References
I.V. Basawa and B.L.S. Prakasa Rao,Statistical Inference for Stochastic Processes (Academic Press, London, 1980).
U.N. Bhat, Imbedded Markov chain analysis of bulk queues,J. Austral. Math. Soc. 4 (1964) 244–263.
P. Brémaud,Point Processes and Queues: Martingale Dynamics (Springer-Verlag, New York, 1980).
E. Çinlar, Theory of continuous storage with Markov additive inputs and a general release rule,J. Math. Anal. Appl. 43 (1973) 207–231.
P. Franken, D. König, U. Arndt and V. Schmidt,Queues and Point Processes (Akademie-Verlag, Berlin, 1981).
J. Gani and N.U. Prabhu, A storage model with continuous infinitely divisible inputs,Proc. Comb. Phil. Soc. 59 (1963) 417–429.
H.M. Goldberg, Analysis of the earliest due data scheduling rule in queueing systems,Math. Operat. Res. 2 (1977) 145–154.
J.A. Hooke and N.U. Prabhu, Priority queues in heavy traffic,Opsearch 8 (1971) 1–9.
M. Kac, Random walk and the theory of Brownian motion,Amer. Math. Monthly 54 (1947) 369–417.
H. Kaspi, On the symmetric Wiener-Hopf factorization for Markov additive processes,Z. Wahrscheinlichkeitsth. 59 (1980) 179–196.
F.P. Kelly,Reversibility and Stochastic Networks (Wiley, New York, 1979).
D.G. Kendall, Some problems in the theory of queues,J.R. Statist. Soc. B13 (1951) 151–185.
D.G. Kendall, Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain,Ann. Math. Statist. 24 (1954) 338–354.
M.G. Kendall,The Advanced Theory of Statistics, Vol. 1 (Griffin, London, 1943).
D.V. Lindley, Theory of queues with a single server,Proc. Camb. Phil. Soc. 49 (1952) 277–289.
E.H. Lloyd, Reservoirs with serially correlated inputs,Technometrics 5 (1963) 85–93.
P.A.P. Moran, A probability theory of dams and storage systems,Austral. J. Appl. Sci. 5 (1954) 116–124.
J. Neyman, Indeterminism in science and new demands on statisticians,J. Amer. Statist. Assoc. 55 (1960) 625–639.
N.U. Prabhu, Some results for the queue with Poisson arrivals,J.R. Statist. Soc. 22 (1960) 104–107.
N.U. Prabhu, On the ruin problem of collective risk theory,Ann. Math. Statist. 32 (1961) 757–764.
N.U. Prabhu,Queues and Inventories: A Study of Their Basic Stochastic Processes (Wiley, New York, 1965).
N.U. Prabhu,Stochastic Processes: Basic Theory and Its Applications (Macmillan, New York, 1965).
N.U. Prabhu, Wiener-Hopf factorization for convolution semigroups,Z. Wahrscheinlichkeitsth. 23 (1972) 103–113.
N.U. Prabhu,Stochastic Storage Processes: Queues, Insurance Risk and Dams (Springer-Verlag, New York, 1980).
N.U. Prabhu, Conferences on stochastic processes and their applications: a brief history,Stock Proc. Appl. 12 (1982) 115–116.
N.U. Prabhu,Stochastic Processes and their Applications. Encyclopedia of Statistical Sciences 8 (1986).
N.U. Prabhu, Wiener-Hopf factorization of Markov semigroups-I. The countable state space case,Proc. 7th Conf. Probability Theory, ed. M. Iosifescu (VNU Science Press, Utrecht, 1985) 315–324.
E. Reich, On the integro-differential equation of Takács I,Ann. Math. Statist. 29 (1958) 563–570.
E. Reich, On the integro-differential equation of Takács II.Ann. Math. Statist. 30 (1959) 143–148.
M. Rubinovitch, Ladder phenomena in stochastic processes with stationary independent increments,Z. Wahrscheinlichkeitsth. 20 (1971) 58–74.
L.W. Smith, On the distribution of queueing times,Proc. Camb. Phil. Soc. 49 (1953) 449–461.
F. Spitzer, The Wiener-Hopf equation whose kernel is a probability density,Duke Math. J. 24 (1957) 327–344.
F. Spitzer, The Wiener-Hopf equation whose kernel is a probability density,Duke Math. J. 27 (1960) 363–372.
D. Stoyan,Comparison Methods for Queues and Other Stochastic Models, English trans., ed. by D.J. Daley (Wiley, New York, 1983).
L. Takács, Investigation of waiting time problems by reduction to Markov processes,Acta Math. (Budapest) 6 (1955) 101–129.
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This article is reproduced from pages 127–138 inThe Craft of Probabilistic Modelling, A Collection of Personal Accounts, ed. J. Gani, published by Springer-Verlag, 1986, ISBN 0-387-96277-8.
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Prabhu, N.U. Probability modelling across the continents. Queueing Syst 24, 7–18 (1996). https://doi.org/10.1007/BF01149076
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DOI: https://doi.org/10.1007/BF01149076