Structure of a Waiting Line System

Slides:

Advertisements

Similar presentations

Waiting Line Management

Advertisements

Trend for Precision Soil Testing % Zone or Grid Samples Tested compared to Total Samples.

Trend for Precision Soil Testing % Zone or Grid Samples Tested compared to Total Samples.

AGVISE Laboratories %Zone or Grid Samples – Northwood laboratory

5.1 Rules for Exponents Review of Bases and Exponents Zero Exponents

Quantitative Methods Topic 5 Probability Distributions

Fill in missing numbers or operations

& dding ubtracting ractions.

Part 3 Probabilistic Decision Models

Addition and Subtraction Equations

Multiplication X 1 1 x 1 = 1 2 x 1 = 2 3 x 1 = 3 4 x 1 = 4 5 x 1 = 5 6 x 1 = 6 7 x 1 = 7 8 x 1 = 8 9 x 1 = 9 10 x 1 = x 1 = x 1 = 12 X 2 1.

Division ÷ 1 1 ÷ 1 = 1 2 ÷ 1 = 2 3 ÷ 1 = 3 4 ÷ 1 = 4 5 ÷ 1 = 5 6 ÷ 1 = 6 7 ÷ 1 = 7 8 ÷ 1 = 8 9 ÷ 1 = 9 10 ÷ 1 = ÷ 1 = ÷ 1 = 12 ÷ 2 2 ÷ 2 =

NTDB ® Annual Report 2010 © American College of Surgeons All Rights Reserved Worldwide National Trauma Data Bank 2010 Annual Report.

We need a common denominator to add these fractions.

Reliability McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

The basics for simulations

Introduction Queuing is the study of waiting lines, or queues.

Waiting Line Management

Chapter 5: Service Processes

Look at This PowerPoint for help on you times tables

Discrete Event (time) Simulation Kenneth.

1 Prediction of electrical energy by photovoltaic devices in urban situations By. R.C. Ott July 2011.

Progressive Aerobic Cardiovascular Endurance Run

Comparison of X-ray diffraction patterns of La 2 CuO 4+   from different crystals at room temperature Pia Jensen.

Least Common Multiples and Greatest Common Factors

© 2007 Pearson Education Waiting Lines Supplement C.

2011 WINNISQUAM COMMUNITY SURVEY YOUTH RISK BEHAVIOR GRADES 9-12 STUDENTS=1021.

Before Between After.

Benjamin Banneker Charter Academy of Technology Making AYP Benjamin Banneker Charter Academy of Technology Making AYP.

2011 FRANKLIN COMMUNITY SURVEY YOUTH RISK BEHAVIOR GRADES 9-12 STUDENTS=332.

Introduction to Queuing Theory

Subtraction: Adding UP

Static Equilibrium; Elasticity and Fracture

Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 1 Chapter 15. Simulation.

Resistência dos Materiais, 5ª ed.

Lial/Hungerford/Holcomb/Mullins: Mathematics with Applications 11e Finite Mathematics with Applications 11e Copyright ©2015 Pearson Education, Inc. All.

Select a time to count down from the clock above

Introduction into Simulation Basic Simulation Modeling.

Schutzvermerk nach DIN 34 beachten 05/04/15 Seite 1 Training EPAM and CANopen Basic Solution: Password * * Level 1 Level 2 * Level 3 Password2 IP-Adr.

Simulation A Queuing Simulation. Example The arrival pattern to a bank is not Poisson There are three clerks with different service rates A customer must.

1 1 Slide © 2005 Thomson/South-Western Chapter 13 Simulation n Advantages and Disadvantages of Using Simulation n Modeling n Random Variables and Pseudo-Random.

Simulation with ArenaChapter 2 – Fundamental Simulation Concepts Discrete Event “Hand” Simulation of a GI/GI/1 Queue.

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-1 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Chapter 14.

1 1 Slide © 2008 Thomson South-Western. All Rights Reserved Slides by JOHN LOUCKS St. Edward’s University.

1 1 Slide © 2001 South-Western College Publishing/Thomson Learning Anderson Sweeney Williams Anderson Sweeney Williams Slides Prepared by JOHN LOUCKS QUANTITATIVE.

Queuing Theory (Waiting Line Models)

Planning and Scheduling Service Operations

1 1 Slide © 2004 Thomson/South-Western Slides Prepared by JOHN S. LOUCKS St. Edward’s University Slides Prepared by JOHN S. LOUCKS St. Edward’s University.

1 1 © 2003 Thomson  /South-Western Slide Slides Prepared by JOHN S. LOUCKS St. Edward’s University.

