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# lec0303 - IEOR 4106 Introduction to Operations Research...

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IEOR 4106: Introduction to Operations Research: Stochastic Models Professor Whitt, Spring 2011 Class Discussion, Thursday, March 3 The Allen&Wycoff (A&W) Barbershop The class discussion is focused on Section 5 of the CTMC notes. The topic is birth-and- death processes. The focus is on models like those in Examples 5.1 and 5.2. Two enterprizing students - Webb Allen and Eliot Wycoff - have decided to earn a little money in their spare time by opening a barbershop in their dormitory: the A&W Barbershop. (They also serve root beer and play music to entertain waiting customers.) They are thinking about adding another barber or possibly enlarging their waiting area. So they are applying their stochastic skills to analyze their current operation. The current A&W Barbershop has two barbers and two barber chairs, plus three extra waiting spaces. We assume that customers arriving when the system is full are blocked, leav- ing without receiving service or affecting future arrivals. We assume that customers arrive according to a Poisson process at rate λ = 6 per hour. We assume that the duration of each haircut is an independent exponential random variable with a mean of μ - 1 = 15 minutes. Thus the service rate of each barber is μ = 4 per hour. We assume customers are served in a first-come first-served manner by the first available barber.

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lec0303 - IEOR 4106 Introduction to Operations Research...

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