Many methods-they all involve-directly or indirectly-solving the master equation for the probability density. It depends on the system, which method is more useful.
Adnan, What type of Markov chain you are talking about? For example, are you asking about the stationary distribution of a discrete-time Markov chains with countably infinite or finite state space?
It is very important what is the object of description / modelling / investigation!
The apparatus of Markov chain is suitable for discrete systems with stochastic processes - stochastic workload which could be presented as a sequence of discrete states. Theoretical, Markov chain is Markov stochastic process with discrete states and probability transaction between them in discrete times.
Another type of Markov process is with “Discrete States and Continuous Time for transactions”, but according determination of some authors this apparatus is NOT Markov Chain.