Consider the three state Markov process below; the number given on edge (i, j) is q ij , the transition rate from i to j. Assume that the process is in steady state. a) Is this process reversible? b)...

Consider the three state Markov process below; the number given on edge (i, j) is q_ij, the transition rate from i to j. Assume that the process is in steady state.

a) Is this process reversible?

b) Find p_i, the time-average fraction of time spent in state i for each i.

c) Given that the process is in state i at time t, find the mean delay from t until the process leaves state i. d) Find π_i, the time-average fraction of all transitions that go into state i for each i.

e) Suppose the process is in steady state at time t. Find the steady state probability that the next state to be entered is state 1.

f) Given that the process is in state 1 at time t, find the mean delay until the process first returns to state 1.

g) Consider an arbitrary irreducible finite-state Markov process in which q_ij
= q_ji
for all i, j. Either show that such a process is reversible or find a counter example.