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Volumn 51, Issue 1, 1999, Pages 71-97

Non-parametric estimation for the M/G/∞ queue

Author keywords

Empirical process; Infinite dimensional delta method; Infinite server queue; Little's formula; Reynolds' formula

Indexed keywords


EID: 6544263867     PISSN: 00203157     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1003831118254     Document Type: Article
Times cited : (59)

References (55)
  • 4
    • 0003553276 scopus 로고
    • with Special Reference to Methods and Applications, Cambridge University Press, Cambridge (1st ed. 1955, 2nd ed. 1966, 3rd ed. 1978)
    • Bartlett, M. S. (1955/78). An Introduction to Stochastic Processes, with Special Reference to Methods and Applications, Cambridge University Press, Cambridge (1st ed. 1955, 2nd ed. 1966, 3rd ed. 1978).
    • (1955) An Introduction to Stochastic Processes
    • Bartlett, M.S.1
  • 5
    • 0041879125 scopus 로고
    • Fluctuations of telephone traffic
    • Beneš, V. E. (1957). Fluctuations of telephone traffic, Bell System Technical Journal, 36, 965-973.
    • (1957) Bell System Technical Journal , vol.36 , pp. 965-973
    • Beneš, V.E.1
  • 9
    • 9844260058 scopus 로고    scopus 로고
    • Estimating diffusion coefficients for count data: Einstein-Smoluchowski theory revisited
    • Bingham, N. H. and Dunham, B. (1997). Estimating diffusion coefficients for count data: Einstein-Smoluchowski theory revisited. Ann. Inst. Statist. Math., 49, 667-679.
    • (1997) Ann. Inst. Statist. Math. , vol.49 , pp. 667-679
    • Bingham, N.H.1    Dunham, B.2
  • 10
    • 0041879123 scopus 로고
    • An M/G/∞ estimation problem
    • Brown, M. (1970). An M/G/∞ estimation problem, Ann. Math. Statist., 41, 651-654.
    • (1970) Ann. Math. Statist. , vol.41 , pp. 651-654
    • Brown, M.1
  • 11
    • 0039712694 scopus 로고    scopus 로고
    • Mean residual life processes
    • Csörgo, M. and Zitikis, R. (1996). Mean residual life processes, Ann. Statist., 24, 1717-1739.
    • (1996) Ann. Statist. , vol.24 , pp. 1717-1739
    • Csörgo, M.1    Zitikis, R.2
  • 13
    • 0000168421 scopus 로고
    • Mean exit times for particles driven by weakly coloured noise
    • Doering, C. R., Hagan, P. S. and Levermore, C. D. (1989a). Mean exit times for particles driven by weakly coloured noise, SIAM J. Appl. Math., 49, 1480-1513.
    • (1989) SIAM J. Appl. Math. , vol.49 , pp. 1480-1513
    • Doering, C.R.1    Hagan, P.S.2    Levermore, C.D.3
  • 14
    • 0039041411 scopus 로고
    • The distribution of exit times for weakly coloured noise
    • Doering, C. R., Hagan, P. S. and Levermore, C. D. (1989b). The distribution of exit times for weakly coloured noise, J. Statist. Phys., 54, 1321-1351.
    • (1989) J. Statist. Phys. , vol.54 , pp. 1321-1351
    • Doering, C.R.1    Hagan, P.S.2    Levermore, C.D.3
  • 16
    • 0003512677 scopus 로고
    • Oxford University Press, Oxford
    • Genstat 5 Committee (1993). Genstat 5 Release 3 Reference Manual, Oxford University Press, Oxford.
    • (1993) Genstat 5 Release 3 Reference Manual
  • 17
    • 0002610193 scopus 로고
    • Non- and semi-parametric maximum likelihood estimators and the von Mises method, I
    • Gill, R. D. (1989). Non- and semi-parametric maximum likelihood estimators and the von Mises method, I, Scand. J. Statist., 16, 97-128.
    • (1989) Scand. J. Statist. , vol.16 , pp. 97-128
    • Gill, R.D.1
  • 18
    • 0001387881 scopus 로고
    • Non- and semi-parametric maximum likelihood estimators and the von Mises method, II
    • Gill, R. D. and van der Vaart, A. W. (1993). Non- and semi-parametric maximum likelihood estimators and the von Mises method, II, Scand. J. Statist, 20, 271-288.
    • (1993) Scand. J. Statist , vol.20 , pp. 271-288
    • Gill, R.D.1    Van Der Vaart, A.W.2
  • 20
    • 0000519697 scopus 로고
    • Ordinary central limit theorem and weak law of large numbers versions of L = λW
    • Glynn, P. W. and Whitt, W. (1988). Ordinary central limit theorem and weak law of large numbers versions of L = λW, Math. Oper. Res., 13, 674-692.
    • (1988) Math. Oper. Res. , vol.13 , pp. 674-692
    • Glynn, P.W.1    Whitt, W.2
  • 21
