Understanding Business
12th Edition
ISBN: 9781259929434
Author: William Nickels
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Question
In an M/M/1 queueing system, the arrival rate is 7 customers per hour and the service rate is 12 customers per hour.
Note: Round your answers to 3 decimal places.
-
What is the probability that the server will be idle?
-
What is the probability of having exactly 4 customers in the system?
-
What is the probability of having 4 or fewer customers in the system?
SAVE
AI-Generated Solution
info
AI-generated content may present inaccurate or offensive content that does not represent bartleby’s views.
Unlock instant AI solutions
Tap the button
to generate a solution
to generate a solution
Click the button to generate
a solution
a solution
Knowledge Booster
Similar questions
- Suppose the waiting time at a certain checkout counter is bi-modal. With probability 0.85, the waiting time follows an exponential distribution with a mean waiting time of four minutes. With probability 0.15, the waiting time equals 20 minutes. a) Compute the mean and median waiting time at the checkout counter. b) Compute the variance of the waiting time at the checkout counter. c) Compute the probability that an individual customer waits longer than 5 minutes at the checkout counter.arrow_forwardSubject - account Please help me. Thankyou.arrow_forwardA crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 5 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 8 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. What is the expected average number of snowplows in the garage (waiting for repair and being repaired)? 5 1.04 1.67 8arrow_forward
- 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 hoursarrow_forwardIn a queueing system, customers arrive once every 3 hours (standard devlation = 4) and services take 2 hours (standard deviation = 6.2). (Do not round intermediate calculations. Round your answer to three decimal places.) What is the average number of customers in the system? customersarrow_forwardWhat is the answer in this number 2?arrow_forward
- A proposal has been presented to the government of Newfoundland and Labrador that would build a new section of highway which would provide improved access for residents of a remote coastal area near Bonavista. The highway would be 16 kilometres in length. The initial proposal called for 7 toll booths, each staffed by an employee. But a subsequent proposal recommended replacing the employees with machines. Many factors must be considered because the intended employees are unionized. However, one of the government's concerns is the effect that replacing the employees with machines will have on the times the drivers spend in the system. Customers will arrive to any one toll booth at a rate of 9 per minute. In the exact-change lanes with employees, the service time is essentially constant at 5 seconds for each driver. With machines, the average service time would still be 5 seconds, but it would be exponential rather than constant, because it takes time for the coins to rattle around in…arrow_forwardAssume trucks arriving for loading/unloading at a truck dock from a single server waiting line. The mean arrival rate is three trucks per hour, and the mean service rate is five trucks per hour. Use the Single Server Queue Excel template to answer the following questions. Do not round intermediate calculations. Round your answers to three decimal places. What is the probability that the truck dock will be idle? What is the average number of trucks in the queue? truck(s) What is the average number of trucks in the system? truck(s) What is the average time a truck spends in the queue waiting for service? hour(s) What is the average time a truck spends in the system? hour(s) What is the probability that an arriving truck will have to wait? What is the probability that more than two trucks are waiting for service?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
- A single server queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 9 customers per hour and an average service rate of 13 customers per hour. The probability of 6 customers in the system is : a. 0.9661 b. 0.8899 c. 0.3077 d. 0.03388arrow_forwardCustomers arrive at a one window drive according to a poison distribution with mean of 10 minutes and service time per customer is exponential with mean of 6 minutes. The space in front of the window can accommodate only three vehicles including the serviced ones. Other vehicles are have to wait outside this space. Calculate:a. A. probability that an arriving customer can drive directly to the space in front of the windowb. Probability that an arriving customer will have to wait outside the directed space c. How long an arriving customer is expected to wait before getting the service?arrow_forwardConsider a Poisson queue with the following steady-state probabilities: po = 1/3, p1 = 1/2, p2 = 1/6, and pn = for n = 3,4,5, ... . What is the minimum number of stools that would accommodate all customers in the system at least 75% of the time in steady state? 3 stools O 2 stools none of the other choices O 1 stoolarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Understanding BusinessManagementISBN:9781259929434Author:William NickelsPublisher:McGraw-Hill EducationManagement (14th Edition)ManagementISBN:9780134527604Author:Stephen P. Robbins, Mary A. CoulterPublisher:PEARSONSpreadsheet Modeling & Decision Analysis: A Pract...ManagementISBN:9781305947412Author:Cliff RagsdalePublisher:Cengage Learning
- Management Information Systems: Managing The Digi...ManagementISBN:9780135191798Author:Kenneth C. Laudon, Jane P. LaudonPublisher:PEARSONBusiness Essentials (12th Edition) (What's New in...ManagementISBN:9780134728391Author:Ronald J. Ebert, Ricky W. GriffinPublisher:PEARSONFundamentals of Management (10th Edition)ManagementISBN:9780134237473Author:Stephen P. Robbins, Mary A. Coulter, David A. De CenzoPublisher:PEARSON
Understanding Business
Management
ISBN:9781259929434
Author:William Nickels
Publisher:McGraw-Hill Education
Management (14th Edition)
Management
ISBN:9780134527604
Author:Stephen P. Robbins, Mary A. Coulter
Publisher:PEARSON
Spreadsheet Modeling & Decision Analysis: A Pract...
Management
ISBN:9781305947412
Author:Cliff Ragsdale
Publisher:Cengage Learning
Management Information Systems: Managing The Digi...
Management
ISBN:9780135191798
Author:Kenneth C. Laudon, Jane P. Laudon
Publisher:PEARSON
Business Essentials (12th Edition) (What's New in...
Management
ISBN:9780134728391
Author:Ronald J. Ebert, Ricky W. Griffin
Publisher:PEARSON
Fundamentals of Management (10th Edition)
Management
ISBN:9780134237473
Author:Stephen P. Robbins, Mary A. Coulter, David A. De Cenzo
Publisher:PEARSON