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Volumn 37, Issue 1, 2005, Pages 185-211

Generalized product-form stationary distributions for markov chains in random environments with queueing applications

Author keywords

Continuous time Markov chain; ESTA property; Partial balance; Potential; Product form stationary distribution; Queueing; Random environment; Resolvent

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; PROBABILITY; QUEUEING THEORY; RANDOM PROCESSES;

EID: 17744391300     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1113402405     Document Type: Article
Times cited : (33)

References (35)
  • 1
    • 0024700671 scopus 로고
    • Asymptotic analysis of some complex renewable systems operating in random environments
    • Anisimov, V. and Sztrik, J. (1989). Asymptotic analysis of some complex renewable systems operating in random environments. Europ. J. Operat. Res. 41, 162-168.
    • (1989) Europ. J. Operat. Res. , vol.41 , pp. 162-168
    • Anisimov, V.1    Sztrik, J.2
  • 2
    • 1642398216 scopus 로고
    • On determining absorption probabilities for Markov chains in random environments
    • Bourgin, R. D. and Cogburn, R. (1981). On determining absorption probabilities for Markov chains in random environments. Adv. Appl. Prob. 13, 369-387.
    • (1981) Adv. Appl. Prob. , vol.13 , pp. 369-387
    • Bourgin, R.D.1    Cogburn, R.2
  • 3
    • 0005643933 scopus 로고
    • Perturbation analysis of the M/M/1 queue in a Markovian environment via the matrix-geometric method
    • Chang, C.-S. and Nelson, R. (1993). Perturbation analysis of the M/M/1 queue in a Markovian environment via the matrix-geometric method. Commun. Statist. Stoch. Models 9, 233-246.
    • (1993) Commun. Statist. Stoch. Models , vol.9 , pp. 233-246
    • Chang, C.-S.1    Nelson, R.2
  • 6
    • 0039672847 scopus 로고
    • On the central limit theorem for Markov chains in random environments
    • Cogburn, R. ( 1991 ). On the central limit theorem for Markov chains in random environments. Ann. Prob. 19, 587-604.
    • (1991) Ann. Prob. , vol.19 , pp. 587-604
    • Cogburn, R.1
  • 7
    • 0019753308 scopus 로고
    • Birth and death processes with random environments in continuous time
    • Cogburn, R. and Torrez, W. C. (1981). Birth and death processes with random environments in continuous time. J. Appl. Prob. 18, 19-30.
    • (1981) J. Appl. Prob. , vol.18 , pp. 19-30
    • Cogburn, R.1    Torrez, W.C.2
  • 9
    • 0020179344 scopus 로고
    • The generalized MIG/k blocking system with heterogeneous servers
    • Fakinos, D. (1982). The generalized MIG/k blocking system with heterogeneous servers. J. Operat. Res. Soc. 33, 801-809.
    • (1982) J. Operat. Res. Soc. , vol.33 , pp. 801-809
    • Fakinos, D.1
  • 10
    • 0026398343 scopus 로고
    • Insensitivity of generalized semi-Markov processes evolving in a random environment
    • Fakinos, D. (1991). Insensitivity of generalized semi-Markov processes evolving in a random environment. J. Operat. Res. Soc. 42, 1111-1115.
    • (1991) J. Operat. Res. Soc. , vol.42 , pp. 1111-1115
    • Fakinos, D.1
  • 11
    • 0542421193 scopus 로고    scopus 로고
    • Overall station balance and decomposability for non-Markovian queueing networks
    • Fakinos, D. and Economou, A. (1998). Overall station balance and decomposability for non-Markovian queueing networks. Adv. Appl. Prob. 30 870-887.
    • (1998) Adv. Appl. Prob. , vol.30 , pp. 870-887
