메뉴 건너뛰기




Volumn 48, Issue 3-4, 2004, Pages 365-397

An algorithmic approach for sensitivity analysis of perturbed quasi-birth-and-death processes

Author keywords

Markovian arrival process (MAP); perturbation analysis; perturbed Markov chain; phase type (PH) distribution; QBD process; RG factorization; sensitivity analysis; stochastic integral functional

Indexed keywords

CONTINUOUS TIME SYSTEMS; FACTORIZATION; INTEGRAL EQUATIONS; MARKOV CHAINS; STOCHASTIC SYSTEMS; TRANSIENT ANALYSIS;

EID: 8144221250     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1023/B:QUES.0000046582.57514.35     Document Type: Article
Times cited : (14)

References (58)
  • 2
    • 0030212015 scopus 로고    scopus 로고
    • First- and second-derivatives estimators for cyclic closed-queueing networks
    • G. Bao, C.G. Cassandras and M.A. Zazanis, First- and second-derivatives estimators for cyclic closed-queueing networks, IEEE Trans. Automat. Control 41 (1996) 1106-1124.
    • (1996) IEEE Trans. Automat. Control , vol.41 , pp. 1106-1124
    • Bao, G.1    Cassandras, C.G.2    Zazanis, M.A.3
  • 3
    • 0032210293 scopus 로고    scopus 로고
    • Ergodic control of singularly perturbed Markov process in discrete time with general state and compact action spaces
    • T.R. Bielecki and L. Stettner, Ergodic control of singularly perturbed Markov process in discrete time with general state and compact action spaces, Appl. Math. Optim. 38 (1998) 261-281.
    • (1998) Appl. Math. Optim. , vol.38 , pp. 261-281
    • Bielecki, T.R.1    Stettner, L.2
  • 4
    • 84959949711 scopus 로고
    • Calculating the equilibrium distribution in level-dependent quasi-birth-and-death processes
    • L.W. Bright and P.G. Taylor, Calculating the equilibrium distribution in level-dependent quasi-birth-and-death processes, Stochastic Models 11 (1995) 497-526.
    • (1995) Stochastic Models , vol.11 , pp. 497-526
    • Bright, L.W.1    Taylor, P.G.2
  • 5
    • 0141865798 scopus 로고    scopus 로고
    • Equilibrium distribution in level-dependent quasi-birth-and-death processes
    • eds. A.S. Alfa and S. Chakravarthy (Marcel Dekker, New York)
    • L.W. Bright and P.G. Taylor, Equilibrium distribution in level-dependent quasi-birth-and-death processes, in: Matrix Analytic Methods in Stochastic Models, eds. A.S. Alfa and S. Chakravarthy (Marcel Dekker, New York, 1996) pp. 359-375.
    • (1996) Matrix Analytic Methods in Stochastic Models , pp. 359-375
    • Bright, L.W.1    Taylor, P.G.2
  • 7
    • 0009843739 scopus 로고    scopus 로고
    • The Maclaurin series for performance functions of Markov chains
    • X.R. Cao, The Maclaurin series for performance functions of Markov chains, Adv. in Appl. Probab. 30 (1998) 676-692.
    • (1998) Adv. in Appl. Probab. , vol.30 , pp. 676-692
    • Cao, X.R.1
  • 8
    • 0032027940 scopus 로고    scopus 로고
    • The relations among potentials, perturbation analysis, and Markov decision processes
    • X.R. Cao, The relations among potentials, perturbation analysis, and Markov decision processes, Discrete Event Dyn. Systems 8 (1998) 71-87.
    • (1998) Discrete Event Dyn. Systems , vol.8 , pp. 71-87
    • Cao, X.R.1
  • 9
    • 0037289322 scopus 로고    scopus 로고
    • From perturbation analysis to Markov decision processes and reinforcement learning
    • X.R. Cao, From perturbation analysis to Markov decision processes and reinforcement learning, Discrete Event Dyn. Systems 13 (2003) 9-39.
