Multivariate Markov Processes Research Articles

A general software availability/reliability model: numerical exploration via the matrix laguerre transform

Abstract : In this paper, a new software availability/reliability model is developed where lifetimes and repair times have general system-state-dependent distributions. Multiple errors may be introduced or removed through repairs. The model is formulated as a multivariate Markov process and contains many other models appeared in the literatures as special cases. The exponentiality assumption prevalent in the literature is totally eliminated. Expressions of various performance measures of practical interest combining availability and reliability of the software system at time t are derived. Using the matrix Leguerre transform of Sumita (1984), corresponding computational procedures are also developed. A numerical example is given, demonstrating speed, accuracy and stability of these procedures. (Author)

Sojourn times, exit times and jitter in multivariate Markov processes

To treat the transient behavior of a system modeled by a stationary Markov process in continuous time, the state space is partitioned into good and bad states. The distribution of sojourn times on the good set and that of exit times from this set have a simple renewal theoretic relationship. The latter permits useful bounds on the exit time survival function obtainable from the ergodic distribution of the process. Applications to reliability theory and communication nets are given.

Sojourn times, exit times and jitter in multivariate Markov processes

To treat the transient behavior of a system modeled by a stationary Markov process in continuous time, the state space is partitioned into good and bad states. The distribution of sojourn times on the good set and that of exit times from this set have a simple renewal theoretic relationship. The latter permits useful bounds on the exit time survival function obtainable from the ergodic distribution of the process. Applications to reliability theory and communication nets are given.

Weak Convergence Results for a Class of Multivariate Markov Processes

Weak Convergence Results for a Class of Multivariate Markov Processes