Answer the given question with a proper explanation and step-by-step solution. Use the information. A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poison distribution at the rate of 2.5 per minute. In serving themselves, customers take about 22 seconds, exponentially distributed.Use formulas to solve, no excel. Show all work. a. How many customers would you expect to see, on average, at the coffee urn? b.How long would you expect it to take to get a cup of coffee? c.What percentage of time is the urn being used?

Answer the given question with a proper explanation and step-by-step solution. Use the information. A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poison distribution at the rate of 2.5 per minute. In serving themselves, customers take about 22 seconds, exponentially distributed.Use formulas to solve, no excel. Show all work. a. How many customers would you expect to see, on average, at the coffee urn? b.How long would you expect it to take to get a cup of coffee? c.What percentage of time is the urn being used?

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

See similar textbooks

Similar questions

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?
A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the um follow a Poisson distribution at the rate of three per minute. In serving themselves, customers take about 15 seconds, exponentially distributed. a. How many customers would you expect to see on the average at the coffee um? b. How long would you expect it to take to get a cup of coffee? c. What percentage of time is the urn being used?
A student arrive in a photocopy service. There is only one photocopy operator, and the time required for inquiry varies from student to student. The average arrival rate is 12 students per hour, and the average service rate is 20 students per hour. What is the average service time for this problem? Select one: a. 2.28 minutes b. 4.35 minutes c. 3 minutes d. 1 minute
A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of three per minute. In serving themselves, customers take about 15 seconds, exponentially distributed.a. How many customers would you expect to see, on average, at the coffee urn?b. How long would you expect it to take to get a cup of coffee?c. What percentage of time is the urn being used?d. What is the probability that three or more people are in the cafeteria?e. If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constanttime of 15 seconds, how does this change your answers to (a) and (b)?
A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of 4.0 per minute. In serving themselves, customers take about 11 seconds, exponentially distributed. a. How many customers would you expect to see on the average at the coffee urn? b. How long would you expect it to take to get a cup of coffee? c. What percentage of time is the urn being used? d. What is the probability that three or more people are in the cafeteria? e. If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 11 seconds, how many customers would you expect to see at the coffee urn (waiting and/or pouring coffee)? f.If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 11 seconds, how long would you expect it to take (in minutes) to get a cup of coffee, including waiting time?
Circle Electric Supply is considering opening a second service counter to better serve their electrical contractor customers. The arrival rate is 11 per hour. The service rate is 16 per hour. If the cost of waiting is $31 and the cost of each service counter is $23 per hour, should the second counter be opened? (Give your numerical values in dollars per hour. Round your answers to two decimal places.) With one counter, the cost per hour is $ . With two counters, the cost per hour is $ . The second counter ---Select--- should should not be opened.
Benny the Barber owns a one-chair shop. At barber college, they told Benny that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of two per hour. It will take Benny an average of 20 minutes to give a haircut. Based on these figures, find the following: Part (a): The average number of customers waiting. Arrival Time, λ =2 customers per hour Service Time, μ = 20 minute, or 60/20= 3 customer per hour Lq = (2)2 / 3*(3-2) = 1.333 customers Part (b): The average time a customer waits. Wq= 1.333/2=0,665 \~ 0,67 or 40 minutes Part (c): The average time a customer is in the shop. LS = 2/ 3-2 =2 customers. WS = 2/2 = 1 hour Part (d): The average utilization of Benny’s time. P= λ/ μ = 2/3=0,666 percent ~ 0,67 % Benny the Barber (see Question 1) is considering the addition of a second chair. Customers would be selected for a haircut on a FCFS basis from…
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…
The coefficient of variation for inter-arrival times of customers arriving at a sandwich shop is equal to 3. If the standard deviation of the inter-arrival times is 1 minute(s). What is the average inter-arrival time in minutes? Round answer to two decimal places.
A suburban specialty restaurant has developed a single drive-thru window. Customers order, pay, and pick up their food at the same window. Arrivals follow a Poisson distribution, while service times follow an exponential distribution. If the average number of arrivals is 6 per hour and the service rate is 2 every 15 minutes, what is the average number of customers in the system? a.0.50 b.4.00 c.2.25 d.3.00 e.none of the above The answer is not 2.25
Patients arrive at your emergency room at a rate of 2 per hour. The average service time per patient is 20 minutes. In other words, you treat an average of 3 patients per hour if patients come in that fast. 1. To proceed with your analysis, what do you assume about the distributions of arrivals and service times? 2. What is the average number of patients in the ER (waiting or being served?) (Use formulae on p.21-22) 3. What is the average length of time that patients spend from the time they enter the ER to the time they leave?
A vending machine dispenses hot chocolate or coffee. Service time is 45 seconds per cup and is constant. Customers arrive at a mean rate of 59 per hour, and this rate is Poisson-distributed. a. Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.) Average number of customer b. Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average time minutes c. Determine the average number of customers in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average number customers