(M/M/s/K Model). Leia is responsible for 13 data units in the IT offices in a small business called Data Wish. Each data unit runs on an average for 3 weeks and requires an average of ½ or 0.5 weeks to get reset by Leia before it start up again. If we assign the Poisson distribution to the "arrival" of each data unit for service and an exponentia distribution to the actual service provided, answer the following questions: a. The arrival rate would be units per week and the service rate would be per week. b. Calculate the following operating characteristics for the M/M/s/K system: Utilization Factor (p) % Performance Measures
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- At the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 = average; 4 = bad. The weekly revenue earned by a machine in state 1, 2, 3, or 4 is 100, 90, 50, or 10, respectively. After observing the condition of the machine at the beginning of the week, the company has the option, for a cost of 200, of instantaneously replacing the machine with an excellent machine. The quality of the machine deteriorates over time, as shown in the file P10 41.xlsx. Four maintenance policies are under consideration: Policy 1: Never replace a machine. Policy 2: Immediately replace a bad machine. Policy 3: Immediately replace a bad or average machine. Policy 4: Immediately replace a bad, average, or good machine. Simulate each of these policies for 50 weeks (using at least 250 iterations each) to determine the policy that maximizes expected weekly profit. Assume that the machine at the beginning of week 1 is excellent.Users are connected to a database server through a network. Users request files from the Database server. The database server takes a period of time that is exponentially distributed with mean 5 seconds to process a request. Find the probability that 10 requests are processed by the server during the first 1 minutes. Determine the probability that no request is processed by the server during the first 2 minutes Determine the average number of requests processed in 2 minutesLarry Ellison starts a company that manufactures high-end custom leather bags. He hires two employees. Each employee only begins working on a bag when a customer order has been received and then she makes the bag from beginning to end. The average production time of a bag is 1.7 days, with a standard deviation of 3 days. Larry expects to receive one customer order per day on average. The interarrival times of orders have a coefficient of variation of one. X Answer Is complete but not entirely correct. (Carry at least 4 decimal places in all intermediate calculations. Round your final answer to 2 decimal places.) What is the expected duration, in days, between when an order is received and when production begins on the bag? 30.39 8 days
- The owner of an automobile repair shop studied the waiting times for customers who arrive at the shop for an oil change. The following data with waiting times in minutes were collected over a one-month period. 2 5 22 6 5 0-4 5-9 10-14 (a) Develop a frequency distribution using classes of 0-4, 5-9, 10-14, 15-19, and 20-24. Class 15-19 20-24 Total 5 6 7 15 21 0-4 5-9 10-14 15-19 20-24 Class Total 0-4 5-9 10-14 Class 15-19 0-4 20-24 5-9 (b) Develop a relative frequency distribution using the classes in part (a). If required, round your answers to two decimal places. Relative Frequency 11 4 9 6 Class 16 10-14 15-19 12 21 8 20-24 9 10 Frequency 2 % 10 3 2 3 20 .1 .50 (c) Develop a cumulative frequency distribution using the classes in part (a) .15 .1 .15 1 M ✔ ✔ ✔ S (d) Develop a cumulative relative frequency distribution using the classes in part (a). If required, round your answers to two decimal places. 10 ✔ ✓ ✔ ✔ ✔ Cumulative Frequency Cumulative Relative Frequency X X (e) What…Two methods are used to predict how many customers will call in for help in the next four days. The first method predicts the numbers of callers to be 23, 5, 14, and 20 for the four respective days. The second method predicts 20, 13, 14, and 20 for the four respective days. The actual numbers of callers turn out to be 23, 10, 15, and 19. Which method has the smaller mean absolute error (MAE)? Multiple Choice The first method The second method Cannot be determined Both methods have the same MAEWould you expect the Poisson distribution to be a good approximation of a) Runners crossing the finish line in the Boston Marathon? b) Arrival times of the students in your OSCM class?
- Larry Ellison starts a company that manufactures high-end custom leather bags. Hehires two employees. Each employee only begins working on a bag when a customerorder has been received and then she makes the bag from beginning to end. The average production time of a bag is 1.8 days, with a standard deviation of 2.7 days. Larryexpects to receive one customer order per day on average. The interarrival times oforders have a coefficient of variation of one. What is the expected duration, in days,between when an order is received and when production begins on the bag?A fast-food restaurant offers a variety of products: from pre-made packaged sandwiches to milkshakes with different flavors. Many customers order one item time, other customers order multiple items. Sometimes customers buy the pre- made items, and some customers actually ask the restaurant to cook their food while they wait. The restaurant manager has kept careful records of some queuing statistics over several weeks. According to this data, the staff needs 4 minutes on average to serve a random customer. On average, the restaurant served 120 customers on a given day. This restaurant is open from 9 AM to 9 PM every day, and has a single service counter. If you want to help the manager measure this restaurant's waiting line performance, which of the following should you use? Exponential Service Rate Model The Finite Source Model Constant Service Rate Model O The multi phase single channel modelMr Smith is working as the director of credit collection department at SISHGC Building Supplies Limited. The credit collection department recently shifted from the legacy system to a new system that was installed four months ago. Mr Smith is not happy with this newly installed system. His complaint is that the data flow from the billing and account receivable departments is not occurring in the manner originally requested. Further, the updates to the database files are not occurring as frequently as he had envisioned. Thus, the hope that the new system would provide more current and timely information has not materialised. Mr Smith claims that the systems analysts spent three days interviewing him and other workers in his department. During that time, he and the other workers thought they had clearly conveyed their needs. At this stage, Mr Smith feels as if their needs were ignored, and their time was wasted. Required: Identify the issues in the system design process. How can these…
- The University of Central Lancashire has decided to adopt a new human access control system for both employees and students using biometricfingerprint recognition. For students, the system automatically links to the central attendance management system and logs a student’s attendance,and lateness based on when they scan their fingerprint before entering the classroom. For faculty, it automatically records a staff member’s workstatus and commitment, including work status, overtime hours and holiday record. The system should interact with other local and enterprise levelapplications including scheduling and facilities management to develop the staff and student weekly schedule and also grant both faculty and studentsaccess to the specific rooms and facilities based on their schedule through fingerprint recognition software. Analysis using business support matrix. (create the table please)Assume that during minute t (the current minute isminute 1), the following sequence of events occurs: (1) Atthe beginning of the minute, xt customers arrive at the cashregister; (2) the store manager decides how many cashregisters should be operated during the current minute;(3) if s cash registers are operated and i customers arepresent (including the current minute’s arrivals), c(s, i)customers complete service; and (4) the next minute begins.A cost of 10¢ is assessed for each minute a customerspends waiting to check out (this time includes checkouttime). Assume that it costs c(s) cents to operate s cashregisters for 1 minute. Formulate a dynamic programmingrecursion that minimizes the sum of holding and servicecosts during the next 60 minutes. Assume that before thefirst minute’s arrivals, no customers are present and thatholding cost is assessed at the end of each minute.Telephone calls come into an office at random. The time between calls is the following discrete distribution: Service time Probability 6 .40 7 .30 8 .20 9 .10 When the receptionist is busy, a telephone message tells the caller that the call is important and to please wait on the line until the next reservation agent becomes available. We can assume that customers don’t hang up once they join the call queue. The service time for call follows a normal distribution with a mean of 8 mins and standard deviation of 2.5 mins Simulate the operation of the office telephone system for 1100 customers. Discard the first 100 customers and use data over the next 1000 customers to answer the following questions: What is the average waiting time for customers? What is the utilization of the receptionist? What is the probability that a customer waits for longer than 1 min before their call is answered?