3 The M/M/1 QueueDuring peak time, customers arrive at a bank teller window (with a single teller) at a rate of 23per hour, where the teller can serve 25 per hour. This problem will allow you to investigate (via asimple extension of the mean queue size formula) the effect of highly-variable service times on ourfamiliar queuing metrics. The diagram below stylizes the queuing system:WaitingServiceCalculate the marginal probability P (T > oT).a.O b. 0.25O c. 0.63O d. 0.75Calculate the mean time a customer spends at the bank (waiting time plus service time) inminutes.O a. 30 minutesO b. 27.6 minutesO c. 2.4 minutesO d. 7 minutes

λ = Arrival rate = 23 customers/hrμ = Service rate = 25 customers/hr1λ=a = Inter arrival time

Answered: 3 The M/M/1 Queue During peak time,…

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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Customers arrive at Best-Bank-in-Town’s (BBT) sole ATM location at a rate of 21 customers per hour. It is assumed that the arrival process is random. BBT recently hired an intern who estimated that the average service time is 2 minutes per customer with a standard deviation of 1.2 minutes. [Assume that the arrival rate is the same throughout the day without peak and off-peak considerations and that there is only one ATM machine at that location] 1. Calculate average waiting time for ATM user at the BBT location 2. Calculate average length of queue at the ATM location (i.e. average numbers of customers waiting for service)? 3. What is the probability that an arriving customer has no waiting time to use the ATM? 4. BBT wants to cut the average waiting time in half without necessarily adding another ATM machine. They are in discussions with their ATM software provider who has told them that their new software is very consistent with information retrieval and can greatly minimize the…
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Customers enter the camera department of a store at an average rate of six per hour. The department is staffed by one employee, who takes an average of six minutes to serve each arrival. Assume this is a simple Poisson arrival, exponentially distributed service time situation. (Use the Excel spreadsheet Queue Models.) a-1. As a casual observer, how many people would you expect to see in the camera department (excluding the clerk)? Note: Round your answer to 2 decimal places. a-2. How long would a customer expect to spend in the camera department (total time)? Note: Do not round intermediate calculations. Round your answer to the nearest whole number. b. What is the utilization of the clerk? Note: Do not round intermediate calculations. Round your answer to the nearest whole number. c. What is the probability that there are more than two people in the camera department (excluding the clerk)? Note: Round your intermediate calculations to 3 decimal places and final answer to 1…
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Wesley is having a busy afternoon working at the Cool ice cream shop. He is the only employee working because his co-worker for this shift has called in sick. It is a hot summer day and a customer arrives every five minutes on average. Wesley takes an average of four minutes to serve a customer. Assume M/M/1 and FIFO queuing system and no limits on queue size. Select the best choice. a. Since his average service capacity is greater than the average customer demand, Wesley is never busy at the Cool ice cream place. b. Wesley is busy about 85% of the time at the Cool ice cream place. c. Wesley is busy about 25% of the time at the Cool ice cream place. d. Wesley is idle (i.e., not busy) about 20% of the time at the Cool ice cream place.
Lambda Mu Probability system is empty Average number waiting for service in the queue Average number in system (queue and in service) Average time waiting for service (time in queue) vaiting time in system (waiting time plus service time) Probability arrival has to wait n= bability of n units in the system (queue and in service) 10 12 0.167 4.167 5.000 0.417 0.500 0.833 3 0.096
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Suppose the waiting time at a certain checkout counter is bi-modal. With probability 0.85, the waiting time follows an exponential distribution with a mean waiting time of four minutes. With probability 0.15, the waiting time equals 20 minutes. a) Compute the mean and median waiting time at the checkout counter. b) Compute the variance of the waiting time at the checkout counter. c) Compute the probability that an individual customer waits longer than 5 minutes at the checkout counter.
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