    • (2003) Discrete Event Dyn. Systems , vol.13 , pp. 9-39
    • Cao, X.R.1
  • 10
    • 0038631988 scopus 로고    scopus 로고
    • Semi-Markov decision problems and performance sensitivity analysis
    • X.R. Cao, Semi-Markov decision problems and performance sensitivity analysis, IEEE Trans. Automat. Control 48 (2003) 758-769.
    • (2003) IEEE Trans. Automat. Control , vol.48 , pp. 758-769
    • Cao, X.R.1
  • 11
    • 0031258478 scopus 로고    scopus 로고
    • Perturbation realization, potentials, and sensitivity analysis of Markov processes
    • X.R. Cao and H.F. Chen, Perturbation realization, potentials, and sensitivity analysis of Markov processes, IEEE Trans. Automat. Control 42 (1997) 1382-1393.
    • (1997) IEEE Trans. Automat. Control , vol.42 , pp. 1382-1393
    • Cao, X.R.1    Chen, H.F.2
  • 12
    • 0032122986 scopus 로고    scopus 로고
    • Algorithms for sensitivity analysis of Markov systems through potentials and perturbation realization
    • X.R. Cao and Y.W. Wan, Algorithms for sensitivity analysis of Markov systems through potentials and perturbation realization, IEEE Trans. Control Systems Technol. 6 (1998) 482-494.
    • (1998) IEEE Trans. Control Systems Technol. , vol.6 , pp. 482-494
    • Cao, X.R.1    Wan, Y.W.2
  • 13
    • 0030409198 scopus 로고    scopus 로고
    • A single sample path-based performance sensitivity formula for Markov chains
    • X.R. Cao, X.M. Yuan and L. Qiu, A single sample path-based performance sensitivity formula for Markov chains, IEEE Trans. Automat. Control 41 (1996) 1814-1817.
    • (1996) IEEE Trans. Automat. Control , vol.41 , pp. 1814-1817
    • Cao, X.R.1    Yuan, X.M.2    Qiu, L.3
  • 15
    • 0005643933 scopus 로고
    • Perturbation analysis of the M/M/1 queue in a Markovian environment via the matrix-geometric method
    • C.S. Chang and F. Nelson, Perturbation analysis of the M/M/1 queue in a Markovian environment via the matrix-geometric method, Stochastic Models 9 (1993) 233-246.
    • (1993) Stochastic Models , vol.9 , pp. 233-246
    • Chang, C.S.1    Nelson, F.2
  • 16
    • 0030159511 scopus 로고    scopus 로고
    • Sensitivity analysis of stationary performance measures for general Markov chains
    • L.Y. Dai, Sensitivity analysis of stationary performance measures for general Markov chains, Special Issue on Discrete-Event Dynamic Systems of Math. Computer Modeling 23 (12) (1996) 143-160.
    • (1996) Discrete-Event Dynamic Systems of Math. Computer Modeling , vol.23 , Issue.12 SPEC. ISSUE , pp. 143-160
    • Dai, L.Y.1
  • 17
    • 4944245274 scopus 로고
    • The total waiting time in a busy period of a stable single-server queue, I
    • D.J. Daley, The total waiting time in a busy period of a stable single-server queue, I, J. Appl. Probab. 6 (1969) 550-564.
    • (1969) J. Appl. Probab. , vol.6 , pp. 550-564
    • Daley, D.J.1
  • 18
    • 0040904353 scopus 로고
    • The total waiting time in a busy period of a stable single-server queue, II
    • D.J. Daley and D.R.J. Jacobs, The total waiting time in a busy period of a stable single-server queue, II, J. Appl. Probab. 6 (1969) 565-572.
