Project 2: ATM’s & QueuesATM’s & QueuesSlide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11ATM’s & QueuingSlide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Project 2: ATM’s & QueuesATM’s & QueuesCertain business situations require customers to wait in line for a serviceExamples:Waiting to use an ATM machinePaying for groceries at the supermarketA line of people or objects is called a “queue”ATM’s & QueuesQueues occur in many places:Running multiple programs on a computerA print queue is formed when many documents are sent to the printerTelephone calls on a switchboardVehicles waiting at a traffic lightATM’s & QueuesStudying how these lines form and how to manage them is called Queuing TheoryQueuing Theory has become an important tool in business decisions regarding quality and expense of customer serviceExample: Supermarket manager sees checkout lines are too long, so more cashiers are called to work the registers, but this costs more moneyATM’s & QueuesAutomated services make queue theory important when direct monitoring of service isn’t possibleExample: Bank manager can’t monitor ATM machine service at mid-night.Opening up more machines might improve customer service but may cost a lot of moneyATM’s & QueuesManaging queues is a balancing act:Customer Satisfaction$$$$$$$$$$$$$$$$$$ATM’s & QueuesTwo Queue ModelsStandard QueueSerpentine QueueATM’s & QueuesStandard QueueCustomers select what they believe to be the shortest or most rapidly moving line from individual queues at several stations.This model is used at most supermarkets.ATM’s & QueuesSerpentine ModelCustomers form a single line, and advance to the front to get their service.Used at most airline ticket counters and in many post officesATM’s & QueuesAnalyzing how to manage queues often uses computer simulationTwo types of SimulationMonte CarloBootstrappingATM’s & QueuesMonte Carlo SimulationSample data is used to estimate the actual probability distribution of some random variable. This theoretical distribution is then used to generate new samples.ATM’s & QueuingBootstrappingWhen the data does not indicate any known theoretical probability distribution, we can simulate new data by random sampling from the original dataATM’s & QueuesClass ProjectThe People’s Bank has 3 ATM’sAt least one ATM is available 24 hours a day 7 days a weekBank manager has records of ATM usage and customer service times for 5 weeksATM’s & QueuesMean numbers of customers arriving for ATM usage during every hour of the week is contained in Queue Data.xls.The complete arrival data for the 9:00 a.m. and 9:00 p.m. hours on Fridays are shown in that file as well.These hours happen to be the bank’s busiest days of service.ATM’s & QueuesWe will study the queues for the ATM’s during:The 9:00am hour on FridayThe 9:00pm hour on FridayThe starting and ending times of ATM service were recorded for each arriving customer.Data for these service times during the first week of record keeping are shown in Queue Data.xls.ATM’s & QueuesBank manager wants to avoid long wait times, long queue lengths, and do this using the least number of ATM’sThe bank manager would like to know what level of service to provide for managing the queues based on:Services Times for individual customersThe number of customers waiting to be servedATM’s & QueuesTerms:Wait Time (in min): The period of time that a customer must wait between arrival and the start of his or her access to an ATMDelayed: A person who must wait more than 5 minutesNumber in Queue: the number of people in line waiting before an arriving customer can reach an ATMIrritated: queue length is more than 3 customersTotal Present: the total number of patrons present in the queueATM’s & Queues The bank manager is looking at three advertising claims for service times:(Mean Wait Claim) The mean waiting time is at most 1 minute.(Maximum Wait Claim) No one will wait more than 12 minutes.(Percent Delayed Claim) At most 5% of the customers will be delayed (wait more than 5 minutes)ATM’s & QueuesThe bank manager is also looking at three advertising claims for the number of customers waiting in line:(Mean Queue Claim) The mean number of people in the queue will not exceed 8.(Percent Irritated Claim) At most 2% of the customers will be irritated (find more than 3 people in line or waiting to be served).(Maximum Present Claim) The total number present will never exceed 10.ATM’s & QueuesProject Assumptions:No one is using an ATM or waiting for a machine at the start of the hour.Service times for each ATM have the same distribution as sampled in Week 1 Service Times in the sheet Data of Queue Data.xls.ATM’s & QueuesProject Assumptions (cont)The time until the first arrival and the times between arrivals of customers have the same distribution.In the standard queuing model, if more than one ATM is open, arriving customers enter the shortest of the existing queues. If two or more queues are the same length, a customer selects a queue at random.ATM’s & QueuesObjectives:Based only on 9 a.m. hour on Fridays, how many ATM’s should be opened and what queuing model should be used to validate each advertising claim during 9-10 a.m. period?Based only on 9 p.m. hour on Fridays, how many ATM’s should be opened and what queuing model should be used to validate each advertising claim during 9-10 p.m. period?NOTE: We only consider the use of a serpentine model when three ATM’s are in useATM’s & QueuesObjectives (cont)Finding the hourly cost of a gift certificate program for 3 ATM’s Serpentine:If a serpentine queue is used, customers don’t physically stand in a line because the bank currently uses a number dispenser and service indicator that gives customers slips of paper indicating their position in the queue.ATM’s & QueuesObjectives (cont)Finding the cost of gift certificate program (cont)Bank is considering updating to a system that stamps the arrival time of a customer which could be used to document a customer’s wait timeThe hourly cost for such an upgrade (maintenance, purchase price, etc.) is $20ATM’s &
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