A hummingbird feeder has 4 ports where birds may feed. Birds arrive at the feeder at a rate of one per minute. If all of the ports are occupied, an arriving hummingbird will leave. Otherwise, it will begin feeding at an available port and eat for a time that has an exponential distribution with a mean of one minute. Consider this as a continuous time Markov process where the state is the number of occupied ports.

(a) Draw the transition diagram.

(b) Give the transition rate matrix.

(c) If three ports are occupied, what is the expected time until this changes?