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.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 9P

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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?
In most cases, if a firm increases its service capacity by 10 percent, it would expect waiting times to be reduced by what percentage? Assume customerarrivals and service times are random. An ice cream stand has a single window and one employee to serve customers. During their busy season, 30 customers arrive each hour, on average. It takes 1.5 minutes, on average, to serve a customer.What is the utilization of the employee? How long would customers have to wait in line, on average, at the ice cream shop discussed in question 7? Random service times can be modeled by this. A bank teller takes 2.4 minutes, on average, to serve a customer. What would be the hourly service rate used in the queuing formulas? There are three teller windows in the bank described in the prior question. On average, 60 customers per hour arrive at the bank. What will be the average number of customers in line at the bank?
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