Markov Chains

Markov Models - Blue Book

Solution Techniques - Articles in Journals

An Aggregation Technique for the Transient Analysis of Stiff Markov Chains, A. Bobbio and K. S. Trivedi, IEEE Transactions on Computers, Vol. C-35, No. 9, Sept. 1986, pp. 803-814.

Transient Analysis of Acyclic Markov Chains, R. Marie and A. Reibman, and K. S. Trivedi, Performance Evaluation, Vol. 7 (1987), pp. 175-194.

Numerical Transient Analysis of Markov Models, A. Reibman and K. S. Trivedi, Computers and Operations Research, Vol. 15, No. 1, pp. 19-36, 1988. This paper is a standard reference for the transient analysis of Markov chains.

Markov and Markov Reward Models: A Survey of Numerical Approaches, A. Reibman and R. M. Smith, and K. S. Trivedi, European Journal of Operations Research, Vol. 40, pp. 257-267, 1989.

Transient Analysis of Cumulative Measures of Markov Model Behavior, A. Reibman, K. S. Trivedi, Communications in Statistics- Stochastic Models, Vol. 5, No. 4, pp. 683-710, 1989.

Analysis of Stiff Markov Chains, A. Reibman, K. S. Trivedi, S. Kumar and G. Ciardo, ORSA Journal on Computing, Vol. 1, No. 2, pp. 126-133, Spring 1989.

Computing Cumulative Measures of Stiff Markov Chains Using Aggregation, A. Bobbio and K. S. Trivedi, IEEE Transactions on Computers, Vol. C-39, No. 10, pp. 1291-1298, Oct. 1990.

Selecting and Implementing Phase Approximations for Semi-Markov models, Manish Malhotra and Andrew Reibman, Commun. Statist. -Stochastic Models, 9(4), pp. 473-506, 1993.

Stiffness-Tolerant Methods for Transient Analysis of Stiff Markov Chains, Manish Malhotra, Jogesh Muppula, and K. S. Trivedi, Microelectronics and Reliability, Vol. 34, No. 11, pp. 1825-1841, 1994.

Numerical Methods for Reliability Evaluation of Markovian Closed Fault-tolerant Systems, Christoph Lindemann, Manish Malhotra, and K. S. Trivedi, IEEE Transactions on Reliability, Vol. 44, No. 4, pp. 694-704, Dec. 1995.

Accelerating Mean Time to Failure Computations, P. Heidelberger, J. Muppala, and K. S. Trivedi, Performance Evaluation, Vol. 27 & 28, October 1996, North-Holland, pp. 627-645.

Analysis of Conditional MTTF of Fault-Tolerant Systems, H. Choi and W. Wang, and K. S. Trivedi, Microelectronics and Reliability, Vol. 38, No. 3, pp. 393-401, 1998.

Hierarchical Composition and Aggregation of State-Based Availability and Performability Models, M. Lanus, L. Yin, and K. S. Trivedi, IEEE Transactions on Reliability, Vol. 52, No. 1, pp. 44-52, March 2003.

Decompositional analysis of Kronecker structured Markov chains, Y. Bao, I. N. Bozkurt, T. Dayar, X. Sun and K. S. Trivedi, Electronic Transactions on Numerical Analysis, Vol. 31 (2008), pp. 271-294.

Markovian Arrival Process Parameter Estimation with Group Data, H. Okamura, T. Dohi and K. S. Trivedi, ACM/IEEE Transactions on Networks, Vol. 7, No. 4, pp. 1326-1339, August 2009.

Modeling User-Perceived Reliability Based on User Behavior Graphs, D. Wang and K. S. Trivedi, International Journal of Reliability, Quality & Safety Engineering, Vol. 16, No. 4, pp. 303-330, August 2009.

Solution Techniques - Chapters of Books

Transient Analysis of Markov and Markov Reward Models, K. S. Trivedi, A. Reibman, and Roger Smith, in: Computer Performance and Reliability, G. Iazeolla , P. J. Courtois and O. J. Boxma (eds.), Elsevier Science Publishers B.V. (North-Holland), 1988, pp. 535-545.

Numerical Transient Solution of Finite Markovian Queueing Systems, J. Muppala and K. S. Trivedi, in: Queueing and Related Models, U. N. Bhat and I. V. Basawa (ed.), pp. 262-284, Oxford University Press, 1992.

