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Volumn 22, Issue 2, 2001, Pages 342-357

Multilevel solutions for structured Markov chains

Author keywords

Aggregation disaggregation; Continuous time Markov chains; Iterative solution techniques; Stationary analysis

Indexed keywords


EID: 0042330211     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479898342419     Document Type: Article
Times cited : (19)

References (28)
  • 1
    • 0003419038 scopus 로고
    • Numerical Solution of Elliptic Problems
    • SIAM, Philadelphia
    • G. BIRKHOFF AND R. E. LYNCH, Numerical Solution of Elliptic Problems, SIAM Stud. Appl. Math. 6, SIAM, Philadelphia, 1984.
    • (1984) SIAM Stud. Appl. Math. , vol.6
    • Birkhoff, G.1    Lynch, R.E.2
  • 2
    • 84966233568 scopus 로고
    • Multi-level adaptive solutions to boundary value problems
    • A. BRANDT, Multi-level adaptive solutions to boundary value problems, Math. Comp., 31 (1977), pp. 333-390.
    • (1977) Math. Comp. , vol.31 , pp. 333-390
    • Brandt, A.1
  • 4
    • 0031510546 scopus 로고    scopus 로고
    • An aggregation/disaggregation algorithm for stochastic automata networks
    • P. BUCHHOLZ, An aggregation/disaggregation algorithm for stochastic automata networks, Probab. Engrg. Inform. Sci., 11 (1997), pp. 229-253.
    • (1997) Probab. Engrg. Inform. Sci. , vol.11 , pp. 229-253
    • Buchholz, P.1
  • 5
    • 0032635704 scopus 로고    scopus 로고
    • An adaptive aggregation/disaggregation algorithm for hierarchical Markovian models
    • P. BUCHHOLZ, An adaptive aggregation/disaggregation algorithm for hierarchical Markovian models, European J. Oper. Res., 116 (1999), pp. 85-104.
    • (1999) European J. Oper. Res. , vol.116 , pp. 85-104
    • Buchholz, P.1
  • 6
    • 0033338997 scopus 로고    scopus 로고
    • Structured analysis approaches for large Markov chains
    • P. BUCHHOLZ, Structured analysis approaches for large Markov chains, Appl. Numer. Math., 31 (1999), pp. 375-404.
    • (1999) Appl. Numer. Math. , vol.31 , pp. 375-404
    • Buchholz, P.1
  • 7
    • 0003076022 scopus 로고    scopus 로고
    • Projection methods for the analysis of stochastic automata networks
    • B. Plateau, W. J. Stewart, and M. Silva, eds., Prensas Universitarias de Zaragoza
    • P. BUCHHOLZ, Projection methods for the analysis of stochastic automata networks, in Numerical Solution of Markov Chains, B. Plateau, W. J. Stewart, and M. Silva, eds., Prensas Universitarias de Zaragoza, 1999, pp. 149-168.
    • (1999) Numerical Solution of Markov Chains , pp. 149-168
    • Buchholz, P.1
  • 8
    • 0042122112 scopus 로고    scopus 로고
    • Complexity of Kronecker operations and sparse matrices with applications to the solution of Markov models
    • to appear
    • P. BUCHHOLZ, G. CIARDO, S. DONATELLI, AND P. KEMPER, Complexity of Kronecker operations and sparse matrices with applications to the solution of Markov models, INFORMS J. Comput., to appear.
    • INFORMS J. Comput.
    • Buchholz, P.1    Ciardo, G.2    Donatelli, S.3    Kemper, P.4
  • 9
    • 0030092454 scopus 로고    scopus 로고
    • Efficient vector and parallel manipulation of tensor products
    • P. E. BUIS AND W. R. DYKSEN, Efficient vector and parallel manipulation of tensor products, ACM Trans. Math. Software, 22 (1996), pp. 18-23.
    • (1996) ACM Trans. Math. Software , vol.22 , pp. 18-23
    • Buis, P.E.1    Dyksen, W.R.2
  • 10
    • 0000592564 scopus 로고
    • Iterative methods for overflow queueing networks I
    • R. CHAN, Iterative methods for overflow queueing networks I, Numer. Math., 51 (1987), pp. 143-180.
    • (1987) Numer. Math. , vol.51 , pp. 143-180
    • Chan, R.1
  • 11
    • 0008443783 scopus 로고
    • Iterative methods for overflow queueing networks II
    • R. CHAN, Iterative methods for overflow queueing networks II, Numer. Math., 54 (1988), pp. 57-78.
    • (1988) Numer. Math. , vol.54 , pp. 57-78
    • Chan, R.1
  • 12
    • 0042122111 scopus 로고    scopus 로고
    • Circulant preconditioned for stochastic automata networks
    • to appear
    • R. CHAN AND W. CHING, Circulant preconditioned for stochastic automata networks, Numer. Math., to appear.
    • Numer. Math.
    • Chan, R.1    Ching, W.2
  • 13
    • 0019530364 scopus 로고
    • Kronecker products and shuffle algebra
    • M. DAVIO, Kronecker products and shuffle algebra, IEEE Trans. Comput., 30 (1981) pp. 116-125.
    • (1981) IEEE Trans. Comput. , vol.30 , pp. 116-125
    • Davio, M.1
  • 14
    • 0033709988 scopus 로고    scopus 로고
    • Comparison of partitioning techniques for two-level iterative solvers on large, sparse Markov chains
    • T. DAYAR AND W. J. STEWART, Comparison of partitioning techniques for two-level iterative solvers on large, sparse Markov chains, SIAM J. Sci. Comput., 21 (2000), pp. 1691-1705.
    • (2000) SIAM J. Sci. Comput. , vol.21 , pp. 1691-1705
    • Dayar, T.1    Stewart, W.J.2
  • 15
    • 84977510484 scopus 로고
    • Superposed generalized stochastic Petri nets: Definition and efficient solution
