1. A University cafeteria line in the student center is a self-serve facility in which students select the food items they want and then form a single line to pay the cashier. Students arrive at the cashier at a rate of about four per minute according to a Poisson distribution. The single cashier ringing up sales takes about 12 seconds per customer, following an exponential distribution. What is the probability that there are more than two students in the system? More than three students? And more than four? (b) What is the probability that the system is empty? (c) How long will the average student have to wait before reaching the cashier? (d) What is the expected number of students in the queue? (e) What is the average number in the system? (f) Briefly explain the basic concept of queuing discipline. (g) In what kinds of situations is queuing analysis most appropriate?
Added by Katrina E.
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First, we need to find the arrival rate (λ) and service rate (μ). The arrival rate is given as 4 students per minute, and the service rate can be calculated as 1 student per 12 seconds, which is equivalent to 5 students per minute. Show more…
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A University cafeteria line in the student center is a self-serve facility in which students select the food items they want and then form a single line to pay the cashier. Students arrive at the cashier at a rate of about four per minute according to a Poisson distribution. The single cashier ringing up sales takes about 12 seconds per customer, following an exponential distribution. What is the probability that there are more than two students in the system? More than three students? And more than four? (b) What is the probability that the system is empty? (c) How long will the average student have to wait before reaching the cashier? (d) What is the expected number of students in the queue? (e) What is the average number in the system? (f) Briefly explain the basic concept of queuing discipline. (g) In what kinds of situations is queuing analysis most appropriate?
Madhur L.
13-14 A university cafeteria line in the student center is a self-serve facility in which students select the food items they want and then form a single line to pay the cashier. Students arrive at a rate of about four per minute according to a Poisson distribution. The single cashier ringing up sales takes about 12 seconds per customers, following an exponential distribution. (a) What is the probability that there are more than two students in the system? More than three students? More than four? (b) What is the probability that the system is empty? (c) How long will the average student have to wait before reaching the cashier? (d) What is the expected number of students in the queue? (e) What is the average number in the system? (f) If a second cashier is added (who works at the same pace), how will the operating characteristics computed in parts (b), (c), (d), and (e) change? Assume that customers wait in a single line and go to the first available cashier.
Supreeta N.
"college cafeteria has a single check out lane manned by a single cashier: Students arrive at the cash register at the rate of 2 per minute during peak lunch hour: It takes about 20 seconds to check out each student' s tray. Assume that arrival rate follows a Poisson distribution and service time follows an exponential distribution. To determine the efficiency of operations, the cafeteria manager wishes to examine several queue operating characteristics_ What is the utilization rate of this service system? b What is the average number of students in line? What is the average time that each student spends in the queue? What is the average time that each student spends in the queue and being checked out? What is the probability that the cashier will be idle?"
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