CPU-on-Demand (CPUD) offers real-time high-performance computing services. CPUD owns 1 supercomputer that can be accessed through the Internet. Their customers send jobs that arrive, on average, every 5 hours. The standard deviation of the interarrival times is 5 hours. Executing each job takes on average 3 hours on the supercomputer and the standard deviation of the processing time is 4.5 hours. How long does a customer have to wait to have a job completed?

CPU-on-Demand (CPUD) offers real-time high-performance computing services. CPUD owns 1 supercomputer that can be accessed through the Internet. Their customers send jobs that arrive, on average, every 5 hours. The standard deviation of the interarrival times is 5 hours. Executing each job takes on average 3 hours on the supercomputer and the standard deviation of the processing time is 4.5 hours. How long does a customer have to wait to have a job completed?

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Description: CPU-on-Demand (CPUD) offers real-time high-performance computing services. CPUD owns 1 supercomputer that can be accessed through the Internet. Their customers send jobs that arrive, on average, every 5 hours. The standard deviation of the interarriv

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section: Chapter Questions

Problem 52P

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CPU-on-Demand (CPUD) offers real-time high-performance computing services. CPUD owns 1 supercomputer that can be accessed through the Internet. Their customers send jobs that arrive, on average, every 4 hours. The standard deviation of the interarrival times is 4 hours. Executing each job takes, on average, 3 hours on the supercomputer and the standard deviation of the processing time is 3.6 hours. On average, how long will it take to complete a job (from the time it is submitted by the customer until the time it is completed)?
An emergency room (ER) at a Prisma Health Hospital has 10 total beds it can hold patients, i.e., the capacity of the queueing system of this ER is 10. Patients arrive to the ER at a rate of 5 per hour. Therefore, we have that λn = 6 for n = 0, 1, . . . , 9 and λ10 = 0 for this queueing system. A patient is seen by an ER doctor as the ‘service’ of this queueing system. The amount of time required for an ER doctor to treat a patient is exponentially distributed with a mean of .4 hours. We seek the minimum number of ER doctors so that the expected time of a patient waiting to be seen (so the Wq) is less than or equal to 15 minutes (.25 hours). You should begin by analyzing s = 1 and show any calculations that were used to determine Wq for each number of servers that you considered until you meet the target metric.
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!
We are in a M/M/1/3 queueing system in which we wish to determine the cost of operating the system. Each customer in the queue costs us $100 per hour and each customer being served costs us $50 an hour. Customers arrive at a rate of 4 per hour and the server can serve customers at a rate of 5 per hour. The following table in the picture provides Pn values, W, and Wq:
PepsiCo sells its soft drinks in approximately 400,000 retail establishments, such as supermarkets, discount stores, and convenience stores. Sales representatives call on each retail account weekly, which means each account is called on by a sales rep 52 times per year. The average length of a sales call is 75 minutes (or 1.25 hours). An average salesperson works 2,000 hours per year (50 weeks per year * 40 hours perweek), but each spends 10 hours a week on nonselling activities, such as administrative tasks and travel. How many salespeople does PepsiCo need?
The 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.…
The manager of a regional warehouse must decide on the number of loading docks to request fora new facility in order to minimize the sum of dock costs and driver-truck costs. The manager haslearned that each driver-truck combination represents a cost of $300 per day and that each dockplus loading crew represents a cost of $1,100 per day.a. How many docks should be requested if trucks arrive at the rate of three per day, each dockcan handle five trucks per day, and both rates are Poisson?
A manufacturing cell has 4 operators (working independently in parallel) and a shared buffer space that can fit at most 6 incoming jobs. During a production period, jobs arrive to the cell with rate of 10 jobs per hour (Poisson arrival, i.e., exponential inter-arrival time). The average processing time of a job is 30 minutes (exponentially distributed service time). Answer the following questions using the analytical formulas learned in class. (a) Which queueing model should be used to model this problem? (b) What is the long-term average waiting time of a job in the buffer? (c) What is the probability that an arriving job cannot be admitted into the cell due to full occupancy? (d) If the desired the rejection probability is no more than 10% in this case, what would you suggest? Use calculations to justify your answer.
A supermarket has just added a new cash register to reduce the waiting times of the customers during weekends. Since a new cash register is added, the customers expect that their waiting time will be less than the waiting time before the cash register was added. Suppose the sample variance of the waiting times for 25 customers before adding the new cash register is sĩ = 4.8 minutes, while the sample variance of the waiting times for 25 customers after adding the cash register is sź = 2.2 minutes. The manager of the supermarket believes that the waiting times are normally distributed and that the two samples are drawn independently. What is the conclusion? Given that all other criteria are satisfied, should the supermarket continue with the new cash register?