    • 0024481132 scopus 로고
    • Indirect estimation via L = λW
    • Glynn, P. W. and Whitt, W. (1989). Indirect estimation via L = λW, Oper. Res., 37, 82-103.
    • (1989) Oper. Res. , vol.37 , pp. 82-103
    • Glynn, P.W.1    Whitt, W.2
  • 22
  • 23
    • 0009232019 scopus 로고
    • Stochastic models as functionals: Some remarks on the renewal case
    • Grübel, R. (1989). Stochastic models as functionals: some remarks on the renewal case, J. Appl. Probab., 26, 296-303.
    • (1989) J. Appl. Probab. , vol.26 , pp. 296-303
    • Grübel, R.1
  • 24
    • 0000815682 scopus 로고
    • A functional approach to the stationary waiting time and idle period distributions of the GI/G/1 queue
    • Grübel, R. and Pitts, S. M. (1992). A functional approach to the stationary waiting time and idle period distributions of the GI/G/1 queue, Ann. Probab., 20, 1754-1778.
    • (1992) Ann. Probab. , vol.20 , pp. 1754-1778
    • Grübel, R.1    Pitts, S.M.2
  • 25
    • 21344497262 scopus 로고
    • Non-parametric estimation in renewal theory, I: The empirical renewal function
    • Grübel, R. and Pitts, S. M. (1993). Non-parametric estimation in renewal theory, I: the empirical renewal function, Ann. Statist., 21, 1431-1451.
    • (1993) Ann. Statist. , vol.21 , pp. 1431-1451
    • Grübel, R.1    Pitts, S.M.2
  • 29
    • 0000301129 scopus 로고
    • The asymptotic distribution of serial covariances
    • Hannan, E. J. (1976). The asymptotic distribution of serial covariances, Ann. Statist., 4, 396-399.
    • (1976) Ann. Statist. , vol.4 , pp. 396-399
    • Hannan, E.J.1
  • 30
    • 0000000991 scopus 로고
    • On limit theorems for quadratic functions of discrete time series
    • Hannan, E. J. and Heyde, C. C. (1972). On limit theorems for quadratic functions of discrete time series, Ann. Math. Statist., 43, 2058-2066.
    • (1972) Ann. Math. Statist. , vol.43 , pp. 2058-2066
    • Hannan, E.J.1    Heyde, C.C.2
  • 31
    • 84985534965 scopus 로고
    • The convergence of autocorrelations and autoregressions
    • Hannan, E. J. and Kavalieris, L. (1983). The convergence of autocorrelations and autoregressions, Austral. J. Statist., 25, 287-297.
    • (1983) Austral. J. Statist. , vol.25 , pp. 287-297
    • Hannan, E.J.1    Kavalieris, L.2
  • 32
    • 0040087948 scopus 로고
    • The one-sided barrier problem for an integrated Ornstein-Uhlenbeck process
    • Hesse, C. H. (1991). The one-sided barrier problem for an integrated Ornstein-Uhlenbeck process, Comm. Statist. Stochastic Models, 7, 447-480.
    • (1991) Comm. Statist. Stochastic Models , vol.7 , pp. 447-480
    • Hesse, C.H.1
  • 34
    • 0005386113 scopus 로고
    • Convergence rates in the strong law of large numbers for random variables taking values in Banach spaces
    • Lai, T. L. (1974). Convergence rates in the strong law of large numbers for random variables taking values in Banach spaces, Bull. Inst. Math. Acad. Sinica, 2, 67-85.
    • (1974) Bull. Inst. Math. Acad. Sinica , vol.2 , pp. 67-85
    • Lai, T.L.1
  • 35
    • 0041879124 scopus 로고
    • The estimation of velocity distributions from counts
    • Amsterdam, North-Holland, Amsterdam
    • Lindley, D. V. (1956). The estimation of velocity distributions from counts, Proceedings of the. International Congress of Mathematicians (Amsterdam, 1954) III, 427-444, North-Holland, Amsterdam.
    • (1954) Proceedings of The. International Congress of Mathematicians , vol.3 , pp. 427-444
    • Lindley, D.V.1
  • 36
    • 0042380349 scopus 로고
    • Identifiability for random translates of Poisson processes
    • Milne, R. K. (1970). Identifiability for random translates of Poisson processes, Zeit. Wahrscheinlichkeitsth., 15, 195-201.
    • (1970) Zeit. Wahrscheinlichkeitsth. , vol.15 , pp. 195-201
    • Milne, R.K.1
  • 37
    • 0023981190 scopus 로고
    • Estimating average production intervals using inventory measurements: Little's law for partially observable processes
    • Nozari, A. and Whitt, W. (1988). Estimating average production intervals using inventory measurements: Little's law for partially observable processes, Oper. Res., 36, 308-323.
    • (1988) Oper. Res. , vol.36 , pp. 308-323
