At a fashion retailer, there are 3 cashiers providing checkout service simultaneously.On average, customers arrive at the checkout area every 6 minutes. It has beenestimated that the arrival process is a Poisson process. The average checkout timefor each customer is 12 minutes, with its standard deviation equal to 16 minutes.Suppose that customers form a single line.What is the average length of the line (i.e., average number of customers in thewaiting line)?Note: 1. Keep 2 decimal places for your final answer. Either use Excel for yourcalculation, or keep at least 4 decimal places for your intermediate numbers.2. The Poisson arrival process has exponentially distributed inter-arrival times.

A Small Introduction to Retailers Retail is an agreement where the dealer offers little amounts of…

Answered: At a fashion retailer, there are 3…

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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Josh’s Hot Dogs is a one-person hot dog stand, and normally gets about 14 customers per hour. Assuming that Josh can serve one customer in about 3 minutes. What impact does this have on the queuing characteristics? Specifically, the following questions:a. Mean number of customer in the queue b. Mean number of customer in the system: c. Mean waiting time in the queue:d. Mean waiting time in the system:e. Utilization factor for the system:f. Probability of more than 1 customer in the system at any given time.g. Do you think he has an acceptable queuing system?
. At a car washing service facility customers arrive at the rate of 8 cars per hour. The service can manage an average of 12 cars per hour. The arrivals follow a Poisson distribution and the service follows a Exponential distribution. Calculate a) Utilization of the system b) Average number of customers in the system c) Average time customers spend in the system
Give typing answer with explanation and conclusion
1
Last National Bank is concerned about the level of service at its single drive-in window. A study of customer arrivals during the window’s busy period revealed that, on average, 20 customers per hour arrive, with a Poisson distribution, and they are given FCFS service, requiring an average of 2 minutes, with service times having a negative exponential distribution. a. What is the expected number of customers waiting in queue? b. If Last National were using an automated teller machine with a constant service time of 2 minutes, what would be the expected number of drive-in customers in the system? c. There is space in the drive for three cars (including the one being served). What is the probability of traffic on the street being blocked by cars waiting to turn into the bank driveway? d. Last National is considering adding tellers at the current drive-in facility. It has decided on $5 per hour as the imputed cost of customer waiting time in the system. The hourly cost of a teller is $10.…
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.
Consider a bank branch that has three distinct customer arrival patterns throughout the day, as measured by average arrival rates (below). Morning (8:30 - 11:30): arrival 1 = 47 per hour. %3D Lunch (11:30 - 1:30): arrival 2 = 70 per hour. Afternoon (1:30 - 4:00): arrival 3 = 30 per hour. Regardless of the time of day, the average time it takes for a teller to serve customers is 3.17 minutes. Because of competition with other banks in the area, management has developed an internal goal to keep the average customer wait before service to be less than 4 minutes. With that in mind, answer the following: a. During the morning period, what is the minimum number of tellers that the bank needs to hire to achieve the 4-minute service goal mentioned above? [ Select] b. During lunch, what is the minimum number of tellers that the bank needs to hire to achieve the 4 minute service goal mentioned above? [ Select ] c. In the afternoon, what is the minimum number of tellers that the bank
A fast-food restaurant has one drive-through window.On average, 40 customers arrive per hour at thewindow. It takes an average of one minute to serve acustomer. Assume that interarrival and service timesare exponentially distributed.a. On average, how many customers are waiting in line?b. On average, how long does a customer spend at therestaurant (from time of arrival to time service iscompleted)?c. What fraction of the time are more than three carsin line? (Here, the line includes the car, if any,being serviced.)
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?
A university is considering setting up an information desk manned by one employee. Based on information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 18 per hour. It takes an average of 2 minutes to answer a question. It is assumed that arrivals are Poisson and answer times are exponentially distributed. 7. Find the average time a person seeking information spends at the desk. 8. Find the expected time a person spends just waiting in line to have a question answered. 9. What is the probability there are exactly 2 people in the system? 10. What is the probability there are more than 4 people in the system?
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

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