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 birthand
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
firstcome firstserved manner by the first available barber.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '11
 WhitWard
 Operations Research, Probability theory, Customers, CTMC, steadystate probability vector, αi λi

Click to edit the document details