In this thesis, we present several methods which may be used to calculate the Laplace transform of order statistics of Erlang random variables. These methods are based on a probabilistic interpretation of the Laplace transform. A Markov chain analysis is included. Special cases and generalizations are discussed. Source: Masters Abstracts International, Volume: 39-02, page: 0522. Advisers: Myron Hlynka; Percy Brill. Thesis (M.Sc.)--University of Windsor (Canada), 1999