Approximate product form solutions for Markov chains

Performance Evaluation

Volumn 30, Issue 1-2, 1997, Pages 87-110

  Strelen, Johann Christoph ^a,b,c  

^a UNIVERSITY OF BONN   (Germany)

^b IBM Scientific Center ^*  (Germany)

^c IBM   (France)

Author keywords

Aggregation; Aggregation disaggregation algorithms; Approximate solution of discrete time and continuous time Markov chains; Product form

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; ITERATIVE METHODS; MARKOV PROCESSES; PROBABILITY;

AGGREGATION ALGORITHMS;

TELECOMMUNICATION SYSTEMS;

EID: 0031185750     PISSN: 01665316     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0166-5316(96)00053-3     Document Type: Article

References (20)

1. B. Bärk, Aggregationsmethoden für Markovketten, 1996.
2. O.J. Boxma, Workloads and waiting times in single-server systems with multiple customer classes, Queueing Systems 5 (1989) 185-214.
3. G. Ciardo and K.S. Trivedi, A decomposition approach for stochastic reward net models, Performance Evaluation 18 (1) (1993) 37-59.
4. J.F. Gierse, Zustandsraum-Aggregation für fast-unabhängige stochastische Petrinetze, Master's Thesis, Universität Bonn, 1995.
5. W.K. Grassmann, Finding transient solutions in Markovian event systems through randomization, in: W.J. Stewart (Ed.), Numerical Solution of Markov Chains, Marcel Dekker, New York (1991) 357-372.
6. T. Heinrichs, B. Bärk and J.C. Strelen, Wartezeiten für Pollingsysteme mittels numerischer Modelle, in: B. Walke and O. Spaniol (Eds.), Messung, Modellierung und Bewertung von Rechen- und Kommunikationssystemen, Springer, Berlin (1993) 173-185.
7. G. Horton and S.T. Leutenegger, A multi-level solution algorithm for steady-state Markov chains, ACM Performance Evaluation Rev. 22.
8. A. Jennings and W.J. Stewart, Simultaneous iteration for partial eigensolution of real matrices, J. Inst. Math. Appl. 15 (1975) 351-361.
9. V. Jonas, Iterative Analyse von Blockiernetzen mit alternierender Aggregation und Disaggregation, Master's Thesis, Universität Bonn, 1992.
10. A.M. Kagan, J.V. Linnik and C.R. Rao, Characterization Problems in Mathematical Statistics, Wiley, New York (1973).
11. R. Nitzgen, Aggregations-Disaggregationsverfahren für verallgemeinerte stochastische Petrinetze, Master's Thesis, Universität Bonn, 1993.
12. J.M. Ortega and W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York (1970).
13. B. Philippe, Y. Saad and W.J. Stewart, Numerical methods in Markov chain modeling, Oper. Res. 40 (6) (1992).
14. P.J. Schweitzer, A survey of aggregation-disaggregation in large Markov chains, in: W.J. Stewart (Ed.), Numerical Solution of Markov Chains, Marcel Dekker, New York (1991) 63-88.
15. J.E. Shore and R.W. Johnson, Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy, IEEE Trans. Inform. Theory 26 (1) (1980) 26-37.
16. W.J. Stewart, A comparison of numerical techniques in Markov modeling, Comm. ACM 21 (2) (1978) 144-152.
17. J.C. Strelen, A fast simultaneous iteration technique for the analysis of Markov chains, Interner Bericht 11/89/1, Institut für Informatik, Universität Bonn, 1989.
18. J.C. Strelen, Iterative Analyse von Markov-Modellen mit alternierender Aggregation und Disaggregation, in: A. Lehmann and F. Lehmann (Eds.), Messung, Modellierung und Bewertung von Rechensystemen, IFB 286, Springer, Berlin (1991) 320-336.
19. J.C. Strelen and B. Bärk, An approach to the numerical analysis of multiple-queue cyclic service systems, in: G. Stiege and J.S. Lie (Eds.), Messung, Modellierung und Bewertung von Rechensystemen und Netzen, IFB 218, Springer, Berlin (1989) 75-88.
20. J.C. Strelen, B. Bärk, J. Becker and V. Jonas, Analysis of queueing networks with blocking using a new aggregation technique, submitted for publication.