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Kronecker productforms of steadystate probabilities with $C_k$/$C_m$/$1$ by matrix polynomial approaches
1.  Department of Mathematical Science, National Chengchi University, Taipei, Taiwan, Taiwan 
References:
[1] 
R. Bellman, "Introduction to Matrix Analysis," MacGrawHill, London, 1960. 
[2] 
D. Bertsimas, An analytic approach to a general class of G/G/s queueing systems, Operations Research, 38 (1990), 139155. doi: 10.1287/opre.38.1.139. 
[3] 
F. De Terán, F. M. Dopico and J. Moro, Low rank perturbation of Weierstrass structure, SIAM J. Matrix Anal. Appl., 30 (2008), 538547. 
[4] 
R. V. Evans, Geometric distribution in some twodimensional queueing systems, Operations Research, 15 (1967), 830846. doi: 10.1287/opre.15.5.830. 
[5] 
H. R. Gail, S. L. Hantler and B. A. Taylor, Matrixgeometric invariant measures for G/M/1 type Markov chains, Commun. Statist.Stochastic Models, 14 (1998), 537569. 
[6] 
H. R. Gail, S. L. Hantler and B. A. Taylor, Spectral analysis of M/G/1 and G/M/1 Type Markov chains, Advanced Applied Probability, 28 (1996), 114165. doi: 10.2307/1427915. 
[7] 
H. R. Gail, S. L. Hantler, M. Sidi and B. A. Taylor, Linear independence of root equations for M/G/1 type Markov chains, Queueing Systems, 20 (1995), 321339. doi: 10.1007/BF01245323. 
[8] 
I. C. Gohberg, P. Lancaster and L. Rodman, "Matrix Polynomials," Academic Press, New York, 1982. 
[9] 
M. F. Neuts, "MatrixGeometric Solutions in Stochastic Models," The John Hopkins University Press, 1981. 
[10] 
W. K. Grassmann, Real eigenvalues of certain tridiagonal matrix polynomials with queueing applications, Linear Algebra and Its Applications, 342 (2002), 93106. doi: 10.1016/S00243795(01)004621. 
[11] 
W. K. Grassmann and J. Tavakoli, A tandem queue with movable server: an eigenvalue approach, SIAM J. Matrix Anal. Appl, 24 (2002), 465474. 
[12] 
W. K. Grassmann and S. Drekic, An analytical solution for a tandem queue with blocking, Queueing Systems, 36 (2000), 221235. doi: 10.1023/A:1019139405059. 
[13] 
R. A. Horn and C. R. Johnson, "Topics in Matrix Analysis," Cambridge University Press, 1999. 
[14] 
J. Y. Le Boudec, Steadystate probabilities of the PH/PH/1 queue, Queueing Systems, 3 (1988), 7388. doi: 10.1007/BF01159088. 
[15] 
H. Luh, Matrix productform solutions of stationary probabilities in tandem queues, Journal of the Operations Research, 42 (1999), 436656. 
[16] 
A. Van De Liefvoort, The waitingtime distribution and its moments of the PH/PH/1 queue, Operations Research Letters, 9 (1990), 261269. doi: 10.1016/01676377(90)90071C. 
[17] 
V. Wallace, "The Solution of Quasi Birth and Death Processes arising from Multiple Access Computer Systems," Ph. D. diss., Systems Engineering Laboratory, University of Michigan, Tech. Report N 077426T, 1969. 
show all references
References:
[1] 
R. Bellman, "Introduction to Matrix Analysis," MacGrawHill, London, 1960. 
[2] 
D. Bertsimas, An analytic approach to a general class of G/G/s queueing systems, Operations Research, 38 (1990), 139155. doi: 10.1287/opre.38.1.139. 
[3] 
F. De Terán, F. M. Dopico and J. Moro, Low rank perturbation of Weierstrass structure, SIAM J. Matrix Anal. Appl., 30 (2008), 538547. 
[4] 
R. V. Evans, Geometric distribution in some twodimensional queueing systems, Operations Research, 15 (1967), 830846. doi: 10.1287/opre.15.5.830. 
[5] 
H. R. Gail, S. L. Hantler and B. A. Taylor, Matrixgeometric invariant measures for G/M/1 type Markov chains, Commun. Statist.Stochastic Models, 14 (1998), 537569. 
[6] 
H. R. Gail, S. L. Hantler and B. A. Taylor, Spectral analysis of M/G/1 and G/M/1 Type Markov chains, Advanced Applied Probability, 28 (1996), 114165. doi: 10.2307/1427915. 
[7] 
H. R. Gail, S. L. Hantler, M. Sidi and B. A. Taylor, Linear independence of root equations for M/G/1 type Markov chains, Queueing Systems, 20 (1995), 321339. doi: 10.1007/BF01245323. 
[8] 
I. C. Gohberg, P. Lancaster and L. Rodman, "Matrix Polynomials," Academic Press, New York, 1982. 
[9] 
M. F. Neuts, "MatrixGeometric Solutions in Stochastic Models," The John Hopkins University Press, 1981. 
[10] 
W. K. Grassmann, Real eigenvalues of certain tridiagonal matrix polynomials with queueing applications, Linear Algebra and Its Applications, 342 (2002), 93106. doi: 10.1016/S00243795(01)004621. 
[11] 
W. K. Grassmann and J. Tavakoli, A tandem queue with movable server: an eigenvalue approach, SIAM J. Matrix Anal. Appl, 24 (2002), 465474. 
[12] 
W. K. Grassmann and S. Drekic, An analytical solution for a tandem queue with blocking, Queueing Systems, 36 (2000), 221235. doi: 10.1023/A:1019139405059. 
[13] 
R. A. Horn and C. R. Johnson, "Topics in Matrix Analysis," Cambridge University Press, 1999. 
[14] 
J. Y. Le Boudec, Steadystate probabilities of the PH/PH/1 queue, Queueing Systems, 3 (1988), 7388. doi: 10.1007/BF01159088. 
[15] 
H. Luh, Matrix productform solutions of stationary probabilities in tandem queues, Journal of the Operations Research, 42 (1999), 436656. 
[16] 
A. Van De Liefvoort, The waitingtime distribution and its moments of the PH/PH/1 queue, Operations Research Letters, 9 (1990), 261269. doi: 10.1016/01676377(90)90071C. 
[17] 
V. Wallace, "The Solution of Quasi Birth and Death Processes arising from Multiple Access Computer Systems," Ph. D. diss., Systems Engineering Laboratory, University of Michigan, Tech. Report N 077426T, 1969. 
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