At noon time, customers arrive at Metrobank counter managed by a single cashier with mean arrival rate of 6 customers per hour. The cashier attends the customers on first come first served basis at 10 customers per hour. What is the waiting time of a customer in the queue in hours?
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At noon time, customers arrive at Metrobank counter managed by a single cashier with mean arrival rate of 6 customers per hour. The cashier attends the customers on first come first served basis at 10 customers per hour.
What is the waiting time of a customer in the queue in hours?
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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 Petroco Service Station has one pump for regular unleaded gas, which (with an attendant) can service 15 customers per minute . Cars arrive at the regular unleaded pump at a rate of 12 per minute Determine the average queue length, The average number of car in the queuing system, the average time a car is in the system, and the average time a car must wait.The Clip Joint is a hairstyling salon at University Mall. Four stylists are always available toserve customers on a first-come, first-served basis. Customers arrive at an average rate of fiveper hour, and the stylists spend an average of 35 minutes on each customer Determine the average number of customers in the salon, the average time a customer must wait, and the average number waiting to be served.
- The ticket booth on the Tech campus is operated by oneperson, who is selling tickets for the annual Tech versusState football game on Saturday. The ticket seller can servean average of 12 customers per hour (Poisson distributed);on average, 8 customers arrive to purchase tickets eachhour (Poisson distributed). Determine the average time aticket buyer must wait and the portion of time the ticketseller is busy.The ticket booth on the Tech campus is operated by one person, who is selling tickets for the annual Tech versus State football game on Saturday. The ticket seller can serve an average of 12 customers per hour (Poison distributed); on average, 8 customers arrive to purchase tickets each hour (Poison distributed). Determine the average time a ticket buyer must wait and the portion of time the ticket seller is busy.For each of the following queuing systems, indicate whether it is a single or multiple-server model, the queue discipline, and whether it’s calling population is infinite or finite. Hair salon Bank Laundromat Doctor’s office Advisor’s office Airport runway Service station Copy centre Team trainer Mainframe computer