    • Nozari, A.1    Whitt, W.2
  • 38
    • 0001455171 scopus 로고
    • On the weak convergence of empirical processes in sup-norm metrics
    • O'Reilly, N. E. (1974). On the weak convergence of empirical processes in sup-norm metrics, Ann. Probab., 2, 642-651.
    • (1974) Ann. Probab. , vol.2 , pp. 642-651
    • O'Reilly, N.E.1
  • 39
    • 0041378387 scopus 로고    scopus 로고
    • Estimation for an M/G/∞ queue with incomplete information
    • Pickands, J. and Stine, R. A. (1997). Estimation for an M/G/∞ queue with incomplete information, Biometrika, 84, 295-308.
    • (1997) Biometrika , vol.84 , pp. 295-308
    • Pickands, J.1    Stine, R.A.2
  • 40
    • 21844500175 scopus 로고
    • Nonparametric estimation of the stationary waiting-time distribution for the GI/G/1 queue
    • Pitts, S. M. (1994a). Nonparametric estimation of the stationary waiting-time distribution for the GI/G/1 queue, Ann. Statist., 22, 1428-1446.
    • (1994) Ann. Statist. , vol.22 , pp. 1428-1446
    • Pitts, S.M.1
  • 41
    • 0040671482 scopus 로고
    • Nonparametric estimation of compound distributions with applications in insurance
    • Pitts, S. M. (1994b). Nonparametric estimation of compound distributions with applications in insurance, Ann. Inst. Statist. Math., 46, 537-555.
    • (1994) Ann. Inst. Statist. Math. , vol.46 , pp. 537-555
    • Pitts, S.M.1
  • 43
    • 0001791777 scopus 로고
    • On interchanging limits and integrals
    • Pratt, J. W. (1960). On interchanging limits and integrals, Ann. Math. Statist., 31, 74-77.
    • (1960) Ann. Math. Statist. , vol.31 , pp. 74-77
    • Pratt, J.W.1
  • 45
    • 0042881329 scopus 로고
    • On the autocorrelation and spectral functions of queues
    • Reynolds, J. F. (1968). On the autocorrelation and spectral functions of queues, J. Appl. Probab., 5, 467-475.
    • (1968) J. Appl. Probab. , vol.5 , pp. 467-475
    • Reynolds, J.F.1
  • 46
    • 0041378388 scopus 로고
    • On linearly regressive processes
    • Reynolds, J. F. (1972). On linearly regressive processes, J. Appl. Probab., 9, 208-213.
    • (1972) J. Appl. Probab. , vol.9 , pp. 208-213
    • Reynolds, J.F.1
  • 47
    • 0016518527 scopus 로고
    • The covariance structure of queues and related processes: A survey of recent work
    • Reynolds, J. F. (1975). The covariance structure of queues and related processes: a survey of recent work, Advances in Applied Probability, 7, 383-415.
    • (1975) Advances in Applied Probability , vol.7 , pp. 383-415
    • Reynolds, J.F.1
  • 48
    • 0003588680 scopus 로고
    • Telephone traffic time averages
    • Riordan, J. (1951). Telephone traffic time averages, Bell System Technical Journal, 30, 1129-1144.
    • (1951) Bell System Technical Journal , vol.30 , pp. 1129-1144
    • Riordan, J.1
  • 50
    • 0007672310 scopus 로고
    • Insensitivity of steady-state distributions of generalized semi-Markov processes with speeds
    • Schassberger, R. (1978). Insensitivity of steady-state distributions of generalized semi-Markov processes with speeds, Advances in Applied Probability, 10, 836-851.
    • (1978) Advances in Applied Probability , vol.10 , pp. 836-851
    • Schassberger, R.1
  • 52
    • 0040756634 scopus 로고
    • On Erlang's formula
    • Takács, L. (1969). On Erlang's formula, Ann. Math. Statist., 40, 71-78.
    • (1969) Ann. Math. Statist. , vol.40 , pp. 71-78
    • Takács, L.1
  • 54
    • 0001978453 scopus 로고
    • Some applications of probability generating functionals to the study of input-output streams
    • Vere-Jones, D. (1968). Some applications of probability generating functionals to the study of input-output streams, J. Roy. Statist. Soc. Ser. B, 30, 321-333.
    • (1968) J. Roy. Statist. Soc. Ser. B , vol.30 , pp. 321-333
    • Vere-Jones, D.1
  • 55
    • 0000746017 scopus 로고
    • A review of L = λW and extensions
    • Correction: ibid. (1992). 12, 431-432
    • Whitt, W. (1991). A review of L = λW and extensions, Queueing Systems Theory Appl., 9, 235-268 (Correction: ibid. (1992). 12, 431-432).
    • (1991) Queueing Systems Theory Appl. , vol.9 , pp. 235-268
    • Whitt, W.1


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