Question: Lowe’s Cinema is trying to determine how best to arrange the cashiers at one of its movie theaters. The arrival process of ticket buyers to the movie theater is a Poisson process with rate lambda=210 people per hour. The amount of time it takes to serve a customer at one of the cashiers is exponentially distributed with a mean of 2 minutes.

a. What is the minimal number of cashiers required to keep the system stable?

b. Using the number of cashiers from a., what is the average number of people waiting in line to buy a ticket at the movie theater?

c. Using the number of cashiers from a., what is the average number of people in the ticket booth area of the movie theater (including those waiting in line and those who are currently buying tickets).

d. The theater has decided to replace the cashiers with automatic ticket kiosks for the purpose of purchasing tickets. The time it takes for a customer to purchase a ticket at the kiosk is still 2 minutes on average. A kiosk can serve up to one customer at a time. The kiosks are physically spread-out throughout the theater lobby, so that each kiosk has its own line. Customers choose randomly between the lines, and do not switch between lines. How many kiosks will Lowe’s need to guarantee that the total number of people in the system (including those in line and those who are in the process of purchasing their ticket across all of the ticket kiosks) does not exceed the number you got in question c.?