Twelve customers arrive every hour (Poisson distributed) at Andy Johnson's food truck when it parks outside the Orlando Courthouse from11-2 p.m. on weekdays. It takes Andy a mean time of 4 minutes to fill each order (following a negative exponential distribution). The WaitingLaλLine Table is provided below and also we know that W₁ =Table: Average Number of Customer in Waiting LineP.10.15.20.25.30.35.40.45.50.55.30.5560.65.70.75.80.85.90.951.01.21.41.61.82.0Poisson Arrivals, Exponential Service TimesNumber of Service Channels, M2341.0111.0264.0500.0833.1285.1884.2666.3681.5000.67223000.6722.90001.20711.63332.25003.20004.81668.100018.0500.0008.0020.0039.0069.0110.0166.0239.0333.04490333.0449.0593.0767.0976.1227.1523.18732285.2767.3333.67481.34492.84447.6734.0019.0030.00430030.0043.0061.0084.0112.0147.01890239.0300.0371.0454.0904.1778.3128.5320.8888.0031.0041.0053.0067.0158.0324.0604.1051.1739a) What is the average number of customers in the queue?Using the table, the average number of customers in the queue isresponse to four decimalplaces).5.0059.0121.0227.0398customers (round your

Queueing theory can assist in analysing these factors and forecasting queue behaviour. It can…

Answered: Twelve customers arrive every hour…

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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1. 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 is the service rate? (please include units) b.) What is the arrival rate? (please include units)
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.…
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.)
What is the answer in this number 3?
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?
How has technology had an impact on analyzing waiting line systems? How has technologyimproved waiting line performance?
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

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