메뉴 건너뛰기




Volumn 16, Issue 2, 2000, Pages 273-311

A novel computational method for solving finite QBD processes

Author keywords

[No Author keywords available]

Indexed keywords


EID: 1642448357     PISSN: 08820287     EISSN: None     Source Type: Journal    
DOI: 10.1080/15326340008807588     Document Type: Article
Times cited : (28)

References (44)
  • 1
    • 0032095469 scopus 로고    scopus 로고
    • Matrix-geometric solutions of M/G/1-type markov chains: A unifying generalized state-space approach
    • N. Akar, N. C. Oǧuz, and K. Sohraby. Matrix-geometric solutions of M/G/1-type markov chains: a unifying generalized state-space approach. IEEE J. Select. Areas in Comm., 16(5):626-639, 1998.
    • (1998) IEEE J. Select. Areas in Comm. , vol.16 , Issue.5 , pp. 626-639
    • Akar, N.1    Oǧuz, N.C.2    Sohraby, K.3
  • 2
    • 0029781152 scopus 로고    scopus 로고
    • A new paradigm in teletraffic analysis of communication networks
    • N. Akar and K. Sohraby. A new paradigm in teletraffic analysis of communication networks. In Proc. IEEE INFOCOM, pages 1318-1326, 1996.
    • (1996) Proc. IEEE INFOCOM , pp. 1318-1326
    • Akar, N.1    Sohraby, K.2
  • 3
    • 0031333239 scopus 로고    scopus 로고
    • Finite and infinite QBD chains: A simple and unifying algorithmic approach
    • N. Akar and K. Sohraby. Finite and infinite QBD chains: a simple and unifying algorithmic approach. In Proc. IEEE INFOCOM, 1997.
    • (1997) Proc. IEEE INFOCOM
    • Akar, N.1    Sohraby, K.2
  • 4
    • 0001671305 scopus 로고    scopus 로고
    • An invariant subspace approach in M/G/1 and G/M/1 type Markov chains
    • N. Akar and K. Sohraby. An invariant subspace approach in M/G/1 and G/M/1 type Markov chains. Commun. Statist. - Stochastic Models, 13(3), 1997.
    • (1997) Commun. Statist. - Stochastic Models , vol.13 , Issue.3
    • Akar, N.1    Sohraby, K.2
  • 5
    • 0027839022 scopus 로고
    • Two finite queues with relative priority in a single server system with phase-type distributions
    • F. X. Albores and P. P. Bocharov. Two finite queues with relative priority in a single server system with phase-type distributions. Avtomatika i Telemeknanika, 4:96-107, 1993.
    • (1993) Avtomatika i Telemeknanika , vol.4 , pp. 96-107
    • Albores, F.X.1    Bocharov, P.P.2
  • 9
    • 0019241416 scopus 로고
    • Accelerated convergence of the matrix sign function
    • L. Balzer. Accelerated convergence of the matrix sign function. Int. Jour. Contr., 32:1057-1078, 1980.
    • (1980) Int. Jour. Contr. , vol.32 , pp. 1057-1078
    • Balzer, L.1
  • 10
    • 0030492130 scopus 로고    scopus 로고
    • On the solution of a nonlinear matrix equation in queueing problems
    • D. Bini and B. Meini. On the solution of a nonlinear matrix equation in queueing problems. SIAM Journal of Matrix Anal. Appl., 17:906-926, 1996.
    • (1996) SIAM Journal of Matrix Anal. Appl. , vol.17 , pp. 906-926
    • Bini, D.1    Meini, B.2
  • 11
    • 0023542080 scopus 로고
    • Analysis of the queueu length and the output flow in single server with finite waiting room and phase-type distributions
    • P. P. Bocharov. Analysis of the queueu length and the output flow in single server with finite waiting room and phase-type distributions. Probl. Control Info. Theory, 16:211-222, 1987.
    • (1987) Probl. Control Info. Theory , vol.16 , pp. 211-222
    • Bocharov, P.P.1
  • 12
    • 33747252132 scopus 로고
    • Matrix-geometric stationary distribution for the PH/PH/1/r queue
    • P. P. Bocharov and V. A. Naoumov. Matrix-geometric stationary distribution for the PH/PH/1/r queue. J. Info. Proc. Cyber., 22:179-186, 1986.
    • (1986) J. Info. Proc. Cyber. , vol.22 , pp. 179-186
    • Bocharov, P.P.1    Naoumov, V.A.2
  • 13
    • 84959949711 scopus 로고
    • Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes
    • L. Bright and P. G. Taylor. Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes. Commun. Statist. - Stochastic Models, 11(3):497-525, 1995.
    • (1995) Commun. Statist. - Stochastic Models , vol.11 , Issue.3 , pp. 497-525
    • Bright, L.1    Taylor, P.G.2
