Conditions for the non-ergodicity of Markov chains with application to a communication system

1987 ◽  
Vol 24 (2) ◽  
pp. 339-346 ◽  
Author(s):  
Linn I. Sennott
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Communication System ◽  
System Performance ◽  
Multiple Access ◽  
Sufficient Condition ◽  
Performance Bounds ◽  
Communication System Performance ◽  
Null Recurrence ◽  
The Stability

We obtain a sufficient condition for the transience of a Markov chain, and a sufficient condition for its null recurrence. These are applied to characterize the stability of a multiple-access communication system. Performance bounds for the system are also obtained.

Conditions for the non-ergodicity of Markov chains with application to a communication system

1987 ◽  
Vol 24 (02) ◽  
pp. 339-346 ◽  
Author(s):  
Linn I. Sennott
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Communication System ◽  
System Performance ◽  
Multiple Access ◽  
Sufficient Condition ◽  
Performance Bounds ◽  
Communication System Performance ◽  
Null Recurrence ◽  
The Stability

We obtain a sufficient condition for the transience of a Markov chain, and a sufficient condition for its null recurrence. These are applied to characterize the stability of a multiple-access communication system. Performance bounds for the system are also obtained.

On the equivalence of certain Markov chains

1976 ◽  
Vol 13 (02) ◽  
pp. 357-360
Author(s):  
Pedro Vit
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Simple Proof ◽  
Interesting Application ◽  
Null Recurrence ◽  
A Chain

It is shown that an irreducible and aperiodic Markov chain can be altered preserving irreducibility without altering the nature of the chain in the sense that, the modified chain is transient (recurrent) if and only if the original chain is transient (recurrent). Furthermore, it is shown by means of a counterexample that ergodicity (null-recurrence) is not preserved. An interesting application of this result is a simple proof of Pakes's generalization of Foster's criterion for a chain to be recurrent.

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