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Problem 15-9 (Algorithmic) Marty's Barber Shop has one barber. Customers have an arrival rate of 2.3...

Problem 15-9 (Algorithmic)

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 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions:

  1. What is the probability that no units are in the system? If required, round your answer to four decimal places.

    P0 =
  2. 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 =
  3. 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 =
  4. 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 =
  5. 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) =
  6. What is the average time a customer waits for service? If required, round your answer to four decimal places.

    Wq =  hours

Homework Answers

Answer #1
arrival rate λ= 2.3
service period=μ= 4.00

a)

probability of 0 people waiting in system =(1-λ/μ)*(λ/μ)0 = 0.4250

b)

probability that one customer is receiving a haircut and no one is waiting =P(1 unit in the system):

probability of 1 people waiting in system =(1-λ/μ)*(λ/μ)1 = 0.2444

c)

probability of 2 people in system =(1-λ/μ)*(λ/μ)2 = 0.1405

d)

probability of 3 people in system =(1-λ/μ)*(λ/μ)3 = 0.0808

e)

probability that more than two customers are waiting

probability that number of customer in system is 4 or greater=Pn=>k=(λ/μ)4 = 0.1093

f)

average time in queue Wq =λ/(μ(μ-λ))= 0.3382 hours

(please try 0.5882   if this comes wrong)

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