    • (1969) J. Appl. Probab. , vol.6 , pp. 565-572
    • Daley, D.J.1    Jacobs, D.R.J.2
  • 19
    • 8144230005 scopus 로고    scopus 로고
    • Transient solutions for Markov chains
    • ed. W.K. Grassmann (Kluwer Academic, Dordrecht)
    • E. de Souza e Silva and H.R. Gail, Transient solutions for Markov chains, in: Computational Probability, ed. W.K. Grassmann (Kluwer Academic, Dordrecht, 2000) pp. 43-79.
    • (2000) Computational Probability , pp. 43-79
    • De Souza E Silva, E.1    Gail, H.R.2
  • 22
    • 84873011849 scopus 로고
    • Infinitesimal perturbation analysis of a birth and death process
    • P. Glasserman, Infinitesimal perturbation analysis of a birth and death process, Oper. Res. Lett. 40 (1992) 292-308.
    • (1992) Oper. Res. Lett. , vol.40 , pp. 292-308
    • Glasserman, P.1
  • 23
    • 0742326320 scopus 로고
    • Derivative estimates from simulation of continuous-time Markov chains
    • P. Glasserman, Derivative estimates from simulation of continuous-time Markov chains, Oper. Res. 40 (1992) 292-308.
    • (1992) Oper. Res. , vol.40 , pp. 292-308
    • Glasserman, P.1
  • 24
    • 38249014756 scopus 로고
    • Obtaining derivatives of stationary queue length probabilities through the matrix-geometric solution method
    • W.B. Gong, J. Pan and C.G. Cassandras, Obtaining derivatives of stationary queue length probabilities through the matrix-geometric solution method, Appl. Math. Lett. 5 (1992) 69-73.
    • (1992) Appl. Math. Lett. , vol.5 , pp. 69-73
    • Gong, W.B.1    Pan, J.2    Cassandras, C.G.3
  • 25
    • 0005579485 scopus 로고
    • Means and variances in Markov reward systems
    • eds. C.D. Meyer and R.J. Plemmons (Springer, New York)
    • W.K. Grassmann, Means and variances in Markov reward systems, in: Linear Algebra, Markov Chains, and Queueing Models, eds. C.D. Meyer and R.J. Plemmons (Springer, New York, 1993) pp. 193-204.
    • (1993) Linear Algebra, Markov Chains, and Queueing Models , pp. 193-204
    • Grassmann, W.K.1
  • 26
    • 0030574819 scopus 로고    scopus 로고
    • Optimizing steady state Markov chains by state reduction
    • W.K. Grassmann, Optimizing steady state Markov chains by state reduction, European J. Oper. Res. 89 (1996) 277-284.
    • (1996) European J. Oper. Res. , vol.89 , pp. 277-284
    • Grassmann, W.K.1
  • 27
    • 0029208085 scopus 로고
    • The use of derivatives for optimizing steady state queues
    • W.K. Grassmann and X. Chen, The use of derivatives for optimizing steady state queues, J. Oper. Res. Soc. 46 (1995) 104-115.
    • (1995) J. Oper. Res. Soc. , vol.46 , pp. 104-115
    • Grassmann, W.K.1    Chen, X.2
  • 28
    • 0035451609 scopus 로고    scopus 로고
    • Optimal service rates for the state-dependent M/G/1 queues in steady state
    • W.K. Grassmann, X. Chen and B.R.K Kashyap, Optimal service rates for the state-dependent M/G/1 queues in steady state, Oper. Res. Lett. 29 (2001) 57-63.
    • (2001) Oper. Res. Lett. , vol.29 , pp. 57-63
    • Grassmann, W.K.1    Chen, X.2    Kashyap, B.R.K.3
  • 29
    • 0000572102 scopus 로고
    • Equilibrium distribution of block-structured Markov chains with repeating rows
    • W.K. Grassmann and D.P. Heyman, Equilibrium distribution of block-structured Markov chains with repeating rows, J. Appl. Probab. 27 (1990) 557-576.
