Sub-stochastic matrix analysis for bounds computation-Theoretical results

European Journal of Operational Research

Volumn 176, Issue 2, 2007, Pages 999-1015

  Haddad, Serge ^a   Moreaux, Patrice ^b  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

^b Université de Savoie   (France)

Author keywords

Markov process; Stochastic bound; Stochastic process; Strong stochastic ordering; Sub Markov chain

Indexed keywords

ALGORITHMS; CALCULATIONS; MARKOV PROCESSES; NUMERICAL ANALYSIS; POLYNOMIAL APPROXIMATION;

STOCHASTIC BOUND; STOCHASTIC PROCESS; STRONG STOCHASTIC ORDERING; SUB MARKOV CHAIN;

MATRIX ALGEBRA;

EID: 33749854039     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2005.08.016     Document Type: Article

References (30)

1. O. Abu-Amsha, J.M. Vincent, An algorithm to bound functionals of Markov chains with large state space, Rapport MAI 25, IMAG, Grenoble, France, April 1996.
2. O. Abu-Amsha, J.M. Vincent, An algorithm to bound functionals of Markov chains with large state space, in: Proceedings of the 4th INFORMS Conference on Telecommunications, Boca Raton, 1998.
3. Carrasco J.A. Bounding steady-state availability models with group repair and phase type repair distributions. Performance Evaluation 35 (1999) 193-214
4. Carrasco J.A. Markovian dependability/Performability modeling of fault-tolerant systems. Handbook of Reliability Engineering (2003), Springer-Verlag, Berlin 613-642
5. Cassandras C.G. Discrete Event Systems: Modeling and Performance Analysis (1993), Irwin Pub.
6. Courtois P.J., and Semal P. Bounds for the positive eigenvectors of nonnegative matrices and for their approximations by decomposition. Journal of ACM 31 4 (1984) 804-825
7. Courtois P.J., and Semal P. Computable bounds on conditional steady-state probabilities in large markov chains and queueing models. IEEE Journal on Selected Areas in Communication (SAC) 4 6 (1986) 926-937
8. S. Donatelli, S. Haddad, P. Moreaux, M. Sene, Bounds for rewards of systems with clients/servers interactions, in: W.J. Stewart B. Plateau, M. Silva (Eds.), Proceedings of the third International Workshop on Numerical Solution of Markov Chains, Zaragoza, Spain, September 8-10, 1999, Prensas Universitarias de Zaragoza, pp. 208-227.
9. Feller W. An Introduction to Probability Theory and its Applications vol. I, third ed. (1968), John Wiley & Sons, New York
10. Feller W. An introduction to probability theory and its applications vol. II, second ed. (1971), John Wiley & Sons, New York
11. Fourneau J.M., and Pekergin N. An algorithmic approach to stochastic bounds. In: Calzarossa M., and Tucci S. (Eds). Performance Evaluation of Complex Systems: Techniques and Tools, Performance, Tutorial Lectures, Rome, Italy, September 22-27, 2002. LNCS 2459 (2002), Springer-Verlag, Berlin 64-88
12. In: Gelenbe E. (Ed). System Performance Evaluation: Methodologies and Applications (2000), CRC Press, Boca Raton, FL
13. Golubchik L., and Lui J.C.S. Bounding of performance measures for a threshold-based queueing system with hysteresis. ACM Sigmetrics International Conference on Measurement & Modeling of Computer Systems, Seattle, Washington, USA, June 15-18, 1997. Performance Evaluation Review 25 (1997) 147-157 (special issue)
14. S. Haddad, P. Moreaux, Sub-stochastic matrix analysis and performance bounds, Research Report RAP-CReSTIC-1, CReSTIC, Université de Reims Champagne-Ardenne, France, October 2004.
15. In: Haring G., Lindemann Ch., and Reiser M. (Eds). Performance Evaluation: Origins and Directions. LNCS 1769 (2000), Springer-Verlag, Berlin
16. In: Haverkort B.R., Marie R., Rubino G., and Trivedi K. (Eds). Performability Modelling: Techniques and Tools (2001), Wiley, Chichester, England
17. Jain R. The Art of Computer Systems Performance Analysis (1991), John Wiley & Sons, New York
18. Kijima M. Markov Processes for Stochastic Modeling (1997), Chapman and Hall, London, UK
19. Law A.M., and Kelton W.D. Simulation Modeling and Analysis. third ed. (2000), MacGraw-Hill, New York
20. Lui J.C.S., and Muntz R.R. Computing bounds on steady state availability of repairable computer systems. Journal of ACM 41 4 (1994) 676-707
21. Lui J.C.S., Muntz R.R., and Towsley D. Bounding the mean response time of the minimum expected delay routing policy: an algorithmic approach. IEEE Transactions on Computers October (1994)
22. S. Mahévas. Modèles markoviens de grande taille: calculs de bornes, Thèse, Université de Rennes I, IFSIC, December 18, 1997.
23. Mahévas S., and Rubino S. Bound computation of dependability and performance measures. IEEE Transactions on Computers 50 5 (2001) 399-413
24. Majumdar S., and Woodside C.M. Robust bounds and throughput guarantees for closed multiclass queueing networks. Performance Evaluation 32 2 (1998) 101-136
25. M. Ben Mammoun, J.M. Fourneau, N. Pekergin, A. Troubnikoff, An algorithmic and numerical approach to bound the performance of high speed networks, in: Proceedings of the 10th International Workshop on Modeling, Analysis and Simulation of Computer and Telecommunication Systems (MASCOTS 2002), Fort Worth, TX, USA, October 11-16, 2002, pp. 375-382.
26. Muntz R.R., De Souza E Silva E., and Goyal A. Bounding availability of repairable computer systems. Proceedings of 1989 ACM SIGMETRICS and PERFORMANCE'89, May 1989. IEEE Transactions on Computers 38 12 (1989) 1714-1723 (special issue)
27. Rubino G., and Sericola B. Sojourn times in finite Markov processes. Journal of Applied Probability 27 (1989) 744-756
28. Stoyan D. Comparison Methods for Queueing and Other Stochastic Models (1984), John Wiley & Sons, New York
29. M. Trémolière, J.M. Vincent, B. Plateau, Determination of the optimal upper bound of a Markovan generator, Technical Report 106, LGI-IMAG, Grenoble, France, 1992.
30. van Dijk N.M. The importance of bias terms for error bounds and comparison results. In: Stewart W.J. (Ed). Proceedings of the First International Workshop on Numerical Solution of Markov Chains, Raleigh, NC, USA, January 8-10, 1990 (1991), Marcel Dekker, NY, USA