Demand at the Krispy Kreme drive-through has jumped up with the new restrictions on inside dining. Customers are arrivingaccording to a Poisson process, at an average of 5 minutes between customers. It takes 4 minutes to serve a car.There is only one drive through channel.Answer the following questions.a. What model best matches this situation?Model used:(time units)|(time units)arrival rate:perpopulation:("infinite" or a number)service rate:perservers:b. What is the average number cars in the drive-through, including the one being served?c. How long does it take, on average, for a customer to get the product?(time units)d. What is the probability that a customer will show up and not find anyone in the drive-through?e. What is the probability that there will be 3 or more cars in the drive through when a customer arrives?(don't count the customer who is arriving)

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Answered: Demand at the Krispy Kreme…

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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Jolt - Exp The soda machine outside the lecture hall sees a steady stream of customers throughout the day. While the machine takes 4 seconds to deliver a can of carbonated sugar water once the button is pressed, the student customers introduce variation into the delivery process by pondering their selection for a while_ Thus, we can safely say that the service time is governed by a negative exponential probability distribution that averages 10 seconds. Over the course of a twelve hour lecture day, students arrive at the rate of 240 per hour, Poisson distributed of course. Nathan is cutting it close today. At 10:00:00 AM, the professor will close the door to the classroom and ignore any requests to enter the room once his scintillating lecture has begun. What is the probability that he finds only one person at the machine buying a soda?
The Minute Stop Market has one pump for gasoline, which can service 10 customers per hour (Poisson distrib-uted). Cars arrive at the pump at a rate of 5 per hour (Poisson distributed). a. Determine the average queue length, the average time acar is in the system, and the average time a car must wait.b. If, during the period from 4:00 P.M. to 5:00 P.M., thearrival rate increases to 12 cars per hour, what will bethe effect on the average queue length?
I ONLY NEED NUMBER 4 LETTERS A-C 3. Sharp Discounts Wholesale Club has two service desks, one at each entrance of the store. Customers arrive at each service desk at an average of one every six minutes. The service rate at each service desk is four minutes per customer. 4. Sharp Discounts Wholesale Club is considering consolidating its two service desks (see Problem 3) into one location, staffed by two clerks. The clerks will continue to work at the same individual speed of four minutes per customer. a. What is the probability of waiting in line? b. How many customers, on average, are waiting in line? c. How much time does a customer spend at the service desk (waiting plus service time)? d. Do you think the Sharp Discounts Wholesale Club should consolidate the service desks?
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? d. What is the probability that three or more people are in the cafeteria?

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