Sojourn Times in Dependability Modeling

We consider Markovian models of computing or communication systems, subject to failures and, possibly, repairs. The dependability properties of such systems lead to metrics that can all be described in terms of the time that the Markov chain spends in subsets of its state space. Some examples of such metrics are MTTF and MTTR, reliability or availability at a point in time, the mean or the distribution of the interval availability in a fixed time interval, and more generally different performability versions of these measures. This chapter reviews this point of view and its consequences, and discusses some new results related to it.

[1]  Gerardo Rubino,et al.  Interval availability distribution computation , 1993, FTCS-23 The Twenty-Third International Symposium on Fault-Tolerant Computing.

[2]  G. Rubino,et al.  Distribution of operational times in fault-tolerant systems modeled by semi-Markov reward processes , 1989 .

[3]  Edmundo de Souza e Silva,et al.  Calculating Cumulative Operational Time Distributions of Repairable Computer Systems , 1986, IEEE Transactions on Computers.

[4]  Attila Csenki,et al.  Dependability for Systems with a Partitioned State Space: Markov and Semi-Markov Theory and Computational Implementation , 1994 .

[5]  G. Rubino,et al.  A finite characterization of weak lumpable Markov processes. Part II: The continuous time case , 1993 .

[6]  Gerardo Rubino,et al.  Sojourn times in semi-Markov reward processes: application to fault-tolerant systems modeling , 1993 .

[7]  Kishor S. Trivedi.  Probability and Statistics with Reliability, Queuing, and Computer Science Applications , 1984 .

[8]  Hoon Choi,et al.  Analysis of conditional MTTF of fault-tolerant systems , 1998 .

[9]  B. Sericola.  Markov Chains. Theory, Algorithms and Applications , 2013 .

[10]  G. Rubino,et al.  A finite characterization of weak lumpable Markov processes. Part I: The discrete time case , 1991 .

[11]  Gerardo Rubino,et al.  Bound Computation of Dependability and Performance Measures , 2001, IEEE Trans. Computers.

[12]  Gerardo Rubino,et al.  Markov Chains and Dependability Theory: References , 2014 .

[13]  Bruno Sericola,et al.  Performability Analysis Using Semi-Markov Reard Processes , 1990, IEEE Trans. Computers.

[14]  Gerardo Rubino,et al.  Interval Availability Analysis Using Operational Periods , 1992, Perform. Evaluation.

[15]  Kishor S. Trivedi,et al.  Techniques for System Dependability Evaluation , 2000 .

[16]  G. Rubino,et al.  Sojourn times in finite Markov processes , 1989, Journal of Applied Probability.

[17]  A. Hawkes,et al.  Occupancy Times for Markov and Semi‐Markov Models in Systems Reliability , 2013 .

[18]  Kishor S. Trivedi,et al.  An Aggregation Technique for the Transient Analysis of Stiff Markov Chains , 1986, IEEE Transactions on Computers.