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?