Classification of Markov processes of M/G/1 type with a tree structure and its applications to queueing models

Authors:
Qi-Ming He
Affiliations:
Department of Industrial Engineering, DalTech, Dalhousie University, P.O. Box 1000, Halifax, Nova Scotia, Canada, B3J 2X4
Venue:
Operations Research Letters
Year:
2000

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Abstract

This paper studies the classification problem of Markov processes of M/G/1 type with a tree structure. It is shown that the classification of positive recurrence, null recurrence, and transience of the Markov processes of interest is determined completely by the Perron-Frobenius eigenvalue of a nonnegative matrix. The results are used to find classification criteria for a number of discrete time or continuous time queueing systems with multiple types of customers.