Marty's Barber Shop has one barber Customers have an arrival rate of 2 3 customers per hour, and haircuts are given with a service rate of 5 per hour Use the Poisson arrivals and exponential service times model to answer the following questions What is the probability that no units are in the system If required, round your answer to four decimal places P 0 What is the probability that one customer is receiving a haircut and no one is waiting If required, round your answer to four decimal places P 1 What is the probability that one customer is receiving a haircut and one customer is waiting If required, round your answer to four decimal places P 2 What is the probability that one customer is receiving a haircut and two customers are waiting If required, round your answer to four decimal places P 3 What is the probability that more than two customers are waiting If required, round your answer to four decimal places P (More than 2 waiting) What is the average time a customer waits for service If required, round your answer to four decimal places W q hours

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Posted on Jun 25, 2024

Marty's Barber Shop has one barber. Customers have an arrival rate of 2.3 customers per hour, and haircuts are given with a service rate of

Marty's Barber Shop has one barber. Customers have an arrival rate of 2.3 customers per hour, and haircuts are given with a service rate of 5 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions:

What is the probability that no units are in the system? If required, round your answer to four decimal places.
P₀ =
What is the probability that one customer is receiving a haircut and no one is waiting? If required, round your answer to four decimal places.
P₁ =
What is the probability that one customer is receiving a haircut and one customer is waiting? If required, round your answer to four decimal places.
P₂ =
What is the probability that one customer is receiving a haircut and two customers are waiting? If required, round your answer to four decimal places.
P₃ =
What is the probability that more than two customers are waiting? If required, round your answer to four decimal places.
P(More than 2 waiting) =
What is the average time a customer waits for service? If required, round your answer to four decimal places.
W_q = hours

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To solve this problem we will use the formulas related to the MM1 queuing system singleserver queue with Poisson arrival and exponential service times ... blur-text-image