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Project 2: ATM’s & Queues. ATM’s & Queues. Certain business situations require customers to wait in line for a service Examples: Waiting to use an ATM machine Paying for groceries at the supermarket A line of people or objects is called a “queue”. ATM’s & Queues.

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atm s queues
ATM’s & Queues
  • Certain business situations require customers to wait in line for a service
    • Examples:
      • Waiting to use an ATM machine
      • Paying for groceries at the supermarket
  • A line of people or objects is called a “queue”
atm s queues1
ATM’s & Queues
  • Queues occur in many places:
    • Running multiple programs on a computer
    • A print queue is formed when many documents are sent to the printer
    • Telephone calls on a switchboard
    • Vehicles waiting at a traffic light
atm s queues2
ATM’s & Queues
  • Studying how these lines form and how to manage them is called Queuing Theory
  • Queuing Theory has become an important tool in business decisions regarding quality and expense of customer service
    • Example: Supermarket manager sees checkout lines are too long, so more cashiers are called to work the registers, but this costs more money
atm s queues3
ATM’s & Queues
  • Automated services make queue theory important when direct monitoring of service isn’t possible
    • Example:
      • 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 money
atm s queues4
ATM’s & Queues
  • Managing queues is a balancing act:

$$$$$$$$$$$$$$$$$$

Customer Satisfaction

atm s queues5
ATM’s & Queues
  • Two Queue Models
    • Standard Queue
    • Serpentine Queue
atm s queues6
ATM’s & Queues
  • Standard Queue
  • Customers 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 queues7
ATM’s & Queues
  • Serpentine Model
  • Customers form a single line, and advance to the front to get their service.
  • Used at most airline ticket counters and in many post offices
atm s queues8
ATM’s & Queues
  • Analyzing how to manage queues often uses computer simulation
  • Two types of Simulation
    • Monte Carlo
    • Bootstrapping
atm s queues9
ATM’s & Queues
  • Monte Carlo Simulation
    • Sample 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 queuing
ATM’s & Queuing
  • Bootstrapping
    • When the data does not indicate any known theoretical probability distribution, we can simulate new data by random sampling from the original data
atm s queues10
ATM’s & Queues
  • Class Project
  • The People’s Bank has 3 ATM’s
  • At least one ATM is available 24 hours a day 7 days a week
  • Bank manager has records of ATM usage and customer service times for 5 weeks
atm s queues11
ATM’s & Queues
  • Mean 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 queues12
ATM’s & Queues
  • We will study the queues for the ATM’s during:
    • The 9:00am hour on Friday
    • The 9:00pm hour on Friday
  • The 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 queues13
ATM’s & Queues
  • Bank manager wants to avoid long wait times, long queue lengths, and do this using the least number of ATM’s
  • The bank manager would like to know what level of service to provide for managing the queues based on:
    • Services Times for individual customers
    • The number of customers waiting to be served
atm s queues14
ATM’s & Queues
  • Terms:
    • 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 ATM
    • Delayed: A person who must wait more than 5 minutes
    • Number in Queue: the number of people in line waiting before an arriving customer can reach an ATM
    • Irritated: queue length is more than 3 customers
    • Total Present: the total number of patrons present in the queue
atm s queues15
ATM’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 queues16
ATM’s & Queues
  • The 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 queues17
ATM’s & Queues
  • Project 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 queues18
ATM’s & Queues
  • Project 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 queues19
ATM’s & Queues
  • Objectives:
    • 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 use

atm s queues20
ATM’s & Queues
  • Objectives (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 queues21
ATM’s & Queues
  • Objectives (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 time
      • The hourly cost for such an upgrade (maintenance, purchase price, etc.) is $20
atm s queues22
ATM’s & Queues
  • Objectives
    • Finding the cost of the gift certificate program (cont)
      • A $25 gift to any customer who is delayed (waits more than 5 minutes).
      • What is the expected hourly cost of such a plan? How would this change if it is estimated that only 60% of eligible customers would decide to claim the gift?
atm s queues23
ATM’s & Queues
  • Team Data will be posted on class web page
  • Data includes
    • historical records of ATM service times and customer arrival times for two hours out of each week
    • Parameters for six potential advertising strategies.
      • Mean Wait Claim
      • Maximum Wait Claim
      • Percent Delayed Claim
      • Mean Queue Claim
      • Percent Irritated Claim
      • Maximum Present Claim
atm s queues24
ATM’s & Queues

Team Data will be posted after Spring Break

Team Preliminary Report

  • Date: Monday March 31st, 2008