Transforming stochastic matrices for stochastic comparison with the st-order

RAIRO - Operations Research

Volumn 37, Issue 2, 2003, Pages 85-97

  Dayar, Tuǧrul ^a   Fourneau, Jean Michel ^b   Pekergin, Nihal ^b  

^a BILKENT UNIVERSITY   (Turkey)

^b LABORATOIRE DES SCIENCES DU CLIMAT ET DE L ENVIRONNEMENT   (France)

Author keywords

Markov processes; Probability distributions; St order; Stochastic ordering

Indexed keywords

BRANCH AND BOUND METHOD; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; PROBABILITY DISTRIBUTIONS;

STOCHASTIC (ST) ORDER; STOCHASTIC ORDERING; TRANSFORMED MATRIX;

MARKOV PROCESSES;

EID: 33646144038     PISSN: 03990559     EISSN: 28047303     Source Type: Journal    
DOI: 10.1051/ro:2003015     Document Type: Article

References (15)

1. O. Abu-Amsha and J.-M. Vincent, An algorithm to bound functionals of Markov chains with large state space, in 4th INFORMS Conference on Telecommunications. Boca Raton, Florida (1998). Available as Rapport de recherche MAI No. 25. IMAG, Grenoble, France (1996).
2. M. Benmammoun, J.M. Fourneau, N. Pekergin and A. Troubnikoff, An algorithmic and numerical approach to bound the performance of high speed networks, IEEE MASCOTS 2002. Fort Worth, USA (2002) 375-382.
3. J. Keilson and A. Kester, Monotone matrices and monotone Markov processes. Stochastic Process. Appl. 5 (1977) 231-241.
4. J.M. Fourneau and N. Pekergin, An algorithmic approach to stochastic bounds, Performance evaluation of complex systems: Techniques and Tools. Springer, Lecture Notes in Comput. Sci. 2459 (2002) 64-88.
5. J.M. Fourneau, M. Le Coz, N. Pekergin and F. Quessette, An open tool to compute stochastic bounds on steady-state distributions and rewards, IEEE Mascots 03. USA (2003).
6. J.M. Fourneau, M. Le Coz and F. Quessette, Algorithms for an irreducible and lumpable strong stochastic bound, Numerical Solution of Markov Chains. USA (2003).
7. M. Kijima, Markov Processes for stochastic modeling. Chapman & Hall (1997).
8. W.A. Massey, Stochastic orderings for Markov processes on partially ordered spaces. Math. Oper. Res. 12 (1987) 350-367.
9. N. Pekergin, Stochastic delay bounds on fair queueing algorithms, in Proc. of INFOCOM'99. New York (1999) 1212-1220.
10. N. Pekergin, Stochastic performance bounds by state reduction. Performance Evaluation 36-37 (1999) 1-17.
11. M. Shaked and J.G. Shantikumar, Stochastic Orders and their Applications. Academic Press, California (1994).
12. D. Stoyan, Comparison Methods for Queues and Other Stochastic Models. John Wiley & Sons, Berlin, Germany (1983).
13. H.M. Taylor and S. Karlin, An Introduction to Stochastic Modeling. Academic Press, Florida (1984).
14. M. Tremolieres, J.-M. Vincent and B. Plateau, Determination of the optimal upper bound of a Markovian generator, Technical Report 106. LGI-IMAG, Grenoble, France (1992).
15. L. Truffet, Near complete decomposability: bounding the error by stochastic comparison method. Adv. Appl. Probab. 29 (1997) 830-855.