Iterative disaggregation for a class of lumpable discrete-time stochastic automata networks

Performance Evaluation

Volumn 53, Issue 1, 2003, Pages 43-69

  Gusak, Oleg ^a   Dayar, Tuǧrul ^b   Fourneau, Jean Michel ^c  

^a UNIVERSITY OF MISSOURI KANSAS CITY   (United States)

^b BILKENT UNIVERSITY   (Turkey)

^c UNIVERSITY OF VERSAILLES   (France)

Author keywords

Discrete time stochastic automata networks; Iterative disaggregation; Ordinary lumpability; Wireless asynchronous transfer mode system

Indexed keywords

AUTOMATION; COMPUTER SIMULATION; DISCRETE TIME CONTROL SYSTEMS; ITERATIVE METHODS; MATHEMATICAL MODELS; WIRELESS TELECOMMUNICATION SYSTEMS;

ITERATIVE DISAGGREGATION;

AUTOMATA THEORY;

EID: 0037657590     PISSN: 01665316     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-5316(02)00227-4     Document Type: Article

References (38)

1. Buchholz P., Exact and ordinary lumpability in finite Markov chains. J. Appl. Probab. 31:1994;59-75.
2. Buchholz P., Hierarchical Markovian models: symmetries and reduction. Perform. Eval. 22:1995;93-110.
3. P. Buchholz, Equivalence relations for stochastic automata networks, in: W.J. Stewart (Ed.), Computations with Markov Chains, Kluwer Academic Publishers, Boston, MA, 1995, pp. 197-215.
4. Buchholz P., An aggregation/disaggregation algorithm for stochastic automata networks. Probab. Eng. Inform. Sci. 11:1997;229-253.
5. P. Buchholz, Projection methods for the analysis of stochastic automata networks, in: B. Plateau, W.J. Stewart, M. Silva (Eds.), Numerical Solution of Markov Chains, Prensas Universitarias de Zaragoza, Zaragoza, Spain, 1999, pp. 149-168.
6. Buchholz P., Exact performance equivalence: an equivalence relation for stochastic automata. Theoret. Comput. Sci. 215:1999;263-287.
7. Buchholz P., Multilevel solutions for structured Markov chains. SIAM J. Matrix Anal. Appl. 22:2000;342-357.
8. Buchholz P., Ciardo G., Donatelli S., Kemper P., Complexity of memory-efficient Kronecker operations with applications to the solution of Markov models. INFORMS J. Comput. 12:2000;203-222.
9. Chan R.H., Ching W.K., Circulant preconditioners for stochastic automata networks. Numer. Math. 87:2000;35-57.
10. Davio M., Kronecker products and shuffle algebra. IEEE Trans. Comput. C-30:1981;116-125.
11. T. Dayar, Permuting Markov chains to nearly completely decomposable form, Technical Report BU-CEIS-9808, Department of Computer Engineering and Information Science, Bilkent University, Ankara, Turkey, August 1998. ftp://ftp.cs.bilkent.edu.tr/pub/tech-reports/1998/BU-CEIS-9808.ps.z.
12. T. Dayar, O.I. Pentakalos, A.B. Stephens, Analytical modeling of robotic tape libraries using stochastic automata, Technical Report TR-97-189, CESDIS, NASA/GSFC, Greenbelt, MD, January 1997.
13. Dayar T., Stewart W.J., On the effects of using the Grassmann-Taksar-Heyman method in iterative aggregation-disaggregation. SIAM J. Sci. Comput. 17:1996;287-303.
14. Dayar T., Stewart W.J., Comparison of partitioning techniques for two-level iterative solvers on large, sparse Markov chains. SIAM J. Sci. Comput. 21:2000;1691-1705.
15. Fernandes P., Plateau B., Stewart W.J., Efficient descriptor-vector multiplications in stochastic automata networks. J. ACM. 45:1998;381-414.
16. Fernandes P., Plateau B., Stewart W.J., Optimizing tensor product computations in stochastic automata networks. Oper. Res. 32(3):1998;325-351.
17. J.-M. Fourneau, Stochastic automata networks: using structural properties to reduce the state space, in: B. Plateau, W.J. Stewart, M. Silva (Eds.), Numerical Solution of Markov Chains, Prensas Universitarias de Zaragoza, Zaragoza, Spain, 1999, pp. 332-334.
