Irreducible

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Irreducible
  • Definition
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Irreducible

Apr 09, 20261 min read

Definition

A Markov chain is irreducible if there is only one communicating class — all states are communicative.

Interpretation

In an irreducible chain, any state can be reached from any other state.

Related

  • Communicating Classes
  • Communication
  • Regular TPM

Recent Notes

  • M/M/∞ Queueing System

    May 21, 2026

    • M/M/s Queueing System

      May 21, 2026

      • M/M/1 Queueing System

        May 21, 2026

        • Queueing System with Balking

          May 21, 2026

          • Birth and Death Queueing Models

            May 21, 2026

            Graph View

            Related notes

            • Class Properties of CTMC
            • Accessible State
            • Communicating Classes
            • Communication
            • Ergodic State
            • Regular Transition Probability Matrix
            • Stationary Distribution
            • Existence of CTMC Limit Probabilities
            • State Classification Cheatsheet
            • Stochastic State Relationships
            • Stochastic Model
            • Regular Chain is Irreducible and Aperiodic

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