Question

Question 4

You have decided to open a haircutting business.

A customer arrives every 20 minutes and follows a Poisson distribution. You cut the hair on average in 12 minutes and your service follows an exponential distribution.

What is the arrival rate (lambda)?    (Give all answers to three decimals)

What is the service rate (mu)?  

What is average number of customers waiting (in inventory)?

What is the average in the system (waiting plus having hair cut)?  

What is the average time a customer spends waiting for a haircut in minutes?  

What is the average time a customer spends at your shop (wait plus cutting time) in minutes?  

Answer 1

The assumptions in single-server queue theory include: -

Unlimited calling population may enter the queue

Arrivals are random and independent but average number of arrival does not change.

Single waiting line and arriving customers are patient customers who can wait in the queue before they can be served regardless of the length of the line.

Arrivals are served on FIFO basis

Service time of one customer may vary from that of another customer.

Single server and service time is as per the negative exponential probability distribution.

Average service rate is greater than average arrival rate.