# compute the system state probabilities

**Question description**

Customers arrive at a two-chair shoeshine stand at the rate of 10 per hour. The average duration of a shoeshine is 6 minutes. There is only one attendant, so that one chair is used as a waiting position. Customers who find both chairs occupied go away.

a. assuming Poisson input and exponential service times, compute the system state probabilities.

b. find the mean number of customers served per hour.

c. repeat the analysis to calculate the mean number of customers served per hour when there are two attendants at the stand (and no waiting positions).

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