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Volumn 38, Issue 3, 2001, Pages 696-706

On the convergence to stationarity of birth-death processes

Author keywords

Birth death process; Speed of convergence

Indexed keywords


EID: 0035438327     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1005091033     Document Type: Article
Times cited : (12)

References (13)
  • 1
    • 0007301683 scopus 로고
    • Relaxation times for queueing systems
    • eds J. W. de Bakker, M. Hazewinkel and J. K. Lenstra. North-Holland, Amsterdam
    • BLANC, J. P. C. AND VAN DOORN, E. A. (1986). Relaxation times for queueing systems. In Mathematics and Computer Sci., eds J. W. de Bakker, M. Hazewinkel and J. K. Lenstra. North-Holland, Amsterdam, pp. 139-162.
    • (1986) Mathematics and Computer Sci. , pp. 139-162
    • Blanc, J.P.C.1    Van Doorn, E.A.2
  • 4
    • 0002239303 scopus 로고
    • On the convergence of moments in stationary Markov chains
    • HOLEWIJN, P. J. AND HORDIJK, A. (1975). On the convergence of moments in stationary Markov chains. Stoch. Proc. Appl. 3, 55-64.
    • (1975) Stoch. Proc. Appl. , vol.3 , pp. 55-64
    • Holewijn, P.J.1    Hordijk, A.2
  • 5
    • 0000036102 scopus 로고
    • The differential equations of birth-and-death processes, and the Stieltjes moment problem
    • KARLIN, S. AND MCGREGOR, J. L. (1957). The differential equations of birth-and-death processes, and the Stieltjes moment problem. Trans. Amer. Math. Soc. 85, 589-646.
    • (1957) Trans. Amer. Math. Soc. , vol.85 , pp. 589-646
    • Karlin, S.1    McGregor, J.L.2
  • 6
    • 84968465028 scopus 로고
    • The classification of birth and death processes
    • KARLIN, S. AND MCGREGOR, J. L. (1957). The classification of birth and death processes. Trans. Amer. Math. Soc. 86, 366-400.
    • (1957) Trans. Amer. Math. Soc. , vol.86 , pp. 366-400
    • Karlin, S.1    McGregor, J.L.2
  • 8
    • 0007297782 scopus 로고
    • Log-concavity and log-convexity in passage time densities of diffusion and birth-death processes
    • KEILSON, J. (1971). Log-concavity and log-convexity in passage time densities of diffusion and birth-death processes. J. Appl. Prob. 8, 391-398.
    • (1971) J. Appl. Prob. , vol.8 , pp. 391-398
    • Keilson, J.1
  • 10
    • 0033147981 scopus 로고    scopus 로고
    • On the convergence to stationarity of the many-server poisson queue
    • STADJE, W. AND PARTHASARATHY, P. R. (1999). On the convergence to stationarity of the many-server Poisson queue. J. Appl. Prob. 36, 546-557.
    • (1999) J. Appl. Prob. , vol.36 , pp. 546-557
    • Stadje, W.1    Parthasarathy, P.R.2
  • 11
    • 0019576911 scopus 로고
    • The transient state probabilities for a queueing model where potential customers are discouraged by queue length
    • VAN DOORN, E. A. (1981). The transient state probabilities for a queueing model where potential customers are discouraged by queue length. J. Appl. Prob. 18, 499-506.
    • (1981) J. Appl. Prob. , vol.18 , pp. 499-506
    • Van Doorn, E.A.1
  • 12
    • 0000783136 scopus 로고
    • Conditions for exponential ergodicity and bounds for the decay parameter of a birth-death process
    • VAN DOORN, E. A. (1985). Conditions for exponential ergodicity and bounds for the decay parameter of a birth-death process. Adv. Appl. Prob. 17, 514-530.
    • (1985) Adv. Appl. Prob. , vol.17 , pp. 514-530
    • Van Doorn, E.A.1
  • 13
    • 0000552628 scopus 로고
    • Asymptotic formulas for Markov processes with applications to simulation
    • WHITT, W. (1992). Asymptotic formulas for Markov processes with applications to simulation. Operat. Res. 40, 279-291.
    • (1992) Operat. Res. , vol.40 , pp. 279-291
    • Whitt, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.