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Customers arrive at a two-chair shoeshine stand at a rate of 10 customers per hour. The average length of a shoeshine is 5 minutes. There is only one attendant, so that one chair is used as a waiting position. Customers who find both chairs occupied go away. Assume Poisson arrivals and exponential service times.
What is the queuing model that is appropriate here?
What is the probability that the waiting chair will be occupied? (Use two digits to the right of the decimal point.)
(Hint: first figure out what is the state of the system (a.k.a. the number of the users in the queuing system) when the waiting chair is occupied. Then, you can compute the probability of that state)
What is the mean number of customers served per hour? (Use two digits to the right of the decimal point.)
Now, let us modify question 2 by assuming there are 2 attendants at the stand. What is the mean number of customers serviced per hour? (Use two digits to the right of the decimal point.)
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