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IEOR 3106: Introduction to Operations Research: Stochastic Models
Fall 2006, Professor Whitt, Final Exam
Chapters 47 and 10 in Ross, Tuesday, December 19, 4:10pm7:00pm
Open Book: but only the Ross textbook, three 8 £ 11 pages of notes, and
the class lecture notes on Markov mouse (9=21 and 9=28), continuoustime
Markov chains (10=24) and Martingales and Brownian motion (12=07.)
Honor Code: Students are expected to behave honorably when taking exams.
After completing the test, please testify to your adherence by writing the following
on your bluebook and signing your name: \I have neither given nor received
improper help while taking this test."
Justify your answers; show your work.
1. Xu Li's Barbershop (25 points)
Xu Li operates a small barbershop with room for at most three customers, one in service
and two waiting. Suppose that potential customers arrive according to a Poisson process at
a rate of 10 per hour. Suppose that potential arrivals ¯nding the barber shop full, with a
customer in service and two other customers waiting, will leave and not a®ect future arrivals.
Suppose that successive service times are independent exponential random variables with mean
30 minutes. Suppose that waiting customers have limited patience, with each waiting customer
being willing to wait only an independent random, exponentially distributed, time with mean
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 Spring '08
 Stochastic

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