  • 15
    • 38249038136 scopus 로고
    • Solving the algebraic Riccati equation with the matrix sign function
    • R. Byers. Solving the algebraic Riccati equation with the matrix sign function. Lin. Alg. Appl., 85:267-279, 1987.
    • (1987) Lin. Alg. Appl. , vol.85 , pp. 267-279
    • Byers, R.1
  • 16
    • 0002170151 scopus 로고
    • Rank revealing QR factorizations
    • T. F. Chan. Rank revealing QR factorizations. Lin. Alg. Appl., 88/89:67-82, 1987.
    • (1987) Lin. Alg. Appl. , vol.88-89 , pp. 67-82
    • Chan, T.F.1
  • 17
    • 0001860522 scopus 로고
    • Queueing systems having phase-dependent arrival and service rates
    • Marcel Dekker, New York
    • J. N. Daigle and D. M. Lucantoni. Queueing systems having phase-dependent arrival and service rates. In Numerical Solution of Markov Chains, pages 223-238. Marcel Dekker, New York, 1991.
    • (1991) Numerical Solution of Markov Chains , pp. 223-238
    • Daigle, J.N.1    Lucantoni, D.M.2
  • 18
    • 84958310749 scopus 로고
    • Solutions of the basic matrix equation for M/G/1 and G/M/1 type Markov chains
    • H. R. Gail, S. L. Hantler, and B. A. Taylor. Solutions of the basic matrix equation for M/G/1 and G/M/1 type Markov chains. Commun. Statist. - Stochastic Models, 10(1):1-43, 1994.
    • (1994) Commun. Statist. - Stochastic Models , vol.10 , Issue.1 , pp. 1-43
    • Gail, H.R.1    Hantler, S.L.2    Taylor, B.A.3
  • 19
    • 0022788010 scopus 로고
    • A generalization of the matrix-sign-function solution for algebraic Riccati equations
    • J. D. Gardiner and A. J. Laub. A generalization of the matrix-sign-function solution for algebraic Riccati equations. Int. Jour. Contr., 44:823-832, 1986.
    • (1986) Int. Jour. Contr. , vol.44 , pp. 823-832
    • Gardiner, J.D.1    Laub, A.J.2
  • 22
    • 0001210808 scopus 로고
    • Experimental techniques on matrix-analytical solution techniques - Extensions and comparisons
    • L. Gün. Experimental techniques on matrix-analytical solution techniques - extensions and comparisons. Commun. Statist. - Stochastic Models, 5(4):669-682, 1989.
    • (1989) Commun. Statist. - Stochastic Models , vol.5 , Issue.4 , pp. 669-682
    • Gün, L.1
  • 23
    • 0039318897 scopus 로고
    • Matrix-geometric solution for finite capacity queues with phase-type distributions
    • North Holland
    • L. Gün and A. A. Makowski. Matrix-geometric solution for finite capacity queues with phase-type distributions. In Proc. Performance 87, pages 269-282. North Holland, 1988.
    • (1988) Proc. Performance 87 , pp. 269-282
    • Gün, L.1    Makowski, A.A.2
  • 24
    • 0000142055 scopus 로고
    • Birth-and-death processes on the integers with phases and general boundaries
    • B. Hajek. Birth-and-death processes on the integers with phases and general boundaries. J. Appl. Prob., 19:488-499, 1982.
    • (1982) J. Appl. Prob. , vol.19 , pp. 488-499
    • Hajek, B.1
  • 25
    • 0001246152 scopus 로고
    • Rational iterative methods for the matrix sign function
    • C. Kenney and A. J. Laub. Rational iterative methods for the matrix sign function. SIAM Matrix. Anal. Appl., 12(2):273-291, 1991.
    • (1991) SIAM Matrix. Anal. Appl. , vol.12 , Issue.2 , pp. 273-291
    • Kenney, C.1    Laub, A.J.2
  • 26
    • 0000204992 scopus 로고
    • On scaling Newton's method for polar decomposition and the matrix sign function
    • C. Kenney and A. J. Laub. On scaling Newton's method for polar decomposition and the matrix sign function. SIAM Jour. Matrix Anal. Appl., 13(3):688-706, 1992.
    • (1992) SIAM Jour. Matrix Anal. Appl. , vol.13 , Issue.3 , pp. 688-706
    • Kenney, C.1    Laub, A.J.2
  • 29
    • 21344482962 scopus 로고
    • A logarithmic reduction algorithm for quasi-birth-death processes
    • G. Latouche and V. Ramaswami. A logarithmic reduction algorithm for quasi-birth-death processes. J. Appl. Prob., 30:650-674, 1993.
    • (1993) J. Appl. Prob. , vol.30 , pp. 650-674
    • Latouche, G.1    Ramaswami, V.2
  • 30
    • 0018681625 scopus 로고
    • A Schur method for solving algebraic Riccati equations
