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Volumn 12, Issue 3, 2000, Pages 203-222

Complexity of Memory-Efficient Kronecker Operations with Applications to the Solution of Markov Models

Author keywords

Kronecker algebra; Sparse matrices

Indexed keywords


EID: 0000800371     PISSN: 10919856     EISSN: None     Source Type: Journal    
DOI: 10.1287/ijoc.12.3.203.12634     Document Type: Article
Times cited : (115)

References (30)
  • 1
    • 84976753721 scopus 로고
    • A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems
    • Ajmone Marsan, M., G. Balbo, G. Conte. 1984. A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems. ACM Trans. Comp. Syst. 2, 93-122.
    • (1984) ACM Trans. Comp. Syst. , vol.2 , pp. 93-122
    • Ajmone Marsan, M.1    Balbo, G.2    Conte, G.3
  • 3
    • 84958053451 scopus 로고    scopus 로고
    • A toolbox for functional and quantitative analysis of DEDS
    • R. Puigjaner, N. Savino, B. Serra, eds. lecture notes in Computer Science 1469 Springer-Verlag, Berlin
    • Bause, F., P. Buchholz, P. Kemper. 1998. A toolbox for functional and quantitative analysis of DEDS. R. Puigjaner, N. Savino, B. Serra, eds. Proc. 10th Int. Conf. on Modelling Techniques and Tools for Computer Performance Evaluation, lecture notes in Computer Science 1469. Springer-Verlag, Berlin. 356-359.
    • (1998) Proc. 10th Int. Conf. on Modelling Techniques and Tools for Computer Performance Evaluation , pp. 356-359
    • Bause, F.1    Buchholz, P.2    Kemper, P.3
  • 4
    • 0001704301 scopus 로고
    • Numerical solution methods based on structured descriptions of Markovian models
    • G. Balbo and G. Serazzi, eds. Elsevier Science Publishers (North-Holland), Amsterdam
    • Buchholz, P. 1991. Numerical solution methods based on structured descriptions of Markovian models. G. Balbo and G. Serazzi, eds. Computer Performance Evaluation. Elsevier Science Publishers (North-Holland), Amsterdam. 251-267.
    • (1991) Computer Performance Evaluation , pp. 251-267
    • Buchholz, P.1
  • 5
    • 21344495526 scopus 로고
    • A class of hierarchical queueing networks and their analysis
    • Buchholz, P. 1994. A class of hierarchical queueing networks and their analysis. Queueing Systems 15, 59-80.
    • (1994) Queueing Systems , vol.15 , pp. 59-80
    • Buchholz, P.1
  • 6
  • 8
    • 0033338997 scopus 로고    scopus 로고
    • Structured analysis approaches for large Markov chains
    • Buchholz, P. 1999. Structured analysis approaches for large Markov chains. Applied Numerical Mathematics 31, 375-404.
    • (1999) Applied Numerical Mathematics , vol.31 , pp. 375-404
    • Buchholz, P.1
  • 9
    • 0001470680 scopus 로고
    • Automated generation and analysis of Markov reward models using stochastic reward nets
    • C. Meyer and R.J. Plemmons, eds. IMA Volumes in Mathematics and its Applications. Springer-Verlag, Berlin
    • Ciardo, G., A. Blakemore, P.F.J. Chimento, J.K. Muppala, K.S. Trivedi. 1993. Automated generation and analysis of Markov reward models using stochastic reward nets. C. Meyer and R.J. Plemmons, eds. Linear Algebra, Markov Chains, and Queueing Models, IMA Volumes in Mathematics and its Applications 48. Springer-Verlag, Berlin. 145-191.
    • (1993) Linear Algebra, Markov Chains, and Queueing Models , vol.48 , pp. 145-191
    • Ciardo, G.1    Blakemore, A.2    Chimento, P.F.J.3    Muppala, J.K.4    Trivedi, K.S.5
  • 12
    • 0343749269 scopus 로고    scopus 로고
    • On the use of Kronecker operators for the solution of generalized stochastic Petri nets
    • Institute for Computer Applications in Science and Engineering, Hampton, VA
    • Ciardo, G., M. Tilgner. 1996. On the use of Kronecker operators for the solution of generalized stochastic Petri nets. ICASE Report 96-35, Institute for Computer Applications in Science and Engineering, Hampton, VA.
