Matthew the Barber owns a one-chair shop. At barber college, they told Matthew that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of two per hour. It will take Matthew an average of 20 minutes to give a haircut. Based on these figures, find the following: Part (a): The average number of customers waiting. Part (b): The average time a customer waits. Part (c): The average time a customer is in the shop. Part (d): The average utilization of Matthew's time.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Matthew the Barber owns a one-chair shop. At barber college, they told Matthew that his customers
would exhibit a Poisson arrival distribution and that he would provide an exponential service
distribution. His market survey data indicate that customers arrive at a rate of two per hour. It will take
Matthew an average of 20 minutes to give a haircut. Based on these figures, find the
following:
Part (a): The average number of customers waiting.
Part (b): The average time a customer waits.
Part (c): The average time a customer is in the shop.
Part (d): The average utilization of Matthew's time.
Transcribed Image Text:Matthew the Barber owns a one-chair shop. At barber college, they told Matthew that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of two per hour. It will take Matthew an average of 20 minutes to give a haircut. Based on these figures, find the following: Part (a): The average number of customers waiting. Part (b): The average time a customer waits. Part (c): The average time a customer is in the shop. Part (d): The average utilization of Matthew's time.
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