IEOR 3106 Test on Chap4to7

IEOR 3106 Test on Chap4to7 - IEOR 3106: Introduction to...

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IEOR 3106: Introduction to Operations Research: Stochastic Models Fall 2006, Professor Whitt, Final Exam Chapters 4-7 and 10 in Ross, Tuesday, December 19, 4:10pm-7:00pm 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), continuous-time 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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IEOR 3106 Test on Chap4to7 - IEOR 3106: Introduction to...

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