Steve and Shaniqua have two computers running experiments. When one computer turns off, either Steve or Shaniqua manually restart the computer. Assume they always restart the computer in the order that they turn off, and only one computer can be restarted at a time (that is, if both computers are down, the second computer to break down will need to wait for the first computer to be restarted before it can be restarted). The time each computer works before turning off is exponentially distributed. Assume, on average, computer 1 turns off every 2 hours and computer 2 turns off every 1.5 hours. The time it takes to restart the computer is also exponentially distributed with mean 10 minutes.

(a) (7 points) Model this system as a CTMC: define all states, transition rates out of the states (vi), transition probabilities (Pij ), and transition rates between states (qij ). Draw the rate diagram and make sure to label the transition rates.

b- In the long run, what fraction of the time do they have at least one computer on?

c- If a computer turns off in the middle of the experiments, it will stop running the experiment while off, but continues where it left off once it is back on. Assume that, when on, computer 1 can run 2 experiments per hour and computer 2 can run 3 experiments per hour. How many experiments to they expect to be able to run per day? Assume 24 hours in a day