Savemore has 4 check-out counters. Prediction says that the duration of customer transaction is exponentially distributed with a mean of 4.9 minutes. In the peak hour, customer arrivals are exponentially distributed with a mean arrival rate of 17.3 customers/hr. Determine the probability that a customer will wait in a queue? Answer in four decimal places.
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A: Compute P0: Hence, the probability of no customers in the system is 0.2.
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A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…
Q: Note: Formulas to solve the following problems are given in the class and example problems were…
A: Arrival rate λ = 603 =20 per hour Service rate μ = 602.4…
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A: Formulas used:
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A: Below is the solution:-
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A: Find the Calculation methods below: Arrival rate (λ)= 30 customers per hourService rate (μ) = 50…
Q: Customer arrive at one-window drive in bank according to Poisson distribution with mean 10 per hour.…
A: Given- Arrival rate (λ) = 10 customer per hourService rate (μ) = 60 min5= 12 customer per hour
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A: Arrival Rate = Service Rate =
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A: Given- Price of Gasoline if a customer will wait = Php 45 Price of Gasoline if a customer will not…
Q: Auto vehicles arrive at a petrol pump, having one petrol unit, in Poisson fashion with an average of…
A: THE ANSWER IS AS BELOW:
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A: Note: - Since the exact question to be answered is not specified, we will answer only the first…
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A: 1. 0.33 2. Grade F
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A:
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A: This formula shows P or the Probability of having a server that is idle. P0 is the probability of…
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- During nearly four decades of business operations, Memphis-based FedEx has earned a reputation for reliable, on-time delivery of packages to homes and offices around the country. Founder Fred Smith originally focused on overnight deliveries, choosing Memphis as the company’s headquarters because the airport rarely closes due to bad weather. With FedEx’s planes departing and arriving on schedule nearly all the time, its express shipments usually remained on schedule, then and now. To reassure customers that delivery will take place when and where promised, the firm offers a money-back guarantee on time-sensitive express shipments, among other services. FedEx has steadily expanded its portfolio of services since the 1970s. Its original overnight express delivery is currently available to U.S. customers in various forms, including “first-overnight” delivery, next-morning delivery, next-afternoon delivery, and budget-pleasing two- or three-day delivery. The company’s services also include cost-effective ground delivery for parcels and extra-speedy same-day delivery for urgent deliveries within 1,800 cities. Over the years, FedEx has widened its delivery network to more than 220 countries. It has purchased more cargo jets and acquired specialized shipping firms, including Tiger International, Roberts Express, RPS, and TNT Express, to support global growth. For international business customers needing products, parts, or raw materials shipped across countries or continents, the company now offers time-saving services such as commercial freight forwarding and cross-border logistical support. To add the convenience of local drop-off and pickup points for U.S. consumers and small businesses, FedEx acquired the Kinko’s office services company in 2004 and later rebranded it as FedEx Office. This acquisition also added printing and copying to the menu of services offered. Then the company arranged for large U.S. retailers such as Walgreens, Albertsons, Kroger, and Safeway to accept packages for shipment and receive package delivery for customer pickup in thousands of store locations. This means people who want to send a package can head to a nearby retailer and ship where they shop, rather than making a separate trip to the FedEx location. It’s also a safe alternative for packages to be picked up by people who don’t want FedEx shipments left by the front door. Another service FedEx offers to small and mid-sized businesses, including retailers, is FedEx Fulfillment. The purpose is to expedite order fulfillment by having each business store its products in a FedEx warehouse. Then, when the business’s customers place orders, FedEx puts the products into boxes bearing the business’s own logo and ships directly to those customers. The business doesn’t need a separate warehouse or staff for fulfillment, and packages are on their way to customers more quickly because the products were in FedEx’s warehouse, ready to be packed and shipped. This service puts FedEx into direct competition with Amazon.com, which offers a similar service to merchants that sell through the online Amazon Marketplace. But it also gives businesses that don’t sell via Amazon a fast and professional fulfillment alternative. FedEx is careful to let customers know, through media and social-media announcements, when it anticipates that extreme weather or other conditions will cause delays or force it to halt pickups and deliveries. For the duration of Hurricane Irma, for example, FedEx said it would suspend deliveries in Florida. Some Florida customers who had ordered generators to be delivered via FedEx were unhappy, because they worried about being without power during and after the storm. But one FedEx employee loaded several generator orders into his car and took them to customers himself. When a customer posted a grateful compliment to FedEx on Facebook, the message generated thousands of likes, shares, and positive comments. The company also received positive comments for its donations of cash and transportation services to areas devastated by Hurricanes Irma, Harvey, and Maria. According to the American Customer Satisfaction Index (ACSI), FedEx often tops the list of U.S. shipping companies as ranked by customers surveyed. Every day, the company delivers 13 million packages—and during the busy year-end holiday season, it delivers many more. By meeting customers’ expectations for on-time deliveries, FedEx has increased annual revenues beyond $60 billion and positioned itself for continued growth in the future. How does FedEx’s money-back guarantee address customers’ concerns about heterogeneity?The common measures of a queuing system's performance include: O probability that the service facility will be idle, average queue length, and probability that the waiting time will exceed a specified duration. average time each customer spends in the system, probability that the service system will be idle, and average time each customer spends in the queue. average queue length, maximum time a customer may