41
Views
1
CrossRef citations to date
0
Altmetric
Reliability

A Generalized Method for the Transient Analysis of Markov Models of Fault-Tolerant Systems with Deferred Repair

&
Pages 631-661 | Received 03 Sep 2004, Accepted 19 Nov 2004, Published online: 15 Feb 2007

References

  • Abramowitz , M. , Stegun , I. A. , eds. ( 1964 ) . Handbook of Mathematical Functions . New York : Dover Publications, Inc. .
  • Bobbio , A. , Telek , M. ( 1994 ). A benchmark for PH estimation algorithms: results for acyclic-PH . Commun.Statist. Stochastic Mod. 10 : 661 – 677 .
  • Bowerman , P. N. , Nolty , R. G. , Schener , E. M. ( 1990 ). Calculation of the Poisson cumulative distribution function . IEEE Trans. Reliabil. 39 : 158 – 161 . [CSA] [CROSSREF]
  • Carrasco , J. A. ( 2002a ). Computationally efficient and numerically stable reliability bounds for repairable fault-tolerant systems . IEEE Trans. Comput. 51 : 254 – 268 . [CROSSREF]
  • Carrasco , J. A. ( 2002b ) . Transient analysis of large Markov models with absorbing states using regenerative randomization . Technical Report DMSD_99_2 . Universitat Politècnica de Catalunya available at ftp://ftp-eel.upc.es/techreports .
  • Carrasco , J. A. ( 2003 ). Computation of bounds for transient measures of large rewarded Markov models using regenerative randomization . Comput. Operations Res. 30 : 1005 – 1035 . [CSA] [CROSSREF]
  • Carrasco , J. A. ( 2004 ). Transient analysis of some rewarded Markov models using randomization with quasistationarity detection . IEEE Trans. Comput. 53 : 1106 – 1120 . [CROSSREF]
  • Fox , B. L. , Glynn , P. W. ( 1988 ). Computing Poisson probabilities . Communi. ACM 31 : 440 – 445 . [CROSSREF]
  • Grassman , W. K. ( 1977 ). Transient solutions in Markovian queuing systems . Comput. Operat. Res. 4 : 47 – 53 . [CROSSREF]
  • Gross , D. , Miller , D. R. ( 1984 ). The randomization technique as a modelling tool and solution procedure for transient Markov processes . Operations Res. 32 : 343 – 361 .
  • Johnson , B. W. ( 1989 ) . Design and Analysis of Fault Tolerant Digital Systems . Addison-Wesley .
  • Kijima , M. ( 1997 ) . Markov Processes for Stochastic Modeling . London : Chapman &Hall .
  • Knüsel , L. ( 1986 ). Computation of the Chi-square and Poisson distribution . SIAM J. Scientif. Statist.Comput. 7 : 1023 – 1036 .
  • Malhotra , M. ( 1996 ). A computationally efficient technique for transient analysis of repairable Markovian systems . Performance Eval. 24 : 311 – 331 . [CROSSREF]
  • Malhotra , M. , Muppala , J. K. , Trivedi , K. S. ( 1994 ). Stiffness-tolerant methods for transient analysis of stiff Markov chains . Microelectronics Reliabil. 34 : 1825 – 1841 . [CROSSREF]
  • Melamed , B. , Yadin , M. ( 1984 ). Randomization procedures in the computation of cumulative-time distributions over discrete state Markov processes . Operations Res. 31 : 926 – 944 .
  • Miller , D. R. ( 1983 ) . Reliability calculation using randomization for Markovian fault-tolerant computing systems . In: Proc. 13th IEEE Int. Symp. on Fault-Tolerant Computing (FTCS-13) . New York : IEEE Computer Society Press , pp. 284 – 289 .
  • Moorsel , A. P. , Sanders , W. H. ( 1994 ). Adaptive uniformization . Commun. Statist. Stochastic Models 10 : 619 – 647 .
  • Moorsel , A. P. , Sanders , W. H. ( 1997 ). Transient solution of Markov models by combining adaptive and standard uniformization . IEEE Trans. Reliabil. 46 : 430 – 440 . [CSA] [CROSSREF]
  • Neuts , F. ( 1994 ) . Matrix-Geometric Solutions in Stochastic Models. An Algorithmic Approach . New York : Dover Publications Inc. .
  • Reibman , A. , Trivedi , K. S. ( 1988 ). Numerical transient analysis of Markov models . Comput. Operations Res. 15 : 19 – 36 . [CROSSREF]
  • Ross , S. M. ( 1983 ) . Stochastic Processes . New York : John Wiley & Sons. .
  • Sericola , B. (1999). Availability analysis of repairable computer systems and stationarity detection. IEEE Trans. Comput. 48:1166–1172. [CROSSREF]
  • Temsamani , J. , Carrasco , J. A. ( 2004 ) . Transient analysis of Markov models of fault-tolerant systems with deferred repair using split regenerative randomization . Technical Report DMSD_2002_2 . Universitat Politècnica de Catalunya, available at ftp://ftp-eel.upc.es/techreports .
  • Temsamani , J. , Carrasco , J. A. ( 2005 ) . A generalized method for the transient analysis of Markov models of fault-tolerant systems with deferred repair . Technical Report DMSD_2004_1 . Universitat Politècnica de Catalunya, available at ftp://ftp-eel.upc.es/techreports .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.