Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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Twenty-one customers arrive every hour (Poisson distributed) at Andy Johnson's food truck when it parks outside the Orlando Courthouse from 11-2 p.m. on weekdays. It takes Andy a mean time of 2 minutes to fill each order (following a negative exponential distribution). The Waiting Line Table is provided below and also we know that ...
a) What is the average number of customers in the queue?
Using the table, the average number of customers in the queue is ______ customers (round your response to four decimalplaces).
b) How long will a person wait in line on average?
The average time a person spends in the queue is ______ minutes(round your response to two decimal places).
c) If Andy's wife joins him in serving meals (at the same speed as Andy), how will your answers to parts a and bchange?
Using the table, the new average number of customers in the queue is _________ customers (round your response to four decimal places).
The new average time a person spends in the queue is _________ minutes (round your response to two decimal places).
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- Customers in a small retail store arrive at the single cashier on average every 6 minutes. The average service time for the cashier is 5 minutes.Arrivals tend to follow a Poisson distribution, and service times follow anexponential distribution. We need to analyze this waiting-line system. (g) Should the retail store consider creating a second cashier lane?(h) A cash machine manufacturer has offered an advanced system that willreduce service time to 2 minutes per customer. The cost of the newmachine would be the same as opening a second cashier lane, so theowner has decided to buy the new system only if it reduces wait timesover the two-cash option. Evaluate the two options (advanced cash or atwo-cash system) and suggest which option you would choose.arrow_forwardAli 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.arrow_forwardA 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.)arrow_forward
- 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?arrow_forward3 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 minutesarrow_forward
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