    • Fakinos, D.1    Economou, A.2
  • 12
    • 0030548240 scopus 로고    scopus 로고
    • A heterogeneous blocking system in a random environment
    • Falin, G. (1996). A heterogeneous blocking system in a random environment. J. Appl. Prob. 33, 211-216.
    • (1996) J. Appl. Prob. , vol.33 , pp. 211-216
    • Falin, G.1
  • 13
    • 0000021563 scopus 로고
    • Finite birth-and-death models in randomly changing environments
    • Gaver, D. P., Jacobs, P. A. and Latouche, G. (1984). Finite birth-and-death models in randomly changing environments. Adv. Appl. Prob. 16, 715-731.
    • (1984) Adv. Appl. Prob. , vol.16 , pp. 715-731
    • Gaver, D.P.1    Jacobs, P.A.2    Latouche, G.3
  • 14
    • 0011004332 scopus 로고
    • A bivariate random environmental stress model
    • Gupta, P. L. and Gupta, R. D. (1990). A bivariate random environmental stress model. Adv. Appl. Prob. 22, 501-503.
    • (1990) Adv. Appl. Prob. , vol.22 , pp. 501-503
    • Gupta, P.L.1    Gupta, R.D.2
  • 15
    • 0001363966 scopus 로고
    • On the limiting distribution of a supercritical branching process in a random environment
    • Hambly, B. (1992). On the limiting distribution of a supercritical branching process in a random environment. J. Appl. Prob. 29 499-518.
    • (1992) J. Appl. Prob. , vol.29 , pp. 499-518
    • Hambly, B.1
  • 16
    • 0021493856 scopus 로고
    • Optimal control of arrivals to multiserver queues in a random environment
    • Helm, W. E. and Waldmann, K.-H. (1984). Optimal control of arrivals to multiserver queues in a random environment. J. Appl. Prob. 21 602-615.
    • (1984) J. Appl. Prob. , vol.21 , pp. 602-615
    • Helm, W.E.1    Waldmann, K.-H.2
  • 19
    • 0001412392 scopus 로고
    • On the association of the lifelengths of components subjected to a stochastic environment
    • Lefèvre, C. and Milhaud, X. (1990). On the association of the lifelengths of components subjected to a stochastic environment. Adv. Appl. Prob. 22, 961-964.
    • (1990) Adv. Appl. Prob. , vol.22 , pp. 961-964
    • Lefèvre, C.1    Milhaud, X.2
  • 20
    • 85168064716 scopus 로고
    • The ASTA property
    • (Prob. Stoch. Ser.), ed. J. H. Dshalalow, CRC, Boca Raton, FL
    • Melamed, B. and Yao, D. D. (1995). The ASTA property. In Advances in Queueing(Prob. Stoch. Ser.), ed. J. H. Dshalalow, CRC, Boca Raton, FL, pp. 195-224.
    • (1995) Advances in Queueing , pp. 195-224
    • Melamed, B.1    Yao, D.D.2
  • 21
    • 0000842078 scopus 로고
    • Spectral expansion solution for a class of Markov models: Application and comparison with the matrix-geometric method
    • Mitrani, I. and Chakka, R. (1995). Spectral expansion solution for a class of Markov models: application and comparison with the matrix-geometric method. Perf. Eval. 23, 241-260.
    • (1995) Perf. Eval. , vol.23 , pp. 241-260
    • Mitrani, I.1    Chakka, R.2
  • 22
    • 0003636743 scopus 로고
    • Matrix-Geometric Solutions in Stochastic Models. An Algorithmic Approach
    • Johns Hopkins University Press, Baltimore, MD
    • Neuts, M. F. (1981). Matrix-Geometric Solutions in Stochastic Models. An Algorithmic Approach (Johns Hopkins Ser. Math. Sci. 2). Johns Hopkins University Press, Baltimore, MD.
    • (1981) Johns Hopkins Ser. Math. Sci. , vol.2
    • Neuts, M.F.1
  • 23
    • 0003781238 scopus 로고    scopus 로고
    • Cambridge University Press
    • Norris, J. R. (1997). Markov Chains. Cambridge University Press.