    • (1996) ICASE Report , vol.96 , Issue.35
    • Ciardo, G.1    Tilgner, M.2
  • 13
    • 0019530364 scopus 로고
    • Kronecker products and shuffle algebra
    • Davio, M. 1981. Kronecker products and shuffle algebra. IEEE Trans. Comp. C-30, 116-125.
    • (1981) IEEE Trans. Comp. , vol.C-30 , pp. 116-125
    • Davio, M.1
  • 16
    • 0027626274 scopus 로고
    • Superposed stochastic automata: A class of stochastic Petri nets with parallel solution and distributed state space
    • Donatelli, S. 1993. Superposed stochastic automata: A class of stochastic Petri nets with parallel solution and distributed state space. Perf. Eval. 18, 21-26.
    • (1993) Perf. Eval. , vol.18 , pp. 21-26
    • Donatelli, S.1
  • 19
    • 0032058359 scopus 로고    scopus 로고
    • Efficient descriptor-vector multiplication in stochastic automata networks
    • Fernandes, P., B. Plateau, W.J. Stewart. 1998. Efficient descriptor-vector multiplication in stochastic automata networks. Journal of the ACM 45, 381-414.
    • (1998) Journal of the ACM , vol.45 , pp. 381-414
    • Fernandes, P.1    Plateau, B.2    Stewart, W.J.3
  • 21
    • 0001189029 scopus 로고    scopus 로고
    • Numerical analysis of superposed GSPNs
    • Kemper, P. 1996a. Numerical analysis of superposed GSPNs. IEEE Trans. Softw. Eng. 22, 615-628.
    • (1996) IEEE Trans. Softw. Eng. , vol.22 , pp. 615-628
    • Kemper, P.1
  • 24
    • 0022506289 scopus 로고
    • A chaotic asynchronous algorithm for computing the fixed point of nonnegative matrices with unit spectral radius
    • Lubachevsky, B., D. Mitra. 1986. A chaotic asynchronous algorithm for computing the fixed point of nonnegative matrices with unit spectral radius. J. ACM 33, 130-150.
    • (1986) J. ACM , vol.33 , pp. 130-150
    • Lubachevsky, B.1    Mitra, D.2
  • 25
    • 84967578593 scopus 로고
    • On the stochastic structure of parallelism and synchronisation models for distributed algorithms
    • Austin, TX, ACM Sigmetrics, New York
    • Plateau, B. 1985. On the stochastic structure of parallelism and synchronisation models for distributed algorithms. Proc. 1985 ACM SIGMETRICS Conf. on Measurement and Modeling of Computer Systems, Austin, TX, ACM Sigmetrics, New York, 147-153.
    • (1985) Proc. 1985 ACM SIGMETRICS Conf. on Measurement and Modeling of Computer Systems , pp. 147-153
    • Plateau, B.1
  • 26
    • 0026239753 scopus 로고
    • Stochastic automata network for modeling parallel systems
    • Plateau, B., K. Atif. 1991. Stochastic automata network for modeling parallel systems. IEEE Trans. Softw. Eng. 17, 1093-1108.
    • (1991) IEEE Trans. Softw. Eng. , vol.17 , pp. 1093-1108
    • Plateau, B.1    Atif, K.2
  • 27
    • 0026203351 scopus 로고
    • A methodology for solving Markov models of parallel systems
    • Plateau, B., J.-M. Fourneau. 1991. A methodology for solving Markov models of parallel systems. J. Par. and Distr. Comp. 12, 370-387.
    • (1991) J. Par. and Distr. Comp. , vol.12 , pp. 370-387
    • Plateau, B.1    Fourneau, J.-M.2
  • 29
    • 0000392810 scopus 로고
    • The numerical solution of stochastic automata networks
    • Stewart, W.J., K. Atif, B. Plateau. 1995. The numerical solution of stochastic automata networks. Eur. J. of Oper. Res. 86, 503-525.
    • (1995) Eur. J. of Oper. Res. , vol.86 , pp. 503-525
    • Stewart, W.J.1    Atif, K.2    Plateau, B.3
  • 30
    • 0032188734 scopus 로고    scopus 로고
    • Iterative methods based on splittings for stochastic automata networks
    • Uysal, E., T. Dayar. 1998. Iterative methods based on splittings for stochastic automata networks. Eur. J. Op. Res. 110, 166-186.
    • (1998) Eur. J. Op. Res. , vol.110 , pp. 166-186
    • Uysal, E.1    Dayar, T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.