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.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Please do not give solution in image format thanku 1. In a queueing system, customers arrive once every 4 seconds (standard deviation = 4) and services take 3 seconds (standard deviation = 5.1). What is the average time a customer wiill spend in the system (in seconds)?
Ali Baba‘s Car Wash Service Centre is open 6 days a week, but its busiest day isalways on Sunday. From the previous data, Ali Baba estimates that dirty carsarrive at the rate of one every two minutes. One car at a time is cleaned in thisexample of a single-channel waiting line. Assuming Poisson arrivals andexponential service times, find the following: a) Compute the average number of cars in line.
Customers arrive at a bank counter at an average rate of 3customers per hour.a) Suggest a suitable distribution to model the number ofcustomers arriving at the counter, X, per minute.b) State clearly any assumptions you have made by suggestingthis model.c) Using your model,I. Find the probability that no customer arrive in a givenminute.II. Find the probability that at most 4 customers arrive in agiven minute.III. In any given 4 minutes period, find ? such that?(? > ?) = 0.0487.IV. Check the answer of part I and part ii using RStudio.
d. What is the expected number of customers in the queue (Lg)? Number of customers(queue) e. What is the expected waiting time (in hours) in the queue (Wg)? Waiting time(queue)
What is the answer in this number 3?
4. The problem: In a queueing problem modelled as (M/M/2), if L (number of units in the system) 0.75 units and service rate for each s (server) is 3 units per hour, what is the arrival rate? To answer the problem or question, you were given the following data/statements: = (1) The average time a unit spends in the queue is 2.5 mins. (2) The average time a unit spends in the system is 22.5 hours. Which of the following appropriately describes the data/statements provided? Select the corresponding letter and support your answer. A. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient. B. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient.
The office has a single line for customers waiting for the next available clerk. There are two clerks who work at the same rate. On average customers arrive every 8 minutes and the average service rate is 5 per hour for each of the two clerks. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. b.) What proportion of time are both clerks idle? c.) Counting each person being served and the people in line, on average, how many customers would be in this system?
4.) The DMV Licensing office has a single line for customers waiting for the next available clerk. There are two clerks who work at the same rate. On average customers arrive every 8 minutes and the average service rate is 5 per hour for each of the two clerks. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. a.) What percentage of the total available service time is being used? b.) Due to Covid restrictions, only two customers are allowed in the office at the same time. What percent of the time will there be customers waiting outside?
Many banks and post offices have switched from having a line at each teller or clerk to a single waiting line cordoned off by a set of ropes or chains. Examine this change by considering the following two cases: A. Case 1. Customers arrive at a bank at an average rate of 80 per hour and form a single line. There are five tellers, and the average service time is 3.0 minutes for each teller. Assuming exponential interarrival and service times, how long is the average wait in line? B. Case 2. Customers arrive at a teller's window at a rate of 16 per hour. There are five tellers so that the total arrival rate is 80 per hour. There is separate line at each window (with no switching between lines). As in Case 1, the average service time for each teller is 3.0 minutes. How long is the average wait in line? C. Comment on the results of Cases 1 and 2. What additional factors might affect waiting times in a real banking situation?
3 The M/M/1 Queue During peak time, customers arrive at a bank teller window (with a single teller) at a rate of 23 per hour, where the teller can serve 25 per hour. This problem will allow you to investigate (via a simple extension of the mean queue size formula) the effect of highly-variable service times on our familiar queuing metrics. The diagram below stylizes the queuing system: Waiting Service Calculate the marginal probability P (T > oT). a. O b. 0.25 O c. 0.63 O d. 0.75 Calculate the mean time a customer spends at the bank (waiting time plus service time) in minutes. O a. 30 minutes O b. 27.6 minutes O c. 2.4 minutes O d. 7 minutes
please dont answer in image format. Do type Thnks
Ali Baba‘s Car Wash Service Centre is open 6 days a week, but its busiest day isalways on Sunday. From the previous data, Ali Baba estimates that dirty carsarrive at the rate of one every two minutes. One car at a time is cleaned in thisexample of a single-channel waiting line. Assuming Poisson arrivals andexponential service times, find the following: a.Compute the average number of cars in line. b.Calculate the value of probability that there are no car in the system. c.Compute the average time that a car spends in the system.

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