Question: Consider the closed queueing network in Fig. There are three customers who are doomed forever to cycle between queue I and queue 2. The service times at the queues are independent and exponentially distributed with mean μ1 and μ2. Assume that μ2 μ1·
(a) The system can be represented by a four-state Markov chain. Find the transition rates of the chain.
(b) Find the steady-state probabilities of the states.
(c) Find the customer arrival rate at queue 1.
(d) Find the rate at which a customer cycles through the system.
(e) Show that the Markov chain is reversible. What does a departure from queue I in the forward process correspond to in the reversed process? Can the transitions of a single customer in the forward proces be associated with transitions of a single customer in the reverse process?
