Date of Award
Mathematics and Statistics
CC BY-NC-ND 4.0
In this thesis, we discuss a probabilistic interpretation of the Laplace transform of probability density functions (p.d.f.) for waiting times in queues. We interpret the Laplace transform of a p.d.f. as the probability that the corresponding random variable wins a race against (i.e., is less than) an exponential random variable. This interpretation is used to compute Laplace transforms of some p.d.f.'s, interpret some properties of the Laplace transform and prove some results for M/G/1 queues. In addition, we explore probabilistic interpretations of the z-transform (probability generating function) and its relationship to the Laplace transform.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1997 .R69. Source: Masters Abstracts International, Volume: 37-02, page: 0626. Advisers: Myron Hlynka; Richard Caron. Thesis (M.S.)--University of Windsor (Canada), 1997.
Roy, Kirk Andrew., "Laplace transforms, probabilities and queues." (1997). Electronic Theses and Dissertations. 2572.