Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 12.5, Problem 16P
Summary Introduction
To determine: Why λ<µ is not appropriate condition for steady state.
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
Trending nowThis is a popular solution!
Students have asked these similar questions
Suppose that 8 customers per hour arrive at a bank during the 11a-1p. "lunch-hour", period. It is observed that there are, on average, 6
customers in the bank during this same "lunch-hour" period. Which of the following statements are true assuming the system is in steady-
state during that period? (Hint: What law govern's the behavior of systems in "steady-state"?)
The average customer spends 45 minutes in the bank.
The bank must have at least 2 bank tellers.
There is always a line of customers waiting during the 11a-1p period.
The average service time (not including waiting) at the bank is 3/4 of an hour.
Exactly two answers are correct.
None of the answers are correct.
A firm is engaged in both shipping and receiving activities. The management is always
interested in improving the efficiency of new innovations in loading and unloading procedures.
The arrival distribution of trucks is found to be Poisson with arrival rate of 3 trucks per
The service time distribution is exponential with unloading rate of 4 trucks per hour. Determine
(i) expected number of trucks in the queue,
hour.
(ii) expected waiting time of the truck in the queue,
(iii) probability that the loading and unloading dock and workers will be idle,
(iv) what reductions in waiting time are possible if loading and unloading is standardised?
(Please do not give solution in image format thanku)
A single Automated Teller Machine (ATM) is located on the ground floor of a popular shopping mall. Service time at this machine is exponentially distributed. On average, the ATM machine can serve a customer in 3 minutes. Customer arrivals at the machine are Poisson distributed, with an average of 15 customers an hour. Relevant formulas to analyze this M/M/1 model are available in your textbook.
What percent of the time is this machine idle?
25%
0%
75%
50%
100%
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
- Consider 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_forwardCompute the expected queueing time in an M/G/1 queue with an arrival rate of 10 per hour and the following service time distributions, all with mean 5 minutes: (1) exponential;(2) uniform over (0,a);(3) deterministic. Which distribution produces the smallest Wq and which the largest?arrow_forwardPlease do not give solution in image formate thanku. We consider a level-2 IT service desk with 2 staff members. Each staff member can handle one service request in 4 working hours on average. Service times are exponentially distributed. Requests arrive at a mean rate of one request every 3 hours according to a Poisson process. What is the average time between the moment a service request arrives at this desk and the moment is fulfilled? (Show all the formulas and computations - since Lq (avg number of jobs in queue) is complex to calculate assume that it is = 1.02 (requests).)arrow_forward
- Customers arrive randomly to an airport shoe-shine stand at a rate of 8 per hour. The average length of a shoe shine is 12 minutes. There are two attendants. Arriving customers who find both chairs occupied by other customers will wait only if NO customers are waiting. Assume that service times are exponentially distributed and that the calling population is infinite. (a) VWhat is the queuing model? (b) To the nearest third decimal place, what is the expected total time in steady state that a customer spends at the stand? O (M/M/2): (GD/2/infınity), 18.333 minutes O (M/G/2): (GD/infinity/infinity), 0.467 hours none of the other choices O (M/M/2) : (GD/3/infinity), 0.233 hoursarrow_forwardConsider a base case where a customer arrives every 52 seconds and the Customer Service Champion can handle 115 customers per hour. There are two Food Champions, each capable of handling 100 orders per hour. On average, how many cars do you expect to have in the drive-thru line? (Include those waiting to place orders and those waiting for food.) (Use the Excel spreadsheet Queue Models.). (Do not round intermediate calculations. Round "Lg" value and final answers to 4 decimal places.) Average total customers waiting in line Average number of customers in the systemarrow_forwardA bank official finds that the length of time customers wait to be served by teller are approximately normally distributed with a mean of 5 minutes and a standard deviation of 3 minutes. What probability that a customer has to wait for at least 6.7 minutes?arrow_forward
- Why does a (M/M/2):(GD/5/infinity) queuing system have a steady state regardless of the values of A > 0 and u > 0? O No further calling unit can enter the system when there are 5 in it. O A and u are both positive O The queue is not a Poisson queue. none of the abovearrow_forward10. Customers arrive an average of 8 per hour and an average of 12 customers can be served in an hour. Assume this is an M/M/1 model. (Noteshaper Quick Start #18 - #20) what is the system utilization? what is the average length of the line? what is the average number of customers in the system? what is the average amount of time spent waiting in the line? what is the average amount of time a customer spends in the system? what is the probability of no customers in the system? 11. Customers arrive at a ferry ticket office at the rate of 18 per hour on Monday mornings. This can be described as a M/M/1 model. Selling the tickets and providing general information takes an average of 2 minutes per customer. One ticket agent is on duty on Mondays. (Noteshaper Scenario #34) a. What is the average length of the line on Monday mornings? b. On average, how long does a customer wait to buy a ticket on Monday mornings (in minutes)? c. How long does it take to successfully buy a ticket on Monday…arrow_forwardConsider 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_forward
- A small bagel stand known as Andres by the Sea offers drive-thru service to customers in Sants Barbra. Andres by the Sea has two customers arrive every hour on average. Suppose that this bagel stand follows an M/M/1 FIFO queuing system with no limits on queue length. They have one employee working at all times that spends 15 minutes per customer. Assume that the employee is paid $10 per hour and a customer’s waiting cost in queue is estimated to be $12 per hour. The average number of customers in the queue (before rounding up), and the total cost per hour are: a. 0.4; $15. b. 0.8; $18. c. 0.6; $21. d. 0.3; $17. e. 0.5; $16.arrow_forwardA typical TSA agent at Piedmont Triad International Airport takes approximately 1.15 minutes to screeneach passenger that arrives at the security gate. During the day, a passenger arrives at the gate onaverage every 1.3 minutes. Both the service rate and arrival rate follow a Poisson distribution. Based onthis information and the assumption that only one screening line is open at the security gate, answer thefollowing questions. Round calculations to at least 3 decimal places.Note: Round each calculation to at least 3 decimal places. a) What is the average number of passengers waiting in line to be screened? b) What is the average amount of time (in minutes) passengers spend waiting in line? c) What is the average amount of time (in minutes) passengers spend in the screening system? d) What is percent of the time does the typical TSA agent spend actively screening passengers? e) Throughout the day, passenger arrival rates vary with the greatest number of passengers arriving about 45…arrow_forwardVisitors' parking space is limited only to four spaces. Cars making use of this space arrive according to a Poisson distribution at a rate of 10 cars per hour. Parking time is exponential with mean 40 minutes. Visitors who cannot find an empty space immediately on arrival may temporarily wait outside the compound until a parked car leaves. That temporary space can hold only four cars. All other cars that cannot park or find a temporary waiting space must go elsewhere. Determine the average number of occupied parking space.arrow_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,