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Original Articles

Rational Generating Functions and Matrix-Geometric Invariant Measures

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Pages 551-573 | Received 01 Aug 2005, Accepted 01 Mar 2007, Published online: 02 Nov 2007

REFERENCES

  • Akar , N. ; Sohraby , K. Matrix geometric solutions in M/G/1 type Markov chains with multiple boundaries: a generalized state-space approach . In Teletraffic Contributions for the Information Age ; Ramaswami , V. ; Wirth , P.E. , Eds., Elsevier , 1997 ; 487 – 496 .
  • Akar , N. ; Oguz , N.C. ; Sohraby , K. Matrix-geometric solutions of M/G/1 type Markov chains: a unifying generalized state-space approach . IEEE J. on Selected Areas in Comm. 1998 , 16 ( 5 ), 626 – 639 .
  • Derman , C. Some contributions to the theory of denumerable Markov chains . Trans. Amer. Math. Soc. 1955 , 79 , 541 – 555 .
  • Gail , H.R. ; Hantler , S.L. ; Taylor , B.A. M/G/1 type Markov chains with rational generating functions . In Advances in Matrix Analytic Methods for Stochastic Models ; Alfa , A.S. ; Chakravarthy , S.R. , Eds., Notable Publications , 1998 ; 1 – 16 .
  • Gail , H.R. ; Hantler , S.L. ; Taylor , B.A. Matrix-geometric invariant measures for G/M/1 type Markov chains . Commun. Statist.-Stochastic Models 1998 , 14 ( 3 ), 537 – 569 .
  • Gail , H.R. ; Hantler , S.L. ; Taylor , B.A. Use of characteristic roots for solving infinite state Markov chains . In Computational Probability ; Grassmann , W.K. , Ed.; Kluwer : Boston , 2000 ; pp. 205 – 255 .
  • Gohberg , I. ; Goldberg , S. ; Kaashoek , M.A. Classes of Linear Operators, Vol. 2 ; Operator theory: Advances and Applications, Vol. 63 ; Birkhäuser : Basel , 1993 .
  • Gohberg , I. ; Kaashoek , M.A. Block Toeplitz Operators with Rational Symbols ; Operator Theory: Advances and Applications , Vol. 35 ; Birkhäuser Verlag : Basel , 1988 ; 385 – 440 .
  • Gohberg , I. ; Lancaster , P. ; Rodman , L. Matrix Polynomials ; Academic Press : New York , 1982 .
  • Lancaster , P. A fundamental theorem on lambda-matrices with applications – I. Ordinary differential equations with constant coefficients . Linear Alg. Appl. 1977 , 18 , 189 – 211 .
  • Lancaster , P. A fundamental theorem on lambda-matrices with applications – II. Difference equations with constant cefficients . Linear Alg. Appl. 1977 , 18 , 213 – 222 .
  • Latouche , G ; Pearce , C.E.M. ; Taylor , P.G. Invariant measures for quasi- birth-and-death processes . Commun. Statist.-Stochastic Models 1998 , 14 ( 1–2 ), 443 – 460 .
  • Latouche , G. ; Ramaswami , V. Introduction to Matrix Analytic Methods in Stochastic Modeling ; ASA-SIAM : Philadelphia , 1999 .
  • Laursen , K.B. ; Neumann , M.M. An Introduction to Local Spectral Theory ; Clarendon Press : Oxford , 2000 .
  • Miller , K.S. Linear Difference Equations ; Benjamin : New York , 1968 .
  • Neuts , M.F. Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach ; Johns Hopkins Univ. Press : Baltimore , Maryland , 1981 .
  • Neuts , M.F. Structured Stochastic Matrices of M/G/1 Type and Their Applications ; Marcel Dekker : New York , 1989.
  • Prössdorf , S. Some Classes of Singular Equations ; North-Holland : Amsterdam , 1978 .
  • Revuz , D. Markov Chains ; North-Holland : Amsterdam , 1975 .
  • Seneta , E. Non-Negative Matrices and Markov Chains ; Springer : New York , 1981 .
  • Sontag , E.D. Mathematical Control Theory, , 2nd ed. ; Springer : New York , 1998 .

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