Consider a single-server queueing system with capacity 3 and is initially empty. A customer arrives at time 0, and successive inter-arrival times are exactly x minutes. The service times are exactly y minutes. When x > y, draw a sample trajectory of X(t). When y > x, draw a sample trajectory of X(t). Write down π∗ = [π0∗,π1∗,π2∗,π3∗] and πˆ. What is the long-run fraction of time that X(t) spends in the state 1? When y > x, draw a sample trajectory of X(t).