    • (1990) J. Appl. Probab. , vol.27 , pp. 557-576
    • Grassmann, W.K.1    Heyman, D.P.2
  • 30
    • 0040539256 scopus 로고
    • Computation of steady-state probabilities for infinite-state Markov chains with repeating rows
    • W.K. Grassmann and D.P. Heyman, Computation of steady-state probabilities for infinite-state Markov chains with repeating rows, ORSA J. Comput. (1993) 282-303.
    • (1993) ORSA J. Comput. , pp. 282-303
    • Grassmann, W.K.1    Heyman, D.P.2
  • 31
    • 0009169037 scopus 로고
    • Differentiability of matrices R and G in the matrix-analytic method
    • Q.M. He, Differentiability of matrices R and G in the matrix-analytic method, Stochastic Models 11 (1995) 123-132.
    • (1995) Stochastic Models , vol.11 , pp. 123-132
    • He, Q.M.1
  • 33
    • 21844499487 scopus 로고
    • A decomposition theorem for infinite stochastic matrices
    • D.P. Heyman, A decomposition theorem for infinite stochastic matrices, J. Appl. Probab. 32 (1995) 893-901.
    • (1995) J. Appl. Probab. , vol.32 , pp. 893-901
    • Heyman, D.P.1
  • 38
    • 8144221202 scopus 로고
    • Perturbation analysis of phase-type queue with weakly correlated arrivals
    • G. Latouche, Perturbation analysis of phase-type queue with weakly correlated arrivals, Adv. in Appl. Probab. 20 (1988) 896-912.
    • (1988) Adv. in Appl. Probab. , vol.20 , pp. 896-912
    • Latouche, G.1
  • 39
    • 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. Probab. 30 (1993) 650-674.
    • (1993) J. Appl. Probab. , vol.30 , pp. 650-674
    • Latouche, G.1    Ramaswami, V.2
  • 41
    • 0037886166 scopus 로고    scopus 로고
    • A constructive method for finding β-invariant measures for transition matrices of M/G/1 type
    • eds. G. Latouche and P.G. Taylor (World Scientific, Singapore)
    • Q.L. Li and Y.Q. Zhao, A constructive method for finding β-invariant measures for transition matrices of M/G/1 type, in: Matrix Analytic Methods Theory and Applications, eds. G. Latouche and P.G. Taylor (World Scientific, Singapore, 2002) pp. 237-263.
    • (2002) Matrix Analytic Methods Theory and Applications , pp. 237-263
    • Li, Q.L.1    Zhao, Y.Q.2
  • 43
    • 0037592879 scopus 로고    scopus 로고
    • β-invariant measures for transition matrices of GI/M/1 type
    • Q.L. Li and Y.Q. Zhao, β-invariant measures for transition matrices of GI/M/1 type, Stochastic Models 19 (2003) 201-233.
    • (2003) Stochastic Models , vol.19 , pp. 201-233
    • Li, Q.L.1    Zhao, Y.Q.2
  • 44
    • 0019047765 scopus 로고
    • On evaluating the performability of degradable computing systems
    • J. Meyer, On evaluating the performability of degradable computing systems, IEEE Trans. Comput. 29 (1980) 720-731.
    • (1980) IEEE Trans. Comput. , vol.29 , pp. 720-731
    • Meyer, J.1
  • 46
    • 0009948677 scopus 로고    scopus 로고
    • Matrix-multiplicative approach to quasi-birth-and-death processes
    • eds. A.S. Alfa and S. Chakravarthy Marcel Dekker, New York
    • V. Naoumov, Matrix-multiplicative approach to quasi-birth-and-death processes, in: Matrix Analytic Methods in Stochastic Models, eds. A.S. Alfa and S. Chakravarthy (Marcel Dekker, New York, 1996) pp. 87-106.