18. J.-M. Fourneau, H. Maisonniaux, N. Pekergin, V. Véque, Performance evaluation of a buffer policy with stochastic automata networks, in: Proceedings of the IFIP Workshop on Modelling and Performance Evaluation of ATM Technology, vol. C-15, La Martinique, IFIP Transactions, North-Holland, Amsterdam, 1993, pp. 433-451.
19. Fourneau J.-M., Kloul L., Pekergin N., Quessette F., Véque V., Modelling buffer admission mechanisms using stochastic automata networks. Rev. Ann. Télécommun. 49(5-6):1994;337-349.
20. J.-M. Fourneau, F. Quessette, Graphs and stochastic automata networks, in: W.J. Stewart (Ed.), Computations with Markov Chains, Kluwer Academic Publishers, Boston, MA, 1995, pp. 217-235.
21. O. Gusak, T. Dayar, J.-M. Fourneau, Stochastic automata networks and near complete decomposability, Technical Report BU-CE-0016, Department of Computer Engineering, Bilkent University, Ankara, Turkey, October 2000. http://www.cs.bilkent.edu.tr/tech-reports/2000/BU-CE-0016.ps.z.
22. Gusak O., Dayar T., Fourneau J.-M., Stochastic automata networks and near complete decomposability. SIAM J. Matrix Anal. Appl. 23:2001;581-599.
23. J. Hillston, Compositional Markovian modelling using a process algebra, in: W.J. Stewart (Ed.), Computations with Markov Chains, Kluwer Academic Publishers, Boston, MA, 1995, pp. 177-196.
24. J.R. Kemeny, J.L. Snell, Finite Markov Chains, Van Nostrand, New York, 1960.
25. Marek I., Mayer P., Convergence analysis of an iterative aggregation-disaggregation method for computing stationary probability vectors of stochastic matrices. Numer. Linear Algebra Appl. 5:1998;253-274.
26. Meyer C.D., Stochastic complementation, uncoupling Markov chains, and the theory of nearly reducible systems. SIAM Rev. 31:1989;240-272.
27. B. Plateau, De l'évaluation du parallélisme et de la synchronisation, Thèse d'état, Université Paris Sud Orsay, 1984.
28. B. Plateau, On the stochastic structure of parallelism and synchronization models for distributed algorithms, in: Proceedings of the ACM SIGMETRICS Conference on Measurement and Modelling of Computer Systems, Austin, TX, 1985, pp. 147-154.
29. Plateau B., Tripathi K., Performance analysis of synchronization for two communicating processes. Perform. Eval. 8:1988;305-320.
30. Plateau B., Atif K., Stochastic automata network for modeling parallel systems. IEEE Trans. Software Eng. 17:1991;1093-1108.
31. B. Plateau, J.-M. Fourneau, K.-H. Lee, PEPS: a package for solving complex Markov models of parallel systems, in: R. Puigjaner, D. Ptier (Eds.), Modeling Techniques and Tools for Computer Performance Evaluation, Palma de Majorca, Spain, 1988, pp. 291-305.
32. Plateau B., Fourneau J.-M., A methodology for solving Markov models of parallel systems. J. Parallel Distrib. Comput. 12:1991;370-387.
33. M. Siegle, Structured Markovian performance modeling with automatic symmetry exploitation, in: Short Papers and Tool Descriptions of the 7th International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, Vienna, Austria, 1994, pp. 77-81.
34. G.W. Stewart, W.J. Stewart, D.F. McAllister, A two-stage iteration for solving nearly completely decomposable Markov chains, in: G.H. Golub, A. Greenbaum, M. Luskin (Eds.), Recent Advances in Iterative Methods, IMA Vol. Math. Appl. 60, Springer, New York, 1994, pp. 201-216.
35. W.J. Stewart, Introduction to the Numerical Solution of Markov Chains, Princeton University Press, Princeton, NJ, 1994.
36. Stewart W.J., Atif K., Plateau B., The numerical solution of stochastic automata networks. Eur. J. Oper. Res. 86:1995;503-525.
37. Uysal E., Dayar T., Iterative methods based on splittings for stochastic automata networks. Eur. J. Oper. Res. 110:1998;166-186.
38. Vèque V., Ben-Othman J., MRAP: a multiservices resource allocation policy for wireless ATM network. Comput. Networks ISDN Syst. 29:1998;2187-2200.