A positive recurrence criterion associated with multidimensional queueing processes
- 1 March 1980
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 17 (03) , 790-801
- https://doi.org/10.1017/s0021900200033891
Abstract
A criterion is given for positive recurrence of a multidimensional, aperiodic, irreducible Markov chain with a denumerable state space. This criterion extends to the multidimensional case Foster's one-dimensional criterion. The multidimensional criterion consists of several conditions, one for each coordinate of the process. The usefulness of this criterion is shown through a queueing network example.Keywords
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