Students arrive randomly at the counter of the CIT Library. There is only one library assistant, and the time required for inquiry varies from student to student. The average arrival rate is 12 students per hour, and the average service rate is 20 students per hour. What is the average service time for this problem?

Students arrive randomly at the counter of the CIT Library. There is only one library assistant, and the time required for inquiry varies from student to student. The average arrival rate is 12 students per hour, and the average service rate is 20 students per hour. What is the average service time for this problem?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 9P

See similar textbooks

Similar questions

The Clip Joint is a hairstyling salon at University Mall. Four stylists are always available toserve customers on a first-come, first-served basis. Customers arrive at an average rate of fiveper hour, and the stylists spend an average of 35 minutes on each customer Determine the average number of customers in the salon, the average time a customer must wait, and the average number waiting to be served.
Students arrive randomly at the counter of the CIT Library. There is only one library assistant, and the time required for inquiry varies from student to student. The average arrival rate is 12 students per hour, and the average service rate is 20 students per hour. What is the utilization factor?
Customers arrive at Best-Bank-in-Town’s (BBT) sole ATM location at a rate of 21 customers per hour. It is assumed that the arrival process is random. BBT recently hired an intern who estimated that the average service time is 2 minutes per customer with a standard deviation of 1.2 minutes. [Assume that the arrival rate is the same throughout the day without peak and off-peak considerations and that there is only one ATM machine at that location] 1. Calculate average waiting time for ATM user at the BBT location 2. Calculate average length of queue at the ATM location (i.e. average numbers of customers waiting for service)? 3. What is the probability that an arriving customer has no waiting time to use the ATM? 4. BBT wants to cut the average waiting time in half without necessarily adding another ATM machine. They are in discussions with their ATM software provider who has told them that their new software is very consistent with information retrieval and can greatly minimize the…
The computer laboratory at a State University has a help desk to assist students working on computer spreadsheet assignments. The students patiently form a single line in front of the desk to wait for help. Students are served based on a first-come, first-served priority rule. On the average, 15 students per hour arrive at the help desk. Student arrivals are best described using a Poisson distribution. The help desk server can help an average of 20 students per hour, with the service rate being described by a constant distribution. Calculate the following characteristics of the system: The average utilization of the help desk server. The average number of students waiting in line. The average number of students waiting in the system. The average time a student spends in the system
Marty's Barber Shop has one barber. Customers have an arrival rate of 2.2 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that one customer is receiving a haircut and two customers are waiting? If required, round your answer to four decimal places.P3 = fill in the blank 4 What is the probability that more than two customers are waiting? If required, round your answer to four decimal places.P(More than 2 waiting) = fill in the blank 5 What is the average time a customer waits for service? If required, round your answer to four decimal places.Wq = fill in the blank 6 hours
Marty's Barber Shop has one barber. Customers have an arrival rate of 2.2 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that no units are in the system? If required, round your answer to four decimal places.P0 = fill in the blank 1 What is the probability that one customer is receiving a haircut and no one is waiting? If required, round your answer to four decimal places.P1 = fill in the blank 2 What is the probability that one customer is receiving a haircut and one customer is waiting? If required, round your answer to four decimal places.P2 = fill in the blank 3
The computer lab at State University has a help desk to assist students working on computer spreadsheet assignments. The students patiently form a single line in front of the desk to wait for help. Students are served based on a first-come, first-served priority rule. On average, 15 students per hour arrive at the help desk. Student arrivals are best described using a Poisson distribution. The help desk server can help an average of 20 students per hour, with the service rate being described by an exponential distribution. Calculate the following operating characteristics of the service system.(a) The average utilization of the help desk server (b) The average number of students in the system(c) The average number of students waiting in line (d) The average time a student spends in the system (e) The average time a student spends waiting in line
Students arrive at the administrative services office at an average of one every 15 minute, and their request take on average 10 minutes to be processed. The service counter is staffed by only one clerk, Judy who works eight hours per day. Assume poisson arrivals and exponential service times a) what is the probability that am arriving student will find at least one other student waiting in line?
A university cafeteria line in the student center is a self-serve facility in which students select the food items they want, 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 customer, 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 chareristics computed in parts (b), (c), (d), and (e) change? Assume that customers wait in a single line and go to the first available cashier.
Customers arrive at a store randomly, following a Poisson distribution at an average rate of 20 per hour. What is the probability of exactly 0, 1, 2, and 3 arrivals in a 15 minute period?