Rational interpolation for stochastic DES's: Convergence issues

IEEE Transactions on Automatic Control

Volumn 44, Issue 5, 1999, Pages 1070-1073

  Nananukul, Soracha ^a   Gong, Wei Bo ^b  

^a NOKIA RESEARCH CENTER   (United States)

^b University of Massachusetts at Amherst   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CONTROL SYSTEM ANALYSIS; CONTROL SYSTEM SYNTHESIS; CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; INTERPOLATION; QUEUEING THEORY; STOCHASTIC CONTROL SYSTEMS;

PADE APPROXIMATIONS; RATIONAL APPROXIMATIONS; SINGLE-SERVER QUEUE;

DISCRETE TIME CONTROL SYSTEMS;

EID: 0032630084     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.763231     Document Type: Article

References (20)

1. F. Baccelli and V. Schmidt, "Taylor series expansion for Poisson driven (max. +)-linear systems," Annals Appl. Probability, no. 6, pp. 138-185, 1996.
2. G. A. Baker and P. Graves-Morris, Padé Approximants - Part II: Extensions and Applications Reading, MA: Addison-Wesley, 1981.
3. R. P. Boas, Jr., Entire Functions New York: Academic, 1954.
4. J. W. Cohen, The Single Server Queue. Amsterdam, The Netherlands North-Holland, 1969.
5. W.-B. Gong and J. Q. Hu, "The MacLaurin series for the GI/G/1 queue," J. Appl. Probability, vol. 29, pp. 176-184, 1992.
6. W.-B. Gong and S. Nananukul, "Rational interpolation for rare event probabilities," Stochastic Networks: Stability and Rare Events, Lecture Notes in Statistics, no. 117. New York: Springer-Verlag, 1996.
7. W.-B. Gong, S. Nananukul, and A. Yan, "Padé approximations for stochastic discrete event systems," IEEE Trans. Automat. Contr., vol. 40, pp. 1349-1358, Aug. 1995.
8. W.-B. Gong, A. Yan, and D. Tang, "Rational representations for performance functions of queueing systems," in Proc. Princeton Conf. Systems Information Sciences, Mar. 1992, p. 204.
9. W.-B. Gong and H. Yang, "Rational approximants for some performance analysis problems," IEEE Trans. Comput., vol. 44, pp. 1394-1404, Dec. 1995.
10. E. Hille, Analytic Function Theory, vol. 2. New York: Ginn, 1962.
11. H. Li and Y. Zhu, "A new approach to the GI/G/1 queue with generalized setup time and exhaustive service," J. Appl. Probability, vol. 31, pp. 1083-1097, 1994.
12. S. Nananukul and W.-B. Gong, "The mean waiting time of a GI/G/1 queue in light traffic via random thinning," J. Appl. Probability, vol. 32, pp. 256-266, 1995.
13. H. Stahl, "On the convergence of generalized Padé approximants," Constr. Approx., vol. 5, pp. 221-240, 1989.
14. _, "General convergence results for rational approximants," Approximation Theory VI, C. K. Chui, L. L. Schumaker, and J. D. Ward, Eds. New York: Academic, 1989, pp. 605-634.
15. _, "Convergence of rational interpolants," in Numerical Analysis - A Conf. in Honor of Jean Meinguet, Supplement to the Bulletin of the Belgian Mathematical Society, Brussels, Belgium, 1996, pp. 11-33.
16. W. Van Den Hout and H. Blanc, "Development and justification of the power-series algorithm for BMAP-systems," Commun. Statist. Stochastic Models, vol. 11, no. 3, pp. 471-496, 1995.
17. H. Wallin, "Potential theory and approximation of analytic functions by rational interpolation," in Proc. Complex Analysis, Joensuu, Lecture Notes in Mathematics no. 747. Springer-Verlag, 1978, pp. 434-450.
18. R. W. Wolff, Stochastic Modeling and the Theory of Queues. Englewood Cliffs, NJ: Prentice Hall, 1988.
19. H. Yang, W.-B. Gong, and D. Towsley, "Efficient calculation of cell loss in ATM multiplexers," in Proc. GLOBECOM, Nov. 1995.
20. Y. Zhu and H. Li, "The MacLaurin expansion for a GI/G/1 queue with Markov-modulated arrivals and services," Queueing Syst., vol. 14, pp. 125-134, 1993.