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1. | Department of Mathematical Science, National Chengchi University, Taipei, Taiwan, Taiwan |
References:
[1] |
R. Bellman, "Introduction to Matrix Analysis," MacGraw-Hill, London, 1960. |
[2] |
D. Bertsimas, An analytic approach to a general class of G/G/s queueing systems, Operations Research, 38 (1990), 139-155.
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), 538-547. |
[4] |
R. V. Evans, Geometric distribution in some two-dimensional queueing systems, Operations Research, 15 (1967), 830-846.
doi: 10.1287/opre.15.5.830. |
[5] |
H. R. Gail, S. L. Hantler and B. A. Taylor, Matrix-geometric invariant measures for G/M/1 type Markov chains, Commun. Statist.-Stochastic Models, 14 (1998), 537-569. |
[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), 114-165.
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), 321-339.
doi: 10.1007/BF01245323. |
[8] |
I. C. Gohberg, P. Lancaster and L. Rodman, "Matrix Polynomials," Academic Press, New York, 1982. |
[9] |
M. F. Neuts, "Matrix-Geometric 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), 93-106.
doi: 10.1016/S0024-3795(01)00462-1. |
[11] |
W. K. Grassmann and J. Tavakoli, A tandem queue with movable server: an eigenvalue approach, SIAM J. Matrix Anal. Appl, 24 (2002), 465-474. |
[12] |
W. K. Grassmann and S. Drekic, An analytical solution for a tandem queue with blocking, Queueing Systems, 36 (2000), 221-235.
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, Steady-state probabilities of the PH/PH/1 queue, Queueing Systems, 3 (1988), 73-88.
doi: 10.1007/BF01159088. |
[15] |
H. Luh, Matrix product-form solutions of stationary probabilities in tandem queues, Journal of the Operations Research, 42 (1999), 436-656. |
[16] |
A. Van De Liefvoort, The waiting-time distribution and its moments of the PH/PH/1 queue, Operations Research Letters, 9 (1990), 261-269.
doi: 10.1016/0167-6377(90)90071-C. |
[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 07742-6-T, 1969. |
show all references
References:
[1] |
R. Bellman, "Introduction to Matrix Analysis," MacGraw-Hill, London, 1960. |
[2] |
D. Bertsimas, An analytic approach to a general class of G/G/s queueing systems, Operations Research, 38 (1990), 139-155.
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), 538-547. |
[4] |
R. V. Evans, Geometric distribution in some two-dimensional queueing systems, Operations Research, 15 (1967), 830-846.
doi: 10.1287/opre.15.5.830. |
[5] |
H. R. Gail, S. L. Hantler and B. A. Taylor, Matrix-geometric invariant measures for G/M/1 type Markov chains, Commun. Statist.-Stochastic Models, 14 (1998), 537-569. |
[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), 114-165.
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), 321-339.
doi: 10.1007/BF01245323. |
[8] |
I. C. Gohberg, P. Lancaster and L. Rodman, "Matrix Polynomials," Academic Press, New York, 1982. |
[9] |
M. F. Neuts, "Matrix-Geometric 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), 93-106.
doi: 10.1016/S0024-3795(01)00462-1. |
[11] |
W. K. Grassmann and J. Tavakoli, A tandem queue with movable server: an eigenvalue approach, SIAM J. Matrix Anal. Appl, 24 (2002), 465-474. |
[12] |
W. K. Grassmann and S. Drekic, An analytical solution for a tandem queue with blocking, Queueing Systems, 36 (2000), 221-235.
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, Steady-state probabilities of the PH/PH/1 queue, Queueing Systems, 3 (1988), 73-88.
doi: 10.1007/BF01159088. |
[15] |
H. Luh, Matrix product-form solutions of stationary probabilities in tandem queues, Journal of the Operations Research, 42 (1999), 436-656. |
[16] |
A. Van De Liefvoort, The waiting-time distribution and its moments of the PH/PH/1 queue, Operations Research Letters, 9 (1990), 261-269.
doi: 10.1016/0167-6377(90)90071-C. |
[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 07742-6-T, 1969. |
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