Ergodic theorem for a finite continuous-time Markov chain ($T^{-1}{\int }_0^{T}f(X_t)dt\to {\sum }_n\pi (n)f(n)$)

For a finite irreducible Markov chain in continuous time, time averages converge almost surely to averages under its unique stationary distribution, from any initial state. Applying this to an activation indicator yields the corresponding throughput.