Barry works at an ice cream counter of a food court. Customers arrive at a mean rate of 6 per hour. The mean service rate is 9.5 per hour. Assume it is a single-server waiting line model.
(a) Determine the mean arrival rate and the mean service rate.
(b) Determine the probability that a customer will have an empty queue.
(c) Determine the probability that 2 customers are in the queuing system.
(d) Determine the average number of customers in the queue and the average number of customers in the system.
(e) Determine the average waiting time in the queue and the average total time in the system for a customer.
(f) Find the utilization factor of the server.
suppose Barry can be replaced by another server, Nina, who must be paid $15 per hour whereas Barry is paid $10 per hour. Nina can serve 12 customers per hour. If a customer's time is considered to be worth $8 per hour, is it worth to replace Barry with Nina?