    • Application and Theory of Petri Nets, Zaragoza, 1994, R. Valette, ed., Springer-Verlag, Berlin
    • S. DONATELLI, Superposed generalized stochastic Petri nets: Definition and efficient solution, in Application and Theory of Petri Nets, Zaragoza, 1994, R. Valette, ed., Lecture Notes in Comput. Sci. 815, Springer-Verlag, Berlin, 1994, pp. 258-277.
    • (1994) Lecture Notes in Comput. Sci. , vol.815 , pp. 258-277
    • Donatelli, S.1
  • 16
    • 0032058359 scopus 로고    scopus 로고
    • Efficient descriptor-vector multiplication in stochastic automata networks
    • P. FERNANDES, B. PLATEAU, AND W. J. STEWART, Efficient descriptor-vector multiplication in stochastic automata networks, J. ACM, 45 (1998), pp. 381-414.
    • (1998) J. ACM , vol.45 , pp. 381-414
    • Fernandes, P.1    Plateau, B.2    Stewart, W.J.3
  • 17
    • 84985316667 scopus 로고
    • On the use of two QMR for solving singular systems and applications in Markov chain modelling
    • R. W. FREUND AND M. HOCHDRUCK, On the use of two QMR for solving singular systems and applications in Markov chain modelling, Numer. Linear Algebra Appl., 1 (1994), pp. 403-420.
    • (1994) Numer. Linear Algebra Appl. , vol.1 , pp. 403-420
    • Freund, R.W.1    Hochdruck, M.2
  • 18
    • 0028428645 scopus 로고
    • A multi-level solution algorithm for steady state Markov-chains
    • G. HORTON AND S. LEUTENEGGER, A multi-level solution algorithm for steady state Markov-chains, ACM Perform. Eval. Rev., 22 (1994), pp. 191-200.
    • (1994) ACM Perform. Eval. Rev. , vol.22 , pp. 191-200
    • Horton, G.1    Leutenegger, S.2
  • 19
    • 0000126599 scopus 로고
    • Matrix methods for queuing problems
    • L. KAUFMAN, Matrix methods for queuing problems, SIAM J. Sci. Statist. Comput., 4 (1983), pp. 525-552.
    • (1983) SIAM J. Sci. Statist. Comput. , vol.4 , pp. 525-552
    • Kaufman, L.1
  • 20
    • 0032344877 scopus 로고    scopus 로고
    • Convergence analysis of an iterative aggregation/disaggregation method for computing the probability vector of stochastic matrices
    • I. MAREK AND P. MAYER, Convergence analysis of an iterative aggregation/disaggregation method for computing the probability vector of stochastic matrices, Numer. Linear Algebra Appl., 5 (1998), pp. 253-274.
    • (1998) Numer. Linear Algebra Appl. , vol.5 , pp. 253-274
    • Marek, I.1    Mayer, P.2
  • 21
    • 0026223819 scopus 로고
    • Analysis of a kanban discipline for cell coordination in production lines II: Stochastic demands
    • D. MITRA AND I. MITRANI, Analysis of a kanban discipline for cell coordination in production lines II: Stochastic demands, Oper. Res., 39 (1991), pp. 807-823.
    • (1991) Oper. Res. , vol.39 , pp. 807-823
    • Mitra, D.1    Mitrani, I.2
  • 22
    • 0001507857 scopus 로고
    • On the stochastic structure of parallelism and synchronisation models for distributed algorithms
    • B. PLATEAU, On the stochastic structure of parallelism and synchronisation models for distributed algorithms, ACM Perform. Eval. Rev., 13 (1985), pp. 142-154.
    • (1985) ACM Perform. Eval. Rev. , vol.13 , pp. 142-154
    • Plateau, B.1
  • 23
    • 0026239753 scopus 로고
    • Stochastic automata networks for modeling parallel systems
    • B. PLATEAU AND K. ATIF, Stochastic automata networks for modeling parallel systems, IEEE Trans. Software Engrg., 17 (1991), pp. 1093-1108.
    • (1991) IEEE Trans. Software Engrg. , vol.17 , pp. 1093-1108
    • Plateau, B.1    Atif, K.2
  • 24
    • 38249039987 scopus 로고
    • An iterative aggregation-disaggregation algorithm for solving linear equations
    • P. SCHWEITZER AND K. W. KINDLE, An iterative aggregation-disaggregation algorithm for solving linear equations, Appl. Math. Comput., 18 (1986), pp. 313-353.
    • (1986) Appl. Math. Comput. , vol.18 , pp. 313-353
    • Schweitzer, P.1    Kindle, K.W.2
  • 26
    • 0000392810 scopus 로고
    • The numerical solution of stochastic automata networks
    • W.J. STEWART, K. ATIF, AND B. PLATEAU, The numerical solution of stochastic automata networks, European J. Oper. Res., 86 (1995), pp. 503-525.
    • (1995) European J. Oper. Res. , vol.86 , pp. 503-525
    • Stewart, W.J.1    Atif, K.2    Plateau, B.3
  • 27
    • 0032188734 scopus 로고    scopus 로고
    • Iterative methods based on splittings for stochastic automata networks
    • E. UYSAL AND T. DAYAR, Iterative methods based on splittings for stochastic automata networks, European J. Oper. Res., 110 (1998), pp. 166-186.
    • (1998) European J. Oper. Res. , vol.110 , pp. 166-186
    • Uysal, E.1    Dayar, T.2
  • 28
    • 0000005482 scopus 로고
    • Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems
    • H. A. VAN DER VORST, Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Statist. Comput., 13 (1992), pp. 631-644.
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , pp. 631-644
    • Van Der Vorst, H.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.