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 27P
Summary Introduction
To determine: The time taken by the user to wait before the CPU acts on the request of the user.
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 solutionStudents have asked these similar questions
The Decision Sciences Department is trying to determine whether to rent a slow or a fast copier. The department believes that an employee’s time is worth $15 per hour. The slow copier rents for $4 per hour, and it takes an employee an average of 10 minutes to complete copying. The fast copier rents for $15 per hour, and it takes an employee an average of six minutes to complete copying. On average, four employees per hour need to use the copying machine. (Assume the copying times and interarrival times to the copying machine are exponentially distributed.) Which machine shouldthe department rent to minimize expected total cost per hour?
A data storage system consists of 3 disk drives sharinga common queue. An average of 50 storage requests arriveper second. The average time required to service a requestis .03 second. Assuming that interarrival times and servicetimes are exponential, determine:a The probability that a given disk drive is busyb The probability that no disk drives are busyc The probability that a job will have to waitd The average number of jobs present in the storagesystem
suppose tht a queueing system has two identical servers, and an exponential service-time distribution with a mean of 1/u=10minutes. furthermore, a customer has just arrived to find two in the system. how long would you expect him to wait before being able to start service?
Note:-
Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism.
Answer completely.
You will get up vote for sure.
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 queueing theory, λ represents the mean arrival rate; for example, the number of peoplearriving at the service counter per hour. What does 1/λ represent?o Service rateo Interarrival timeo Service time Nonearrow_forwardWhat do we mean by the term queue discipline?o Queue discipline refers to how people should behave in a queue.o Queue discipline refers to the study of queues and waiting lines.o Queue discipline refers to policies for deciding the order of receiving service byarrivals.o Queue discipline refers to removing customers from a queue when they misbehave.arrow_forward. For the MyMy1 queueing model, why do the following results hold? (Hint: Remember that 1ym is the meanservice time. Then think how long a typical arrival must wait in the system or in the queue.) a. W 5 (L 1 1)ym b. WQ 5 Lymarrow_forward
- The Decision Sciences Department is tyring to determine whether to rent a slow or fast copier. The department believes that an employee's time is worth $15/hour. The slow copier rents for $4/hr, and it takes an employee an average of 10 minutes to complete copying. The fast copier rents for $15/hr, and it takes an employee an average of 6 minutes to complete copying. On average, four employees per hour need to use the copying machine. (Assume the copying times and interarrival times to the copying machine are exponentially distributed.) Which machine should the department rent to minimize expected total cost per hour? Please note this class revolves around Microsoft Excel so the answer I need needs to show the formulas in Excel, along with any corresponding graphs, etc. Thank you in advance!arrow_forwardA traffic light is red for 20 seconds and green for 40 seconds. Cars arrive at the traffic light as a Poisson process with rate 2 per minute. They take exactly 20 seconds to go through the light. A car cannot start going through until the previous one has cleared the light. Assuming, as an initial condition, that there are no cars at the traffic light when it turns red:a. What is the probability that at least one car will arrive when the light is still red?b. What is the probability that there will be no cars at the light when the light next turns red?arrow_forwardA copier store has four pieces of automatic equipment, but sometimes they are down because they need supplies, maintenance or repair. Each unit requires about two services every hour or, to be exact, each piece of equipment runs an average of 30 minutes before needing service. Service times vary greatly, from a simple service (such as pressing the reset switch or replenishing the paper) to disassembling the equipment in question. However, the average service time is five minutes. The time the equipment is down generates a loss of $60 per hour. The single employee who services the equipment earns $18 per hour. Using finite population analysis, answer the following questions: a. What is the average number of units idling? b. What is the average number of units still operating? c. What is the average number of units being serviced? d. The company is considering adding another manager at the same wage of $18 per hour. should it do so?arrow_forward
- 48. Ships arrive at a port facility at an average rate of twoships every three days. On average, it takes a single crewone day to unload a ship. Assume that interarrival andservice times are exponential. The shipping companyowns the port facility as well as the ships using that facility. The companyestimates that it costs $1000 per dayfor each day that a ship spends in port. The crew servicing the ships consists of 100 workers, each of whom ispaid an average of $30 per day. A consultant has recommended that the shipping company hire an additional40 workers and split the employees into two equal-sizecrews of 70 each. This would give each crew an averageunloading or loading time of 1.5 days. Which crew arrangement would you recommend to the company?arrow_forwardCalls arrive at Lynn Ann Fish's hotel switchboard at a rate of 2.0 per minute. The average time to handle each is 15 seconds. There is only one switchboard operator at the current time. The Poisson and negative exponential distributions appear to be relevant in this situation. The probability that the operator is busy = 0.500.50 (round your response to two decimal places).The average time that a caller must wait before reaching the operator = 0.250.25 minutes (round your response to two decimal places). c) The average number of calls waiting to be answered = calls (round your response to two decimal places).arrow_forwardThe QRS Trucking Services, has one warehouse servicing its 4 clients within the area. The warehouse hasonly one loading harbor with 3 service crews. The manager has observed that there are certain timeswherein their delivery vans are waiting in the harbor to be loaded. Also, there are instances whereintheir three service crews are idle. Thinking about the situation of their business , the manager noticedthat it follows the Single-Channel Queueing Model.Analyzing the record book, he noticed that the customers’ arrival rate is 3 delivery vans per hour, and onthe average service rate is 5 delivery vans per hour. What advise can you give to the manager about theimplication of adding another service crew, or even two or more crews to increase and improve theservice rate of his loading harbor?If the manager adds one or more service crew(s), the loading harbor can still be considered as a single-channel system, because only one delivery truck ( the customer) can be served at any one time.…arrow_forward
- Suppose on a road trip to Texas you observe that three out of every four trucks on the road are followed by a car, while only one out of every five cars is followed by a truck. What fraction of vehicles on the road are trucks?arrow_forwardQueuing theory refers to the fundamental concepts of a phenomenon that we constantly experience, the concept of queues. These queues are in production processes, such as in banks, service providers, etc.Based on the concepts of Production Modeling and Simulation, do the following: a) Assuming that cars arrive at a toll, on average, every 0.5 minutes, and the toll has only one payment window, and both the time between arrivals and the time between calls follow an exponential distribution. The toll attendant takes an average of 0.3 minutes to collect. Calculate the system performance measures, ie the car arrival rate and the toll service rate.arrow_forwardA server operates with 70% utilization. The coefficient of variation for the service process is 0.6 and the coefficient of variation of the arrival process is 1. The average processing time is 3 minutes. What is the average time a customer spends in the system according to the single-server queue model? A. 9 minutes B. 6 minutes C. 3 minutes D. 7.5 minutes Consider an Erlang loss system. The average processing time is 6 minutes. The average interarrival time is 3 minutes. The number of servers is 9. What is the capacity of the system? A. 0.8 customers per minute B. 1.5 customers per minute C. 1.1 customers per minute D. 2.4 customers per minutearrow_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,