In this chapter a series of processes with a variety of transition structures are considered and their analysis is presented in a unifying manner. These processes are grouped under the generic name of Phase-type queues, they include G/M/1-type Markov chains, QBD processes, Markov chains with Toeplitz-like transitions and limited displacements (non-skip-free), and tree-like processes. A duality property between M/G/1 and G/M/1 Markov chains is described and a reduction of M/G/1 and G/M/1 Markov chains to QBD is analysed.
Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
If you think you should have access to this title, please contact your librarian.