    • A. J. Laub. A Schur method for solving algebraic Riccati equations. IEEE Trans. Auto. Contr., 25:913-921, 1979.
    • (1979) IEEE Trans. Auto. Contr. , vol.25 , pp. 913-921
    • Laub, A.J.1
  • 31
    • 0002756084 scopus 로고
    • Invariant subspace methods for the numerical solution of Riccati equations
    • S. Bittanti, A. J. Laub, and J. C. Willems, editors, chapter 7, Springer-Verlag, Berlin
    • A. J. Laub. Invariant subspace methods for the numerical solution of Riccati equations. In S. Bittanti, A. J. Laub, and J. C. Willems, editors, The Riccati Equation, chapter 7, pages 163-196. Springer-Verlag, Berlin, 1991.
    • (1991) The Riccati Equation , pp. 163-196
    • Laub, A.J.1
  • 33
    • 0009952699 scopus 로고    scopus 로고
    • Solving QBD problems: The cyclic reduction algorithm versus the invariant subspace method
    • B. Meini. Solving QBD problems: the cyclic reduction algorithm versus the invariant subspace method. Advances in Performance Analysis, 1:215-225, 1998.
    • (1998) Advances in Performance Analysis , vol.1 , pp. 215-225
    • Meini, B.1
  • 34
    • 0002346095 scopus 로고    scopus 로고
    • Analysis of a multi-server delay-loss system with a general Markovian arrival process
    • S. Chakravarthy and A. Alfa, editors, Marcel Dekker, New York
    • V. A. Naoumov, U. R. Krieger, and D. Wagner. Analysis of a multi-server delay-loss system with a general Markovian arrival process. In S. Chakravarthy and A. Alfa, editors, Matrix-Analytic Methods in Stochastic Models, pages 43-66. Marcel Dekker, New York, 1996.
    • (1996) Matrix-Analytic Methods in Stochastic Models , pp. 43-66
    • Naoumov, V.A.1    Krieger, U.R.2    Wagner, D.3
  • 35
    • 0000922222 scopus 로고
    • Markov chains with applications in queueing theory, which have a matrix-geometric invariant probability vector
    • M. F. Neuts. Markov chains with applications in queueing theory, which have a matrix-geometric invariant probability vector. Adv. Appl. Prob., 10:185-212, 1978.
    • (1978) Adv. Appl. Prob. , vol.10 , pp. 185-212
    • Neuts, M.F.1
  • 39
    • 0030367202 scopus 로고    scopus 로고
    • Some properties of the rate operators in level dependent quasi-birth-and-death processes with a countable number of phases
    • V. Ramaswami and P. G. Taylor. Some properties of the rate operators in level dependent quasi-birth-and-death processes with a countable number of phases. Commun. Statist. - Stochastic Models, 12(1):143-164, 1996.
    • (1996) Commun. Statist. - Stochastic Models , vol.12 , Issue.1 , pp. 143-164
    • Ramaswami, V.1    Taylor, P.G.2
  • 40
    • 0019069037 scopus 로고
    • Linear model reduction and solution of the algebraic Riccati equation by the use of the sign function
    • J. D. Roberts. Linear model reduction and solution of the algebraic Riccati equation by the use of the sign function. Int. Jour. Control, 32:677-687, 1980.
    • (1980) Int. Jour. Control , vol.32 , pp. 677-687
    • Roberts, J.D.1
  • 41
    • 0042750567 scopus 로고
    • Operator-geometric stationary distributions for Markov chains with applications to queueing models
    • R. L. Tweedie. Operator-geometric stationary distributions for Markov chains with applications to queueing models. Adv. Appl. Prob., 14:368-391, 1982.
    • (1982) Adv. Appl. Prob. , vol.14 , pp. 368-391
    • Tweedie, R.L.1
  • 43
    • 0028381180 scopus 로고
    • A computational method for finite QBD processes with level-dependent transitions
    • J. Ye and S. Q. Li. A computational method for finite QBD processes with level-dependent transitions. IEEE Trans. Commun., 42(2):625-639, 1994.
    • (1994) IEEE Trans. Commun. , vol.42 , Issue.2 , pp. 625-639
    • Ye, J.1    Li, S.Q.2
  • 44
    • 0025432130 scopus 로고
    • Congestion control for packet voice by selective packet discarding
    • N. Yin, S. Q. Li, and T. E. Stern. Congestion control for packet voice by selective packet discarding. IEEE Trans. Commun., 38(5):674-683, 1990.
    • (1990) IEEE Trans. Commun. , vol.38 , Issue.5 , pp. 674-683
    • Yin, N.1    Li, S.Q.2    Stern, T.E.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.