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.

Slides:



Advertisements
Similar presentations
Chapter 13 Queueing Models
Advertisements

Decision Maths Lesson 14 – Simulation. Wiltshire Simulation There are many times in real life where we need to make mathematical predictions. How long.
IE 429, Parisay, January 2003 Review of Probability and Statistics: Experiment outcome: constant, random variable Random variable: discrete, continuous.
(Monté Carlo) Simulation
Waiting Lines Example Students arrive at the Administrative Services Office at an average of one every 15 minutes, and their request take on average 10.
QUEUING MODELS Based on slides for Hilier, Hiller, and Lieberman, Introduction to Management Science, Irwin McGraw-Hill.
Operations research Quiz.
QMD: Waiting-line analysis
Mathematics for Business Decisions, Part 1.5a Managing ATM Queues.
Classification of Simulation Models
Probability Distributions
What’s in the Focus file and how do we edit it? Project 2, 115a.
Model Antrian By : Render, ect. Outline  Characteristics of a Waiting-Line System.  Arrival characteristics.  Waiting-Line characteristics.  Service.
Queuing Systems Chapter 17.
Chapter 13 Queuing Theory
1 Queuing Theory 2 Queuing theory is the study of waiting in lines or queues. Server Pool of potential customers Rear of queue Front of queue Line (or.
ATM QUEUES Kemal Cilengir Kristina Feye Jared Kredit James Winfield.
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J F-1 Operations Management Simulation Module F.
To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Chapter 16 Waiting Line Models and.
Project 2: ATM’s & Queues
Queuing Theory. Queuing theory is the study of waiting in lines or queues. Server Pool of potential customers Rear of queue Front of queue Line (or queue)
Mathematics for Business Decisions, Part 1.5a Managing ATM Queues.
Chapter 9: Queuing Models
___________________________________________________________________________ Operations Research  Jan Fábry Waiting Line Models.
Monte Carlo Methods A Monte Carlo simulation creates samples from a known distribution For example, if you know that a coin is weighted so that heads will.
Simulation Pertemuan 13 Matakuliah :K0442-Metode Kuantitatif
Spreadsheet Modeling & Decision Analysis
Introduction to Management Science
QueueTraffic and queuing theory +. 2 Queues in everyday life You have certainly been in a queue somewhere. –Where? –How were they different?  We encounter.
Simulation Examples ~ By Hand ~ Using Excel
Waiting Line Models ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry.
1 Chapter 16 Applications of Queuing Theory Prepared by: Ashraf Soliman Abuhamad Supervisor by : Dr. Sana’a Wafa Al-Sayegh University of Palestine Faculty.
Chapter 10. Simulation An Integrated Approach to Improving Quality and Efficiency Daniel B. McLaughlin Julie M. Hays Healthcare Operations Management.
1 Copyright Ken Fletcher 2004 Australian Computer Security Pty Ltd Printed 26-May-16 07:39 Prepared for: Monash University Subj: CSE4884 Network Design.
© 2007 Pearson Education Simulation Supplement B.
Introduction to Operations Research
Structure of a Waiting Line System Queuing theory is the study of waiting lines Four characteristics of a queuing system: –The manner in which customers.
1 QUEUES. 2 Definition A queue is a linear list in which data can only be inserted at one end, called the rear, and deleted from the other end, called.
1 Queuing Models Dr. Mahmoud Alrefaei 2 Introduction Each one of us has spent a great deal of time waiting in lines. One example in the Cafeteria. Other.
1 Systems Analysis Methods Dr. Jerrell T. Stracener, SAE Fellow SMU EMIS 5300/7300 NTU SY-521-N NTU SY-521-N SMU EMIS 5300/7300 Queuing Modeling and Analysis.
Waiting Lines and Queuing Models. Queuing Theory  The study of the behavior of waiting lines Importance to business There is a tradeoff between faster.
Queuing Queues are a part of life and waiting to be served is never really pleasant. The longer people wait the less likely they are to want to come back.
1 Queuing Systems (2). Queueing Models (Henry C. Co)2 Queuing Analysis Cost of service capacity Cost of customers waiting Cost Service capacity Total.
Computer Science 112 Fundamentals of Programming II Modeling and Simulation.
Queues Chapter 6. Chapter 6: Queues Chapter Objectives To learn how to represent a waiting line (queue) and how to use the five methods in the Queue interface:
Data Structures Using Java1 Chapter 7 Queues. Data Structures Using Java2 Chapter Objectives Learn about queues Examine various queue operations Learn.
Advance Waiting Line Theory and Simulation Modeling.
Monte Carlo Methods Focus on the Project: Now that there are two folders (9am and 9pm) that contain a Queue Focus.xls file, we will create two more folders.
Chapter 10 Verification and Validation of Simulation Models
Simulation Using computers to simulate real- world observations.
1 CMPSCI 187 Computer Science 187 Introduction to Introduction to Programming with Data Structures Lecture 13: Queues Announcements.
CSCI1600: Embedded and Real Time Software Lecture 19: Queuing Theory Steven Reiss, Fall 2015.
Copyright 2006 John Wiley & Sons, Inc. Beni Asllani University of Tennessee at Chattanooga Waiting Line Analysis for Service Improvement Operations Management.
Waiting Lines and Queuing Theory Models
Simulation Chapter 16 of Quantitative Methods for Business, by Anderson, Sweeney and Williams Read sections 16.1, 16.2, 16.3, 16.4, and Appendix 16.1.
Advantages of simulation 1. New policies, operating procedures, information flows and son on can be explored without disrupting ongoing operation of the.
Basic Queuing Insights Nico M. van Dijk “Why queuing never vanishes” European Journal of Operational Research 99 (1997)
Queuing Models.
1 BIS 3106: Business Process Management (BPM) Lecture Nine: Quantitative Process Analysis (2) Makerere University School of Computing and Informatics Technology.
Queueing Theory/Waiting Line: Models and Analysis Navneet Vidyarthi
Simulation of single server queuing systems
Abu Bashar Queuing Theory. What is queuing ?? Queues or waiting lines arise when the demand for a service facility exceeds the capacity of that facility,
Topic V. Multiple-Channel Queuing Model
Monte Carlo Methods Focus on the Project: Enter mean time between arrivals for variable A in cell B31 of the sheet 1 ATM for the Excel file Queue Focus.xls.
© 2006 Prentice Hall, Inc.D – 1 Operations Management Module D – Waiting-Line Models © 2006 Prentice Hall, Inc. PowerPoint presentation to accompany Heizer/Render.
2.7: Simulation.
Chapter 9: Queuing Models
Chapter 10 Verification and Validation of Simulation Models
Variability 8/24/04 Paul A. Jensen
Simulation Supplement B.
Presentation transcript:

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  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 & 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 & 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 & Queues  Managing queues is a balancing act: Customer Satisfaction $$$$$$$$$

ATM’s & Queues  Two Queue Models Standard Queue Serpentine Queue

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 & 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 & Queues  Analyzing how to manage queues often uses computer simulation  Two types of Simulation Monte Carlo Bootstrapping

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  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 & 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 & 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 & 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 & 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 & 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 & 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 & 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 & 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 & 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 & 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 & 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 & Queues Team Data will be posted later this week Team Preliminary Report Date: Friday October 31, 2008