How to interpret stationary of birth death process.

This is a simple question that I can’t seem to find an answer to. Basically if we have a birth death process, then this is true:

π0\pi_0 =آ 11+∑λiμi \frac{1}{1+\sum \frac{\lambda_i}{\mu_i}}

I simply want to know how to interpret π0\pi_0. Does it stand for “Expected time in long run spent non busy”?

Sorry for stupid question but I can’t seem to find an answer to this.




One way of interpreting π0\pi_0 is the proportion of time that the Markov chain spends in state 00. If 00 is the only state that is labeled as ‘non-busy’, then π0\pi_0 is the fraction of time spent ‘non-busy’ in the long run.
– Ritz
2 days ago