A car mechanic, Carlos, can install new mufflers at an average rate of 3 every hour(following an exponential distribution). Customers needing this service arrive at the shop(following a Poisson distribution) on an average of 2 per hour. They are served on a first-in,first-out basis and come from the very large (almost infinite) population of possible buyers.Calculate the following operating characteristics of the service system:a. The probability there are no cars in the system.b. The average number of cars waiting in line.c. The average number of cars in the system.d. The average time a car spends waiting in line.e. The average time a car spends in the system.

Note: - Since we can answer only up to three subparts we will answer the first three subparts(a, b,…

Answered: A car mechanic, Carlos, can install new…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 9P

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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?
Marty's Barber Shop has one barber. Customers have an arrival rate of 2.2 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that no units are in the system? If required, round your answer to four decimal places.P0 = fill in the blank 1 What is the probability that one customer is receiving a haircut and no one is waiting? If required, round your answer to four decimal places.P1 = fill in the blank 2 What is the probability that one customer is receiving a haircut and one customer is waiting? If required, round your answer to four decimal places.P2 = fill in the blank 3
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…
Lambda Mu Probability system is empty Average number waiting for service in the queue Average number in system (queue and in service) Average time waiting for service (time in queue) vaiting time in system (waiting time plus service time) Probability arrival has to wait n= bability of n units in the system (queue and in service) 10 12 0.167 4.167 5.000 0.417 0.500 0.833 3 0.096
You are the manager of a local bank where three tellers provide services to customers. On average, each teller takes four minutes to serve a customer. Customers arrive, on average, at a rate of 40 per hour. Having recently received complaints from some customers that they waited a long time before being served, your boss asks you to evaluate the service system. Specifically, you must provide answers to the following questions: a. The average utilization of the three-teller service system is p= 0.8889. (Enter your response rounded to four decimal places.) b. The probability that no customers are being served by a teller or are waiting in line is Po= 0.0280. (Enter your response rounded to four decimal places.) c. The average number of customers waiting in line is L₁ = customers. (Enter your response rounded to one decimal place.)
An average of 17 cars per hour arrive at a single-server drive-in teller. Assume the average service time for each customer is 4 minutes, and both interarrival times and service times are exponential. Answer the following questions:a. What is the mean arrival time? b. What is the mean service time? c. What is the probability that the teller is busy?d. What is the average number of cars waiting in line for the teller? e. What is the average amount of time a drive-in customer spends waiting in the parking lot? f. What is the average number of cars in the system? g. Describe the possible behavior of customer arrivals. Justify your answer.

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