Question: Chapter: Waiting Line Management QUESTION 2 Mark: 8x1 = 8 a) A university cafeteria is a self-service facility in which a customer selects the food

Chapter: Waiting Line Management

Chapter: Waiting Line Management QUESTION 2 Mark:

QUESTION 2 Mark: 8x1 = 8 a) A university cafeteria is a self-service facility in which a customer selects the food items he/she wants and then following a single line pays the cashier. Customers arrive at a rate of about 4 per minute in a queue according to the Poisson distribution. The single cashier ringing up sales takes about 12 seconds per customer, following the negative exponential distribution. The restaurant has only 20 seats. i. What is the utilization rate of serving the customer? ii. What is the probability that a customer cannot eat the food in the restaurant? What is the probability of no customer in the system? What is the average number of customers in the system? What is the average number of customers in the line? vi. What is the expected sojourn time? vii. What is the average waiting time? viii. What is the probability that the sojourn time exceeds 30 seconds? iii. iv. v

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