The Grand Movie Theater Has One Box Office Clerk

question 39

Essay

The Grand Movie Theater has one box office clerk.On average,each customer that comes to see a movie can be sold a ticket at the rate of six per minute.For the theater's normal offerings of older movies,customers arrive at the rate of three per minute.Assume arrivals follow the Poisson distribution and service times follow the exponential distribution.
a.What is the average number of customers waiting in line?
b.What is the average time a customer spends in the waiting line?
c.What is the average number of customers in the system?
d.What is a customer's average time in the system?
e.What is the probability that someone will be buying tickets when an arrival occurs?
The Grand has booked the Stars Wars Trilogy and expects more customers.From conversations with other theater owners,it estimates that the arrival rate will increase to 10 per minute.Output is supplied for two- and three-cashier systems.
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