Benny the Barber owns a one-chair shop. At barber college, they told Benny 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 Benny an average of 20 minutes to give a haircut. Based on these figures, find the following: Part (a): The average number of customers waiting. Arrival Time, λ =2 customers per hour Service Time, μ = 20 minute, or 60/20= 3 customer per hour Lq = (2)2 / 3*(3-2) = 1.333 customers Part (b): The average time a customer waits. Wq= 1.333/2=0,665 \~ 0,67 or 40 minutes Part (c): The average time a customer is in the shop. LS = 2/ 3-2 =2 customers. WS = 2/2 = 1 hour Part (d): The average utilization of Benny’s time. P= λ/ μ = 2/3=0,666 percent ~ 0,67 % Benny the Barber (see Question 1) is considering the addition of a second chair. Customers would be selected for a haircut on a FCFS basis from those waiting. Benny has assumed that both barbers would take an average of 20 minutes to give a haircut, and that business would remain unchanged with customers arriving at a rate of two per hour. Find the following information to help Benny decide if a second chair should be added: 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.
Benny the Barber owns a one-chair shop. At barber college, they told Benny 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 Benny an average of 20 minutes to give a haircut. Based on these figures, find the following:
Part (a): The average number of customers waiting.
Arrival Time, λ =2 customers per hour
Service Time, μ = 20 minute, or 60/20= 3 customer per hour
Lq = (2)2 / 3*(3-2) = 1.333 customers
Part (b): The average time a customer waits.
Wq= 1.333/2=0,665 \~ 0,67 or 40 minutes
Part (c): The average time a customer is in the shop.
LS = 2/ 3-2 =2 customers. WS = 2/2 = 1 hour
Part (d): The average utilization of Benny’s time.
P= λ/ μ = 2/3=0,666 percent ~ 0,67 %
Benny the Barber (see Question 1) is considering the addition of a second chair. Customers would be selected for a haircut on a FCFS basis from those waiting. Benny has assumed that both barbers would take an average of 20 minutes to give a haircut, and that business would remain unchanged with customers arriving at a rate of two per hour. Find the following information to help Benny decide if a second chair should be added:
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.
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