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Waiting Lines and Queing Theory Models

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Customers enter the waiting line at a cafeteria on a first come, first served basis in two serving lines.

The arrival rate follows a Poisson distribution, while service times follow an exponential distribution.

If the average number of arrivals is two per minute and the average service rate of three customers per minute, what is the average time a customer spends in the queue?

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Queuing Theory - Single-Channel Waiting Line Model

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

a). What is the probability that no units are in the system?
b). What is the probability that one customer is receiving a haircut and no one is waiting?
c). What is the probability that one customer is receiving a haircut and one customer is waiting?
e). What is the probability that more more than two customers are waiting ?
f). What is the average time a customer waits for service?

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