Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 12.4, Problem 7P
Summary Introduction
To determine: How long should a typical customer wait in line.
Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Consider a bank where potential customers arrive at rate of 60 customers per hour. However, because of limited space, one out of every four arriving customers finds the bank full and leaves immediately (without enteringthe bank). Suppose that the average number of customers waiting in line in the bank is 3.5. How long will a typical entering customer have to wait in line? (Hint: In Little’s formula, l refers only to customers who enter the system.)
Consider a bank with two tellers. An average of 2 customers per hour arrive at the bank and wait in a single línea for an idle teller. The average time it takes to serve a customer is triangular (x1=1, y1=0), (x2=4, y2=2/3) Assume that inter-arrival times and services time is exponential. Develop the service (ST) equation?
a. Y=2x-22/6B. Y=2x-22/3C. Y=22/3x-2/3D. Y=2x-3/22
In a queueing system, customers arrive once every 4 hours (standard deviation = 7) and services take 3 hours (standard deviation =
4.9).
(Do not round intermediate calculations. Round your answer to three decimal places.)
What is the average number of customers in the queue?
customers
Chapter 12 Solutions
Practical Management Science
Ch. 12.3 - Prob. 1PCh. 12.3 - Explain the basic relationship between the...Ch. 12.3 - Prob. 3PCh. 12.3 - Prob. 4PCh. 12.4 - Prob. 5PCh. 12.4 - Prob. 6PCh. 12.4 - Prob. 7PCh. 12.4 - Prob. 8PCh. 12.5 - Prob. 9PCh. 12.5 - Prob. 10P
Ch. 12.5 - Prob. 11PCh. 12.5 - Prob. 12PCh. 12.5 - Prob. 13PCh. 12.5 - Prob. 14PCh. 12.5 - Prob. 15PCh. 12.5 - Prob. 16PCh. 12.5 - Prob. 17PCh. 12.5 - Prob. 18PCh. 12.5 - Prob. 19PCh. 12.5 - Prob. 20PCh. 12.5 - Prob. 21PCh. 12.5 - Prob. 22PCh. 12.5 - On average, 100 customers arrive per hour at the...Ch. 12.5 - Prob. 24PCh. 12.5 - Prob. 25PCh. 12.5 - Prob. 26PCh. 12.5 - Prob. 27PCh. 12.5 - Prob. 28PCh. 12.5 - Prob. 29PCh. 12.5 - Prob. 30PCh. 12.5 - Prob. 31PCh. 12.5 - Prob. 32PCh. 12.5 - Prob. 33PCh. 12.5 - Prob. 34PCh. 12.5 - Prob. 35PCh. 12.5 - Two one-barber shops sit side by side in Dunkirk...Ch. 12.5 - Prob. 37PCh. 12 - Prob. 46PCh. 12 - Prob. 47PCh. 12 - Prob. 48PCh. 12 - Prob. 49PCh. 12 - Prob. 50PCh. 12 - Prob. 51PCh. 12 - Prob. 52PCh. 12 - Prob. 54PCh. 12 - Prob. 56PCh. 12 - Prob. 57PCh. 12 - Prob. 58PCh. 12 - Prob. 59PCh. 12 - Prob. 60PCh. 12 - Prob. 61P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, operations-management and related others by exploring similar questions and additional content below.Similar questions
- In a queueing system, customers arrive once every 5 hours (standard deviation = 5) and services take 3 hours (standard deviation = 6.5). (Do not round intermediote calculations. Round your anower to three decimal places.) What is the average number of customers in the system? customersarrow_forwardIn a queueing system, customers arrive once every 4 seconds (standard deviation = 4) and services take 2 seconds (standard deviation = 4.3). (Do not round intermediate calculations. Round your answer to three decimal places.) What is the average time a customer will spend in the queue (in seconds)? secondsarrow_forwardIn a queueing system, customers arrive once every 4 minutes (standard deviation = 7) and services take 3 minutes (standard deviation = 5.5). (Do not round intermediate calculations. Round your answer to three decimal places.) What is the average time a customer will spend in the queue (in minutes)? minutesarrow_forward
- At a fashion retailer, there are three cashiers providing checkout service simultaneously. On average, customers arrive at the checkout area every 6 minutes. It is estimated that the customer arrival process is a Poisson process. The average checkout time for each customer is 12 minutes, with its standard deviation equal to 15 minutes. Suppose that customers form a single line. What is the average waiting time in minutes for a customer? Note: 1. Keep 2 decimal places for your final answer. Either use Excel for your calculation, or keep at least 4 decimal places for your intermediate numbers. 