Paper---Markov Renewal Theory: A Survey , 1975 .

[5]  Ushio Sumita,et al.  Analysis of fault tolerant computer systems , 1987 .

[6]  U. Sumita,et al.  Dynamic Performance Evaluation of Communication/Computer Systems with Highly Reliable Components , 1988, Probability in the Engineering and Informational Sciences.

[7]  J. Keilson,et al.  On the Matrix Renewal Function for Markov Renewal Processes , 1969 .

[8]  E. Çinlar.  Markov renewal theory , 1969, Advances in Applied Probability.

[9]  J. Keilson.  Markov Chain Models--Rarity And Exponentiality , 1979 .

[10]  John F. Meyer,et al.  Closed-Form Solutions of Performability , 1982, IEEE Transactions on Computers.

[11]  Ushio Sumita,et al.  Analysis of a counting process associated with a semi-Markov process: number of entries into a subset of state space , 1987, Advances in Applied Probability.

[12]  Vidyadhar G. Kulkarni,et al.  A New Class of Multivariate Phase Type Distributions , 1989, Oper. Res..

[13]  Ushio Sumita,et al.  The matrix Laguerre transform , 1984 .

[14]  Ushio Sumita,et al.  THE BIVARIATE LAGUERRE TRANSFORM AND ITS APPLICATIONS: NUMERICAL EXPLORATION OF BIVARIATE PROCESSES , 1985 .

[15]  William S. Jewell,et al.  Markov-Renewal Programming. I: Formulation, Finite Return Models , 1963 .

[16]  Ronald Pyke,et al.  Limit Theorems for Markov Renewal Processes , 1964 .

[17]  Lorenzo Donatiello,et al.  Analysis of a composite performance reliability measure for fault-tolerant systems , 1987, JACM.

[18]  G. V. Kulkarni,et al.  The Completion Time of a Job on Multi-Mode Systems , 1985 .

[19]  M. Neuts,et al.  The Integral of a Step Function Defined on a Semi-Markov Process , 1967 .

[20]  Yasushi Masuda,et al.  Dynamic analysis of computer and communication systems : semi-Markov approach , 1987 .

[21]  Sumitaka Ushio,et al.  An alternative approach to the analysis of finite semi-markov and related processes , 1987 .

[22]  Walter L. Smith,et al.  Regenerative stochastic processes , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.