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On a bivariate Markov process arising in the theory of single‐server retrial queues
Author(s) -
Falin G. I.,
GómezCorral A.
Publication year - 2000
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/1467-9574.00126
Subject(s) - retrial queue , bivariate analysis , mathematics , markov process , joint probability distribution , ergodicity , queue , process (computing) , markov chain , state (computer science) , product (mathematics) , discrete mathematics , computer science , queueing theory , algorithm , statistics , computer network , queueing system , operating system , geometry
We introduce a bivariate Markov process which can be seen as the joint process of the channel state and the number of customers in orbit of a Markovian single‐server retrial queue with state dependent intensities. We obtain a necessary and sufficient condition for the process to be regular, and necessary and sufficient conditions for ergodicity and recurrence. A product‐form formula for the stationary distribution is obtained. Besides, we study the busy period, the number of served customers and other related quantities. We show that for all the above problems there exist “equivalent” birth‐and‐death processes. However, a “uniformly equivalent” birth‐and‐death process does not exist.