. M/M/1 Queueing System. Suppose Xn is the queue-length process in Example 21, where p is the probability of an arrival, and q is the probability of a service completion at any discrete time. Show...

. M/M/1 Queueing System. Suppose Xn is the queue-length process in Example 21, where p is the probability of an arrival, and q is the probability of a service completion at any discrete time. Show that an invariant measure for this Markov chain is πi = ρⁱ
, i ≥ 0, where ρ = p(1 − q)/[q(1 − p)]. Prove that the chain is ergodic if and only if pExample 21