What is the average time a car is in the system? b. What is the average number of cars in the system? c. What is the average time cars spend waiting to receive service?
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12-17 Automobiles arrive at the drive-through window at a post office at the rate of four every 10 minutes. The average service time is 2 minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed.
a. What is the average time a car is in the system?
b. What is the average number of cars in the system?
c. What is the average time cars spend waiting to receive service?
d. What is the average number of cars in line behind the customer receiving service?
e. What is the probability that there are no cars at the window?
f. What percentage of the time is the postal clerk busy?
g. What is the probability that there are exactly two cars in the system?
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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?Repair calls are handled by one repairman at a photocopy shop. Repair time, including traveltime, is exponentially distributed, with a mean of two hours per call. Requests for copierrepairs come in at a mean rate of three per eight-hour day (assume Poisson).A) Identify the Queuing Model and sketch the system.B) What is the arrival rate?C) What is the service rate?D) What is the average number of customers awaiting repairs?At a border inspection station, vehicles arrive at the rate of 10 per hour in a Poisson distribution. For simplicity in this problem, assume there are only one lane and one inspector, who can inspect vehicles at the rate of 12 per hour in an exponentially distributed fashion.a. What is the average length of the waiting line?b. What is the average time that a vehicle must wait to get through the system?c. What is the utilization of the inspector?d. What is the probability that when you arrive there will be three or more vehicles ahead of you?
