A crew of mechanics at
the Highway Department garage repair vehicles that break down at an average of
10 vehicles per hour (approximately Poisson in nature). The mechanic crew can
service an average of 2 vehicles every 10 minutes with a repair time
distribution that approximates an exponential distribution. The crew cost is
approximately $50 per hour. The cost associated with lost productivity from the
breakdown is estimated at $80 per vehicle per hour (or any fraction thereof).
Which is cheaper, the existing system with one service crew, or a revised
system with two service crews? The average waiting time for adding the second
crew is 0.02. [5 points]
(b) Peter’s International Barbershop is a
popular haircutting and styling saloon near the campus of the Brooklyn College.
One barber is available to work full time and spend an average of 3 minutes on
each customer. Customers arrive all day long at an average rate of 4 minutes
Arrivals tend to follow the Poisson distribution, and service times are
exponentially distributed. Explain your results. [5 points]
(a) What is the probability that the shop is
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(b) What is the average
number of customers in the barbershop?
(c) What is the average
time spent in the shop?
(d) What percentage of
time the barber is busy?
(e) What is the average
number of customers waiting to be served?