    • (1996) Matrix Analytic Methods in Stochastic Models , pp. 87-106
    • Naoumov, V.1
  • 49
    • 85168062162 scopus 로고
    • Matrix-analytic methods in stochastic models
    • ed. J. Dhashalow (CRC Press, Boca Raton, FL)
    • M.F. Neuts, Matrix-analytic methods in stochastic models, in: Advances in Queueing: Theory, Methods and Open Problems, ed. J. Dhashalow (CRC Press, Boca Raton, FL, 1995) pp. 265-292.
    • (1995) Advances in Queueing: Theory, Methods and Open Problems , pp. 265-292
    • Neuts, M.F.1
  • 50
    • 0013915135 scopus 로고
    • On the homogeneous birth-and-death process and its integral
    • P.S. Puri, On the homogeneous birth-and-death process and its integral, Biometrika 53 (1966) 61-71.
    • (1966) Biometrika , vol.53 , pp. 61-71
    • Puri, P.S.1
  • 51
    • 84971152509 scopus 로고
    • Some further results on the homogeneous birth and death process and its integral
    • P.S. Puri, Some further results on the homogeneous birth and death process and its integral, Proc. Cambridge Philos. Soc. 64 (1968) 141-154.
    • (1968) Proc. Cambridge Philos. Soc. , vol.64 , pp. 141-154
    • Puri, P.S.1
  • 53
    • 0000167911 scopus 로고    scopus 로고
    • A tutorial overview of matrix analytic method: With some extensions & new results
    • eds. A.S. Alfa and S. Chakravarthy (Marcel Dekker, New York)
    • V. Ramaswami, A tutorial overview of matrix analytic method: with some extensions & new results, in: Matrix Analytic Methods in Stochastic Models, eds. A.S. Alfa and S. Chakravarthy (Marcel Dekker, New York, 1996) pp. 261-296.
    • (1996) Matrix Analytic Methods in Stochastic Models , pp. 261-296
    • Ramaswami, V.1
  • 54
    • 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, Stochastic Models 12 (1996) 143-164.
    • (1996) Stochastic Models , vol.12 , pp. 143-164
    • Ramaswami, V.1    Taylor, P.G.2
  • 55
    • 0040504171 scopus 로고
    • An alternative approach to the analysis of finite semi-Markov and related processes
    • U. Sumita and Y. Masuda, An alternative approach to the analysis of finite semi-Markov and related processes, Stochastic Models 3 (1987) 67-87.
    • (1987) Stochastic Models , vol.3 , pp. 67-87
    • Sumita, U.1    Masuda, Y.2
  • 56
    • 0023861174 scopus 로고
    • Perturbation analysis gives strongly consistent sensitivity estimates for the M/G/1 queue
    • R. Suri and M.A. Zazanis, Perturbation analysis gives strongly consistent sensitivity estimates for the M/G/1 queue, Managm. Sci. 34 (1988) 39-64.
    • (1988) Managm. Sci. , vol.34 , pp. 39-64
    • Suri, R.1    Zazanis, M.A.2
  • 57
    • 8144228238 scopus 로고
    • Probabilistic approach to computational algorithms for finding stationary distributions of Markov chains
    • M.I. Taksar and W.K. Grassmann, Probabilistic approach to computational algorithms for finding stationary distributions of Markov chains, J. Comput. Appl. Math. 36 (1991) 131-136.
    • (1991) J. Comput. Appl. Math. , vol.36 , pp. 131-136
    • Taksar, M.I.1    Grassmann, W.K.2
  • 58
    • 0038223730 scopus 로고    scopus 로고
    • Censoring technique in studying block-structured Markov chains
    • eds. G. Latouche and P.G. Taylor (Notable Publications, New York)
    • Y.Q. Zhao, Censoring technique in studying block-structured Markov chains, in: Advances in Algorithmic Methods for Stochastic Models, eds. G. Latouche and P.G. Taylor (Notable Publications, New York, 2000) pp. 417-433.
    • (2000) Advances in Algorithmic Methods for Stochastic Models , pp. 417-433
    • Zhao, Y.Q.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.