Computing the Distribution Function of the Number of Renewals

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References

[1] D. R. Cox, “Renewal Theory,” John Wiley & Sons Inc., New York, 1962.

[2] W. Feller, “Probability Theory and Its Applications Vol. II,” Wiley, New York, 1966.

[3] W. Feller, “An Introduction to Probability Theory and Its Applications,” Wiley, New York, 1967.

[4] L. A. Baxter, E. M. Scheuer, D. J. McConalogue and W. R. Blischke, “On the Tabulation of the Renewal Functions,” Technometrics, Vol. 24, No. 2, 1982, pp. 151-156. doi:10.1080/00401706.1982.10487739

[5] M. L. Chaudhry, “On Computations of the Mean and Variance of the Number of Renewals: A United Approach,” The Journal of the Operations Research Society, Vol. 46, 1995, pp. 1352-1364.

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[7] J. Abate, G. L. Choudhury and W. Whitt, “An Introduction to Numerical Transform Inversion and Its Application to Probability Models,” In: W. Grassman, Ed., Computational Probability, Kluwer, Boston, 1999, pp. 257323.

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[9] J. Abate and W. Whitt, “The Fourier-Series Method for Inverting Transforms of Probability Distributions,” Queueing Systems, Vol. 10, No. 1-2, 1992, pp. 5-88.
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[10] D. R. Cox and W. L. Smith, “Queues,” Methuen and CO Ltd., London, 1967.

[11] L. Kleinrock, “Queueing Systems Volume I: Theory,” John Wilery & Sons, New York, 1975, pp. 212-312.

[12] M. L. Chaudhry and J. G. C. Templeton, “A First Course on Bulk Queues,” John Wiley & Sons Inc., New York, 1983.

[13] G. A. Baker and P. Graves-Morris Jr., “Padé Approximants (Encyclopedia of Mathematics and Its Applications),” 2nd Edition, Cambridge University Press, Cambridge, 1996.

[14] C. M. Harris and W. G. Marchal, “Distribution Estimation Using Laplace Transform,” INFORMS Journal on Computing, Vol. 10, No. 4, 1998, pp. 448-458.
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[15] E. Parzen, “Stochastic Processes,” Holden-Day Inc., San Francisco, 1962.

[16] M. L. Chaudhry and B. Fisher, “Simple and Elegantderivations for Some Asymptotic Results in the DiscreteTime Renewal Process,” Statistics and Probability Letters, Vol. 83, No. 1, 2012, pp. 408-421.

[17] M. Bladt, “Computational Method in Applied Probability,” Aalborg University, 1993.