Laplace transforms, probabilities and queues.

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.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Masters

Discipline thesis:degree_discipline

Mathematics and Statistics

Grantor

University of Windsor

Year dc:date.issued

1997

Author dc:creator

• Roy, Kirk Andrew.

Advisor dc:contributor.advisor

• Hlynka, M.

Licence

• http://creativecommons.org/licenses/by-nc-nd/4.0/

Language dc:language.iso

en_CA

Handle dc:identifier.uri

https://hdl.handle.net/20.500.14776/3768

OAI identifier oai:identifier

oai:uwindsor.scholaris.ca:20.500.14776/3768