Suppose a coffee shop order and fulfillment process is configured simply as a single queue with twosteps: wait and service. Customers enter, wait their turn, and then are served, by placing andreceiving their order all at once. Suppose that an average of 10 customers per hour enter the coffeeshop while the shop is open.On average, there are two customers waiting in line to place their orders. It takes an average of 2minutes to go through the service step, that is, it takes 2 minutes to complete the second step ofplacing and receiving the order.In steady state,O The average wait time before placing an order is 12 minutes.O The average time between customer arrivals is 5 minutes.O None of the answers are correct.There is an average of one customer being served at a time.O The average total time to wait and be served is 15 minutes.

EXPLANATION : To see why, we can use Little's Law, which states that the average number of customers…

Answered: Suppose a coffee shop order and…

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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The program coordinator is out of town at a conference and you, as the assistant program coordinator, find yourself besieged by dozens of students needing permission to get into a very popular (but closed) class. Student arrivals are governed by the Poisson distribution with a mean of 5 minutes. Telling the students that they can't get into the closed class takes about 3 minutes, and this average is exponentially distributed. About how long does it take a student to wait in line and receive your valuable service?
There is only one copying machine in the student lounge of the business school. Students arrive at the rate of λ=50 per hour (according to a Poisson distribution). Copying takes an average of 50 seconds, or μ=72 per hour (according to a negative exponential distribution). a) The percentage of time the machine is used = percent (round your response to the nearest whole number). b) The average length of the queue = students (round your response to two decimal places). c) The average number of students in the system = students (round your response to two decimal places). d) The average time spent waiting in the queue = minutes (round your response to two decimal places). e) The average time in the system = minutes (round your response to two decimal places)
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.)
A waiting-line system that meets the assumptions of M/M/S has λ = 5, μ = 4, and M = 2. For these values, Po is approximately 0.23077, and Ls is approximately 2.05128. What is the average time a unit spends in this system? Select one: a. approximately 0.8013 b. approximately 0.4103 c. Cannot be calculated because λ is larger than μ. d. approximately 0.2083 e. approximately 0.1603
Consider a bank where potential customers arrive at rate of 60 customers per hour. However, because of limited space, one out of every four arriving customers finds the bank full and leaves immediately (without enteringthe bank). Suppose that the average number of customers waiting in line in the bank is 3.5. How long will a typical entering customer have to wait in line? (Hint: In Little’s formula, l refers only to customers who enter the system.)
Joe’s market is a small grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane at an average rate of 15 customers per hour and that the average order takes 3 minutes to ring up and bag. If Joe does not want the average waiting time in the queue to exceed 5 minutes, what would you tell Joe about his current system? Back up your statement with quantitative information and assumptions.
Customers arrive at the lone check-out desk of a certain convenience store at the average rate of 0.23 per minute. If it takes on average four minutes for the store manager to serve each customer, how many customers will on average find themselves waiting in the queue? A. 10.58 B. 0.00024 C. 3.20 D. 0.00351
People arrive randomly at a bank teller at an average rate of 20 an hour. If the teller takes an average of 1 minute to serve each customer, what is the average number of people in the system
A single server queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 6 customers per hour and an average service rate of 15 customers per hour. The average length of time customers will spend in the system is: O a. 2.667 minutes O b. 0.1111 minutes O c. 6.667 minutes O d. 0.04444 minutes
A post office has a single line for customers waiting for the next available postal clerk. There are two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. The average arrival rate is three per minute and the average service rate is two per minute for each of the two clerks. How long does the average person spend waiting for a clerk? 1.143 minutes 3.429 minutes 1.929 minutes 0.643 minute
Dean Smith is dissatisfied with the time it takes to get a new faculty ID made and believes more servers will speed up service and reduce costs thanks to shorter lines. Prof. Karen is tasked to study the situation. Prof. Karen observes an average of 20 customers/hr arriving and each technician (service window) serves 5 customer/hr, on average. Assume an M/M/s queue system. Prof. Karen calculates the operational cost of each server as $20/hr, and assumes a cost of waiting in the SYSTEM as $25/hr per customer. What is the optimal number of service windows to minimize total cost?

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