Tests for the nonergodicity of multidimensional Markov chains. (English) Zbl 0569.60068
A Markov chain is ergodic if it has a proper steady-state distribution. The stability of a queueing system often reduces to the ergodicity of an underlying multidimensional chain. The author gives criteria for the nonergodicity of a multidimensional Markov chain and a generalization to continuous time Markov chains. He also gives queueing model examples.
MSC:
60J10 | Markov chains (discrete-time Markov processes on discrete state spaces) |
60K25 | Queueing theory (aspects of probability theory) |
90B22 | Queues and service in operations research |