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On the rate of convergence of waiting times

Published online by Cambridge University Press:  09 April 2009

C. K. Cheong  and
C. R. Heathcote
C. K. Cheong
Affiliation:
The Australian National University
C. R. Heathcote
Affiliation:
The Australian National University
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Let K(y) be a known distribution function on (−∞, ∞) and let {Fn(y), n = 0, 1,…} be a sequence of unknown distribution functions related by subject to the initial condition If the sequence {Fn(y)} converges to a distribution function F(y) then F(y) satisfies the Wiener-Hopf equation

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 5 , Issue 3 , August 1965 , pp. 365 - 373
Copyright
Copyright © Australian Mathematical Society 1965

References

[1]Belyaev, Ya. K., and Maksimov, V. M., Analytical properties of a generating function for thenumber of renewals, Theory of Probability (SIAM Translation), 8 (1963), 102–104.Google Scholar
[2]Feller, W., An introduction to Probability theory and its applications, Vol. I (2nd ed.), Wiley, New York (1957).Google Scholar
[3]Finch, P. D., On the busy period in the queueing system GI/G/t, J. Austral. Math. Soc., 2 (1961), 217–228.CrossRefGoogle Scholar
[4]Heathcote, C. R., Divergent single server queues. To appear in Proceedings of the Symposium on Congestion Theory, 08, 1964, University of North Carolina Press.Google Scholar
[5]Heyde, C. C., Two probability theorems and their application to some first passage problems, J. Austral. Math. Soc., 4 (1964), 214–222.Google Scholar
[6]Kingman, J. F. C., On queues in heavy traffic, J. Roy. Stat, Soc. (B), 24 (1962), 383–392.Google Scholar
[7]Lindley, D. V., Theory of queues with a single server, Proc. Camb. Phil. Soc., 48 (1952), 277–289.Google Scholar
[8]Smith, W. L., Renewal Theory and its ramifications, J. Roy. Stat. Soc. (B), 20 (1958) 243–302.Google Scholar
[9]Spitzer, F., The Wiener-Hopf equation whose kernel is a probability density, Duke Math. J., Vol. 24 (1957) 327–344.Google Scholar
[10]Takács, L., Introduction to the theory of queues, Oxford University Press, New York (1962).Google Scholar