spend in the queue, and the utilization factor for the system. average time each customer spends in the system, maximum queue length, and probability of a specific number of customers in the system. maximum queue length, maximum time a customer may spend in the queue, and average queue length.Tony’s Barbershop is run, owned, and operated by Anthony Jones, who has been cutting hairfor more than 20 years. Anthony does not take appointments, so the arrival pattern of customers is essentially random. Traditionally, the arrival rate had been about one customer every50 minutes. Two months ago, the local paper ran an article about Anthony that improved business substantially. Currently, the arrival rate is closer to one customer every 35 minutes. Haircutsrequire an average of 25 minutes, but the times vary considerably depending on customerneeds. A trim might require as little as 5 minutes, but a shampoo and styling could take as longas an hour or more. For this reason, the exponential distribution seems to provide a reasonablygood fit of the service time distribution.Anthony’s customers have always been patient, but ever since business picked up, somehave complained that the wait is too long. Anthony is considering taking his cousin Marvin intothe business to improve customer…
- What is the answer in this number 2?OPERATIONS RESEARCH Auto vehicles arrive at a petrol pump, having one petrol unit, in Poisson fashion with an average of 10 units per hour. The service time is distributed exponentially with a mean of 3 minutes. Find the following: Average number of units in the system Average waiting time iii. Average length of queue Probability that a customer arriving at the pump will have to wait The utilization factor for the pump unit Probability that the number of customers in the system is 2.A radio repairer notes that the time he spends on his job has an exponential distribution with a mean of 4 minutes. He follows the first come first serve principle. The arrival time of clients takes a Poisson distribution with an average rate of 8 clients every 1 hour.Determine the arrival rate value , service rate value to be used,time taken by aclient waiting in the queue Determine the client’s average waiting time in the system and Compute the probability that the system is idle; P (idle)
- A computing facility has a large computer server dedicated to service on-line applications from users who are scattered about the country. The facility uses an M/M/1 queueing system where the arrival pattern of requests for online applications are random (Poisson distribution with 1 = 4/sec), and the service time provided is random (exponential distribution with µ = 6/sec). Question: 1. What is the probability that the system is idle? 2. Based on grading scale below, what is the [approximate] grade that depicts the utilization of this system? F D A 10 20 30 40 50 60 70 80 90 100 3. There are talks of upgrading the queueing system to M/M/C such that the workload be equally divided between 2 smaller computer servers each with half the service rate of the original machine. Use the Report or summary R-functions to verify the following claims: a. The mean number of [clients] in the queue will not change. Is this claim justified? b. The mean time spend in the system will not change. Is this…Customer arrive at one-window drive in bank according to Poisson distribution with mean 10 per hour. Service time per customer is exponential with mean 5 minutes. There are three spaces in front of the window, including the car being served. Other arriving cars can wait outside these three spaces. A. What is the probability that an arriving customer can enter one of these three spaces? B. What is the probability that an arriving customer is expected to wait outside the three spaces. C.How long is an arriving customer expected to wait before starting service.Below are the data of the gasoline station. Number of gas pumps = 1 Policy of the gasoline station is "If you want to wait, pay PhP45 per liter; if you do't want to wait, pay PhP55/liter." Service mean time (exponential distribution) = 5 minutes Arrival rate (Poisson distribution) = 10 per hour. Customers usually wait to buy gasoline. a) What is the probability (in decimal) that customer will wait? Answer in 4 decimal places.b) Determine the probability that the customer will not wait. Answer in 4 decimal places.c) How many customers are falling in line? Answer in integer value.d) Determine the expected price of gasoline per liter.
- Given information: A typical TSA agent at Piedmont Triad International Airport takes approximately 1.15 minutes to screen each passenger that arrives at the security gate. During the day, a passenger arrives at the gate on average every 1.3 minutes. Both the service rate and arrival rate follow a Poisson distribution. Based on this information and the assumption that only one screening line is open at the security gate, answers the following questions. Round calculations to at least 3 decimal places. Note: Round each calculation to at least 3 decimal places. Arrival time =60/1.3=46.153 Server Rate =60/1.15=52.174 L=expected number of passengers in queue =6.780 waiting time in queue =.1469 time spent screening=.1660 please answer the 2 foloowing questions What is percent of the time does the typical TSA agent spend actively screening passengers? Throughout the day, passenger arrival rates vary with the greatest number of passengers arriving about 45 minutes before a flight is…13. Movie Tonight is a typical video and DVD movie rental outlet for home viewing customers. During the weeknight evening, customers arrive at Movies Tonight at the average rate of 1.25 customers per minute. The checkout clerk can serve an average of two customers per minute. Assume Poisson arrivals and exponential service times.What is the probability that no customers are in the system?What is the average number of customers waiting services?What is the average time a customer waits for service to begin?Do the operating characteristics indicate that the one-clerk check out system provides an acceptable level of service?Consider a bank branch that has three distinct customer arrival patterns throughout the day, as measured by average arrival rates (below). Morning (8:30 - 11:30): arrival 1 = 47 per hour. %3D Lunch (11:30 - 1:30): arrival 2 = 70 per hour. Afternoon (1:30 - 4:00): arrival 3 = 30 per hour. Regardless of the time of day, the average time it takes for a teller to serve customers is 3.17 minutes. Because of competition with other banks in the area, management has developed an internal goal to keep the average customer wait before service to be less than 4 minutes. With that in mind, answer the following: a. During the morning period, what is the minimum number of tellers that the bank needs to hire to achieve the 4-minute service goal mentioned above? [ Select] b. During lunch, what is the minimum number of tellers that the bank needs to hire to achieve the 4 minute service goal mentioned above? [ Select ] c. In the afternoon, what is the minimum number of tellers that the bank
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