Markov Dependability Models of Complex Systems: Analysis Techniques, J. Muppala, M. Malhotra, and K. S. Trivedi, Reliability and Maintenance of Complex Systems, S. Ozekici (ed.), pp. 442-486, Springer-Verlag, Berlin, 1996.

Techniques for System Dependability Evaluation, J. Muppala, R. Fricks, and K. S. Trivedi, in Computational Probability, W. Grassman (ed.), pp. 445-480, Kluwer Academic Publishers, The Netherlands, 2000.

Solution Techniques - Articles in Symposia Proceedings

Importance Analysis with Markov Chains, R. Fricks, and K. S. Trivedi, Proceedings of the 2003 International Reliability and Maintainability Symposium - RAMS 2003, Tampa, FL, USA, Jan. 27-30 2003.

System dependencies in Markov Dependability Modelling, J. K. Muppala and K. S. Trivedi, Fault-Tolerant Systems and Software, Proceedings of FTS-95, pp. 38-47, Narosa Publishing House, New Delhi, India, 1995.

Higher order methods for the transient analysis of stiff Markov chains, with M. Malhotra, Proc. Int. Conf. on the Performance of Distributed Systems and Integrated Communication Networks, Kyoto, Sept. 1991.

On the Sensitivity of Transient Solution of Markov Models, A. V. Ramesh and K. S. Trivedi, Proc. 1993 ACM SIGMETRICS Conference, Santa Clara, CA, May 1993.

Sensitivity Analysis of Reliability and Performability Measures for Multiprocessor Systems, J. T. Blake, A. Reibman and K. S. Trivedi, Proc. 1988 ACM SIGMETRICS Conference.

Markov reward approach to performability and reliability analysis, K. S. Trivedi, M. Malhotra, and R. M. Fricks, Proc. MASCOTS 1994, the Second International Workshop. pp. 7-11 1994


Markov Reliability Models of Flight Control Systems, with J. McGough and A. Reibman, AIAA Journal on Guidance, Control and Dynamics, Vol. 12, No. 2, pp. 209-219, Mar.-Apr. 1989.

Dependability Evaluation of a Class of Multi-Loop Topologies for Local Area Networks, W. E. Smith and K. S. Trivedi, IBM Journal of Research and Development, Vol. 33, No. 5, Sept. 1989, pp. 511-523.

Reliability Modeling of Disk Array Systems, Manish Malhotra and Kishor Trivedi, Sixth International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, Edinburgh, Scotland, Sept. 16-18, 1992.

Reliability Analysis of Redundant Arrays of Inexpensive Disks, Manish Malhotra and Kishor Trivedi, Journal of Parallel and Distributed Computing, Vol. 17, pp. 146-151, 1993.

Data Integrity Analysis of Disk Array Systems with Analytic Modeling of Coverage, Manish Malhotra and Kishor Trivedi, Performance Evaluation, Vol. 22, No. 1, pp. 111-133, 1995.

An Analytic Treatment of the Reliability and Performance of Mirrored Disk Subsystems, Robert Geist and Kishor Trivedi, Proc. Twenty-third International Symposium on Fault-Tolerant Computing, Toulouse, France, June 1993.

Availability Modeling of Energy Management Systems, Ricardo Fricks and Kishor Trivedi, Microelectronics and Relaibility, 1998.

Detecting Performance and Reliablity Bottlenecks of Composite Web Services,, Naoto Sato and Kishor Trivedi, Proc. International Conference on Service Oriented Computing (ICSOC 2007),Vienna, Austria, September 2007.

Markov Regenerative Models - Articles in Symposia Proceedings

Markov Regenerative Models, Dimitris Logothetis, K. S. Trivedi, and Antonio Puliafito, Proc. Int. Computer Performance and Dependability Symp., Erlangen, Germany, pp. 134-143, 1995.

Non-Homogeneous - Chapters of books

Exact Methods for the Transient Analysis of Nonhomogeneous Continuous-Time Markov Chains, A. Rindos, S. Woolet, I. Viniotis, and K. S. Trivedi, 2nd International Workshop on the Numerical Solution of Markov Chains, W. J. Stewart (ed.), Kluwer Academic Publishers, 1995.

Last updated on Sep. 23 2010