A store operates with three cashiers. The store has a policy that the cashier additions will be available if at any time the number of customers queuing exceeds 3 people. So if the number of customers queuing is less than 4 people, then only 1 cashier on duty, 4-6 customers queue for only 2 cashiers on duty and if there are more than 6 the customer queues so the three cashiers will be on duty. The arrival of customers follows Poisson process with an average of 10 customers per hour and average service time for each customers have exponential distribution with an average of 12 minutes. a. Determine the long-term proportion of time that there are exactly n customers in the system this queue. b. Determine the opportunity that only one cashier is on duty. c. Determine the average number of cashiers who are unemployed.


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