A professor supervises four Ph.D. students who all need quite a bit of advice. Three of the four students are quite similar regarding their habits. When any of these students visits the professor, the time to the next visit has an exponential distribution with a mean of 8 hours. The time for the professor to advise a student has a mean value of 1/2 hour.

The fourth student has the same arrival rate as the others, but requires a mean time of one hour with the professor.

All times in this problem have exponential distributions. Students visit the professor one at a time. If the professor is busy, the students wait outside his office.

Answer numerical questions with the Stochastic Analysis Add-in.

a. Construct the CTMC Matrix that describes this situation.

b. At steady-state what proportion of the professor's time does he have to himself (without students)?

c. At steady-state what is the probability distribution for the number of students waiting?

d. Change the situation as follows. Whenever more than one student is waiting, a student may get the information he needs from another student. The average time required to learn from another student is 0.75 hours. What happens to the answers to b and c with this change?