2. The Poisson arrival process has exponentially distributed inter-arrival times.arrow_forwardIn a queueing system, customers arrive once every 6 seconds (standard deviation = 5) and services take 5 seconds (standard deviation = 4). (Do nót round intermediate calculations. Round your answer to three decimal places.) customers What is the average number of customers in the queue?arrow_forwardMany of a bank’s customers use its automated banking machine (ABM). During the early eveninghours in the summer months, customers arrive at an ABM at the rate of one every other minute(assume Poisson). Each customer spends an average of 99 seconds completing the transaction.Transaction times are exponentially distributed. Assume that the length of the queue is not aconstraint. Determine the average time customers spend at the machine, including waiting in line and completing transactions. Determine the probability that a customer will not have to wait upon arrival at the ABM. Determine the utilization of the ABM.arrow_forward
- Consider a Poisson queue with random arrivals at the rate of 12 customers per hour and the following steady- state probabilities: po = 1/3, p1 = 1/2, p2 = 1/6, and p, = 0 for n = 3,4,5, ... . What is the mean (or effective) arrival rate in customers per hour for this queuing system? Consider drawing a rate diagram to assist in your solution. O 10 12 O none of the other choices O 2arrow_forwardA self-service store employs one cashier at its counter. Nine customers 'arrive on an average every 5 minutes while the cashier can serve 10 customers in 5 minutes. Assuming Poisson distribution for arrival rate and exponential distribution for service time, find 1. Average number of customers in the system. 2. Average number of customers in the queue or average queue length. 3. Average time a customer spends in the system. 4. Average time a customer waits before being served. A.1arrow_forwardplease answer in 30 mins.arrow_forward
- Burger Dome sells hamburgers, cheeseburgers, French fries, soft drinks, and milk shakes, as well as a limited number of specialty items and dessert selections. Although Burger Dome would like to serve each customer immediately, at times more customers arrive than can be handled by the Burger Dome food service staff. Thus, customers wait in line to place and receive their orders. Suppose that Burger Dome analyzed data on customer arrivals and concluded that the arrival rate is 33 customers per hour and 1 customer processed per minute. Compare a multiple-server waiting line system with a shared queue to a multiple-server waiting line system with a dedicated queue for each server. Suppose Burger Dome establishes two servers but arranges the restaurant layout so that an arriving customer must decide which server's queue to join. Assume that this system equally splits the customer arrivals so that each server sees half of the customers. How does this system compare with the two-server…arrow_forwardExplain the concept of queue and queue theory or waiting line theory and its importance in business A bank has only one counter for its customers. Suppose that the customers to the bank arrive at random with exponential inter arrival time and their mean inter arrival time is 10 minutes. Suppose the counter takes on an average 15 minutes to serve the customer and this also follow an exponential distribution. What percentage of time the bank counter is busy? On the average, how many customers are in the system? On the average, how many customers are in the queue waiting for the service? How long a customer will take to be out of the service system after being served? How long a customer to wait before being served? What is the probability that there are at most three customers in the system?arrow_forwardA horologist (watchmaker) is typically able to service a mechanical watch in about 120 minutes (exponential distribution). Assuming an 8 hour work-day, the watchmaker averages 3 customers arriving at his shop every day following a poisson distribution. The watchmaker just purchased a new machine that will polish the dial and crystal reducing his service time by 20 minutes per watch. How much will the line for a watch waiting to be serviced be reduced by the watchmaker using this new machine, assuming no increase in customer demand? O 2.25 watches waiting for service O The number waiting to be serviced will be reduced by about 1.2 watches O The number waiting to be serviced will be reduced by about 0.4 watches The number waiting to be serviced will be reduced by about 1.45 watchesarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,
Practical Management Science
Operations Management
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:Cengage,