A matrix continued fraction algorithm for the multiserver repeated order queue

Authors:
T. Hanschke
Affiliations:
Institut für Mathematik, Technische Universität Clausthal Erzstraβe l, 38678 Clausthal-Zellerfeld, Germany and International Business Machines Corporation Department 5200, Hechtshei ...
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
1999

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Abstract

This paper describes a multiserver repeated order queue with an unlimited number of sources, for which the underlying queueing process can be represented as a level-dependent quasi-birth-and-death process. For calculating its steady-state probabilities, a recursive method is proposed, which generalizes the notion of a continued fraction to sequences of matrices. In addition, rigorous proofs of the ergodicity and transience condition are given.