lect0305 - IEOR 4106: Introduction to Operations Research:...

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IEOR 4106: Introduction to Operations Research: Stochastic Models Professor Whitt, Spring 2009 Class Discussion, Thursday, March 5 The Deep-John (DJ) 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 - Monica Deep and Samantha John - have decided to earn a little money in their spare time by opening a barbershop in their dormitory: the DJ Barbershop. (They also 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 DJ 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, leaving 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. We also allow each waiting customer to abandon at a constant rate
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This note was uploaded on 01/26/2011 for the course IEOR 4106 taught by Professor Whitt during the Spring '08 term at Columbia.

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lect0305 - IEOR 4106: Introduction to Operations Research:...

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