Is Little's Law applicable to all Continous Time Markov Chain Models?

Question

I was reading about Little's Law which is in general(infinite capacity system) form L = R*W ( R: throughput rate ,W : expected waiting time of a customer). I know it is applicable on M/M/S type queues;however I am wondering if this law is also applicable to all Continous Time Markov Chain models? Thanks in advance

Answer 1

Little's Law, as defined by wikipedia, only assumes the random process/the system is stationary($P(x_{1, t_1}, x_{2, t_2}...) = P(x_{1, t_1+\tau}, x_{2, t_2 + \tau}...)$, $\forall\tau$). So any such process(eg, it doesn't need to be a queue, can be a small part of it as well) obeys this law.

These Markov processes are analysed here thoroughly, but as a concise answer, you can apply it to all ctmcs whose transition probabilities are time homogenous.

Another intuitive way I personally studied in class said that you can apply it as long as the rate of incoming 'stuff'(or customers) is equal to the rate of outgoing 'stuff', i.e., as long as the system is stable(so the values just need to converge)