Tony’s Barbershop is run, owned, and operated by Anthony Jones, who has been cutting hairfor more than 20 years. Anthony does not take appointments, so the arrival pattern of customers is essentially random. Traditionally, the arrival rate had been about one customer every50 minutes. Two months ago, the local paper ran an article about Anthony that improved business substantially. Currently, the arrival rate is closer to one customer every 35 minutes. Haircutsrequire an average of 25 minutes, but the times vary considerably depending on customerneeds. A trim might require as little as 5 minutes, but a shampoo and styling could take as longas an hour or more. For this reason, the exponential distribution seems to provide a reasonablygood fit of the service time distribution.Anthony’s customers have always been patient, but ever since business picked up, somehave complained that the wait is too long. Anthony is considering taking his cousin Marvin intothe business to improve customer service. Assume that Marvin cuts hair at the same rate asAnthony.b. How much improvement in the performance of the system are customers likely to see withan additional barber in the shop?
Tony’s Barbershop is run, owned, and operated by Anthony Jones, who has been cutting hair
for more than 20 years. Anthony does not take appointments, so the arrival pattern of customers is essentially random. Traditionally, the arrival rate had been about one customer every
50 minutes. Two months ago, the local paper ran an article about Anthony that improved business substantially. Currently, the arrival rate is closer to one customer every 35 minutes. Haircuts
require an average of 25 minutes, but the times vary considerably depending on customer
needs. A trim might require as little as 5 minutes, but a shampoo and styling could take as long
as an hour or more. For this reason, the exponential distribution seems to provide a reasonably
good fit of the service time distribution.
Anthony’s customers have always been patient, but ever since business picked up, some
have complained that the wait is too long. Anthony is considering taking his cousin Marvin into
the business to improve customer service. Assume that Marvin cuts hair at the same rate as
Anthony.
b. How much improvement in the performance of the system are customers likely to see with
an additional barber in the shop?
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