    • (1997) Markov Chains
    • Norris, J.R.1
  • 24
    • 17744381324 scopus 로고    scopus 로고
    • Steady-state analysis of a queue with varying service rate
    • Res. Rep. PNA-R9712, CWI
    • Núñez-Queija, R. (1997). Steady-state analysis of a queue with varying service rate. Res. Rep. PNA-R9712, CWI.
    • (1997)
    • Núñez-Queija, R.1
  • 25
    • 0022680814 scopus 로고
    • The M/M/∞ queue in a random environment
    • O'cinneide, C. A. and Purdue, P. (1986). The M/M/∞ queue in a random environment. J. Appl. Prob. 23, 175-184.
    • (1986) J. Appl. Prob. , vol.23 , pp. 175-184
    • O'Cinneide, C.A.1    Purdue, P.2
  • 26
    • 0007107476 scopus 로고
    • Optimal R & D programs in a random environment
    • Posner, M. J. M. and Zuckerman, D. (1990). Optimal R & D programs in a random environment. J. Appl. Prob. 27, 343-350.
    • (1990) J. Appl. Prob. , vol.27 , pp. 343-350
    • Posner, M.J.M.1    Zuckerman, D.2
  • 28
    • 85168070637 scopus 로고
    • Sample-path techniques in queueing theory
    • (Prob. Stoch. Ser.), ed. J. H. Dshalalow, CRC, Boca Raton, FL
    • Stidham, S., Jr. and El-Taha, M. (1995). Sample-path techniques in queueing theory. In Advances in Queueing (Prob. Stoch. Ser.), ed. J. H. Dshalalow, CRC, Boca Raton, FL, pp. 119-166.
    • (1995) Advances in Queueing , pp. 119-166
    • Stidham Jr., S.1    El-Taha, M.2
  • 29
    • 0023146997 scopus 로고
    • On the heterogeneous M/G/n blocking system in a random environment
    • Sztrik, J. (1987). On the heterogeneous M/G/n blocking system in a random environment. J. Operat. Res. Soc. 38, 57-63.
    • (1987) J. Operat. Res. Soc. , vol.38 , pp. 57-63
    • Sztrik, J.1
  • 30
    • 0036432667 scopus 로고    scopus 로고
    • A product theorem for Markov chains with application to PF-queueing networks
    • Tsitsiashvili, G. Sh., Osipova, M. A., Koliev, N. V. and Baum, D. (2002). A product theorem for Markov chains with application to PF-queueing networks. Ann. Operat. Res. 113, 141-154.
    • (2002) Ann. Operat. Res. , vol.113 , pp. 141-154
    • Tsitsiashvili, G.Sh.1    Osipova, M.A.2    Koliev, N.V.3    Baum, D.4
  • 31
    • 0007137107 scopus 로고    scopus 로고
    • Spectral representation of four finite birth and death processes
    • Van Assche, W., Parthasar Athy, P. R. and Lenin, R. B. (1999). Spectral representation of four finite birth and death processes. Math. Scientist 24, 105-112.
    • (1999) Math. Scientist , vol.24 , pp. 105-112
    • Van Assche, W.1    Parthasarathy, P.R.2    Lenin, R.B.3
  • 33
    • 21844496981 scopus 로고
    • Decomposability in queues with background states
    • Yamazaki, G. and Miyazawa, M. (1995). Decomposability in queues with background states. Queueing Systems 20, 453-469.
    • (1995) Queueing Systems , vol.20 , pp. 453-469
    • Yamazaki, G.1    Miyazawa, M.2
  • 34
    • 0141556476 scopus 로고
    • A Markov-modulated M/M/1 queue with group arrivals
    • Zhu, Y. (1991). A Markov-modulated M/M/1 queue with group arrivals. Queueing Systems 8, 255-263.
    • (1991) Queueing Systems , vol.8 , pp. 255-263
    • Zhu, Y.1
  • 35
    • 38149146084 scopus 로고
    • Markovian queueing networks in a random environment
    • Zhu, Y. (1994). Markovian queueing networks in a random environment. Operat. Res. Lett. 15, 11-17.
    • (1994) Operat. Res. Lett. , vol.15 , pp. 11-17
    • Zhu, Y.1


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