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Original Articles

A graph-theoretic approach to queueing analysis part i: theory

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Pages 791-824 | Received 31 Mar 1997, Accepted 02 Apr 1999, Published online: 21 Mar 2007

References

  • Agrawal , A. , Klein , P. and Ravi , R. 1993 . “ Cutting down on fill using nested dissection: provably good elimination orderings ” . In Graph Theory and Sparse Matrix Computation , 31 – 56 . Springer-Verlag .
  • Berge , C. 1962 . “ The Theory of Graphs and its Applications ” . New York : John Wiley .
  • Lai , R. and Bhat , U. N. 1987 . Reduced systems in Markov chains and their applications in queueing theory . Queueing Syst. , 2 : 147 – 172 .
  • Walrand , J. 1988 . “ An Introduction to Queueing Networks ” . Prentice-Hall .
  • Kemeny , J. G. and Snell , J. L. 1976 . “ Finite Markov chains ” . New York : Springer Verlay .
  • Duff , I. and Reid , J. K. 1986 . “ Direct Methods for Sparse Matrices ” . Oxford University Press .
  • George , A. 1973 . Nested dissection of a regular finite element mesh . SIAM J. Numer. Anal , 10 ( 2 ) Apr : 345 – 363 .
  • George , A. and Liu , J. W. 1981 . “ Computer solution of large sparse positive definite systems ” . Prentice-Hall Inc. .
  • George , A. and Liu , J. W. 1989 . The evolution of the minimum degree ordering algorithm . SIAM Review , 31 ( 1 ) Mar. : 1 – 19 .
  • Golub , G. H. and Van Loan , C. F. 1978 . “ Matrix Computations ” . New York : Academic Press .
  • Haskins , L. and Rose , D. J. 1973 . Toward characterization of perfect elimina tion digraphs . SIAM J. Comput. , 2 ( 4 ) Dec. : 217 – 224 .
  • Jennings , A. and Mckeown , J. J. 1992 . “ Matrix Computation ” . John Wiley &Sons .
  • Krieger , U. R. , Clostermann , B. M. and Sczittnick , M. 1990 . Modelling and Analysis of Communication systems Based on Computational Methods for Markov Chains . IEEE Selected Areas in Commu. , 8 ( 9 ) Dec. : 1630 – 1648 .
  • Lipton , R. J. , Rose , D. J. and Tarjan , R. E. 1979 . Generalized nested dissection . SIAM J. Numer. Anal. , 16 ( 2 ) Apr. : 346 – 358 .
  • Liu , J. W. 1992 . The multifrontal method for sparse matrix solution: Theory and Practice . SIAM Review , 34 ( 1 ) Mar. : 82 – 109 .
  • Liu , W. H. and Sherman , A. H. 1976 . Comparative analysis of the Cuthill-Mckee and the reverse Cuthill-Mckee ordering algorithms for sparse matrices . SIAM J. Numer. Anal. , 13 ( 2 ) Apr. : 198 – 213 .
  • Parter , S. 1961 . The use of linear graphs in Gaussian elimination . SIAM Review , 3 ( 2 ) Apr. : 119 – 130 .
  • Rose , D. J. 1972 . “ A graph-theoretical study of the numerical solution of sparse positive definite systems of linear equations ” . In Graph Theory and Computing , Edited by: Read , R. C. 183 – 217 . Academic Press .
  • Rose , D. J. and Tarjan , R. E. 1978 . Algorithmic Aspects of Vertex Elimination on Directed Graphs . SIAM J. Appl Math. , 34 : 176 – 197 .
  • Rose , D. J. , Tarjan , R. E. and Lueker . 1976 . Algorithmic Aspects of Vertex Elimination on Graphs . SIAM J. Comput. , 5 ( 2 ) Jun. : 266 – 283 .
  • Tang , C. N. Jun. 1995 . “ Graph-Theoretic Approach in Gaussian Elimination and Queueing Analysis”,Master Thesis ” . In Department of Information Engineering, The Chinese University of Hong Kong Jun. ,
  • Tang , C. N. and Yeung , R. W. “ A Graph-Theoretic Approach to Queueing Analysis — Part II: Applications ” . same issue
  • Tarjan , R. E. 1976 . “ Graph theory and Gaussian elimination ” . In Sparse matrix computations , 3 – 22 . Academic Press .
  • Yannakakis , M. 1981 . Computing the minimum fill-in is NP-Complete . SIAM J. Alg. Disc. Meth. , 2 ( 1 ) Mar. : 77 – 79 .
  • Ye , J. and Li , S. Q. “Analysis of Multimedia Traffic Queues with Finite Buffer and Overload Control – Part I: Algorithm” . Proc. of Ieee infocom '91 . Bal Harbor, Floria. pp. 1464 – 1474 .

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