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Computing the Distribution Function of the Number of Renewals
Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Canada
Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Canada
Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Canada
- 1 Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Canada
- 2 Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Canada
- 3 Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Canada
American Journal of Operations Research·Volume 03 (2013)·Pages 380–386·Published 23 May 2013·DOI10.4236/ajor.2013.33035
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Abstract
The method of Laplace transforms is used to find the distribution function, mean, and variance of the number of renewals of a renewal process whose inter-arrival time distribution has a rational Laplace transform. Where the Laplace transform is not rational, we use the Padé approximation method. We apply our method to certain examples and the results are compared to those reported by other researchers.
KeywordsNumber of RenewalsRational ApproximationPadé
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