The Grand Movie Theater has one box office clerk. On average, each customer that

Question

The Grand Movie Theater has one box office clerk. On average, each customer that comes to see a movie can be sold its ticket at the rate of 8 per minute. For the theater's normal offerings of older movies, customers arrive at the rate of 4 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?

Explanation / Answer

Arrival rate, ? = 4 per minute, 15 customers per hour

Service rate, u = 8 per minute

Utilization, p =  ? /u = 0.5

b) Avg. number of customers in the entire system = L = ? /(u-?) = 1

a) Average number of customers waiting in line, Lq = pL = 0.5*1 = 0.5 ~ 1

d) Avg time customer customer spends in the system = 1/u-? = 0.25 hour or 15 minutes

c)Avg time customer customer spends waiting in line = pW = 0.5*15 = 7.5 minutes

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