Prove that a Jackson process is irreducible if and only if its routing process is irreducible. Recall that λij is irreducible if and only if, for any fixed i = j in M, there are i1,...,i in M such...

Prove that a Jackson process is irreducible if and only if its routing process is irreducible. Recall that λij is irreducible if and only if, for any fixed i = j in M, there are i1,...,i in M such that λ_ii1
λ_i1i2 ··· λ_ij
> 0.