Recall that an M/M/1 queueing system is a GI/G/c system in which customers arrive according to a Poisson process with rate λ, and service times are exponential with mean 1/µ. For an M/M/1 queueing...

Recall that an M/M/1 queueing system is a GI/G/c system in which customers arrive according to a Poisson process with rate λ, and service times are exponential with mean 1/µ. For an M/M/1 queueing system, each time that a customer arrives to the system or a customer departs from the system, we say that a transition occurs. Let Xn be the number of customers in the system immediately after the nth transition. Show that {X_n
: n = 1, 2,...} is a Markov chain, and find its probability transition matrix. Find the period of each state of the Markov chain.