1 1 Slide © 2001 South-Western College Publishing/Thomson Learning Anderson Sweeney Williams Anderson Sweeney Williams Slides Prepared by JOHN LOUCKS QUANTITATIVE.

1 1 Slide Simulation. 2 2 Simulation n Advantages and Disadvantages of Simulation n Simulation Modeling n Random Variables n Simulation Languages n Validation.

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.

Waiting Line and Queuing Theory Kusdhianto Setiawan Gadjah Mada University.

Waiting Lines and Queuing Models. Queuing Theory  The study of the behavior of waiting lines Importance to business There is a tradeoff between faster.

1 1 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole.

1 1 Slide © 2009 South-Western, a part of Cengage Learning Slides by John Loucks St. Edward’s University.

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.

Waiting Line Theory Akhid Yulianto, SE, MSc (log).

1 1 Slide Chapter 12 Waiting Line Models n The Structure of a Waiting Line System n Queuing Systems n Queuing System Input Characteristics n Queuing System.

Simple Queueing Theory: Page 5.1 CPE Systems Modelling & Simulation Techniques Topic 5: Simple Queueing Theory  Queueing Models  Kendall notation.

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,

Queuing Systems Don Sutton.

Discrete Event “Hand” Simulation of a GI/GI/1 Queue

Waiting Line Models Waiting takes place in virtually every productive process or service. Since the time spent by people and things waiting in line is.

Presentation transcript:

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 arrive (bulk, individual, by appointment or randomly) The time required for service The priority for determining order of service The number and configuration of servers in the system

Structure of a Waiting Line System In general, arrival of customers into a system is a random event. Frequently the arrival pattern is modeled as a Poisson process. Service time is also usually a random variable. It is often described by the exponential distribution. The most common queue discipline is FIFO. An elevator however would use LIFO and an emergency room would use a highest cost criterion.

Queuing Systems A three part code A/B/s is used to describe various queuing systems where A describes the arrival distribution assumed B describes the service distribution assumed s is the number of channels (servers) per line

Operating Characteristics of a Queuing System What is the average wait time of the customer in the queue? In the system? What is the average number of customers in the queue? In the system? What percent of time is the service facility idle? What is the average amount of server free time between customers? What is the probability that an arriving customer will have to wait?

Example: Wayne International Airport Whenever an international plane arrives at the airport, two customs inspectors on duty set up operations to process the passengers. Incoming passengers must first have their passports and visas checked. This is handled by one inspector. The time required to check a passenger's passports and visas can be described by the probability distribution on the next slide.

Example: Wayne International Airport Random Number Mapping Time Required to Check a Passenger's Random Passport and Visa Probability Numbers 20 seconds .20 00 -19 40 seconds .40 20 - 59 60 seconds .30 60 - 89 80 seconds .10 90 - 99

Example: Wayne International Airport After having their passports and visas checked, the passengers next proceed to the second customs official who does baggage inspections. Passengers form a single waiting line with the official inspecting baggage on a first come, first served basis.

Example: Wayne International Airport Random Number Mapping Time Required For Random Baggage Inspection Probability Numbers No Time .25 00 - 24 1 minute .60 25 - 84 2 minutes .10 85 - 94 3 minutes .05 95 - 99

Example: Wayne International Airport Next-Event Simulation Records For each passenger the following information must be recorded: When his service begins at the passport control inspection The length of time for this service When his service begins at the baggage inspection

Example: Wayne International Airport A chartered plane from abroad lands at Wayne Airport with 80 passengers. Simulate the processing of the first 10 passengers through customs using the random numbers given on the next slides.

Example: Wayne International Airport Passport Control Baggage Inspections Pass. Time Rand. Service Time Time Rand. Service Time Num . Begin Num. Time End Begin Num. Time End 1 0:00 93 1:20 1:20 1:20 13 0:00 1:20 2 1:20 63 1:00 2:20 2:20 08 0:00 2:20 3 2:20 26 :40 3:00 3:00 60 1:00 4:00 4 3:00 16 :20 3:20 4:00 13 0:00 4:00 5 3:20 21 :40 4:00 4:00 68 1:00 5:00

Example: Wayne International Airport Passport Control Baggage Inspections Pass. Time Rand. Service Time Time Rand. Service Time Num . Begin Num. Time End Begin Num. Time End 6 4:00 26 :40 4:40 5:00 40 1:00 6:00 7 4:40 70 1:00 5:40 6:00 40 1:00 7:00 8 5:40 55 :40 6:20 7:00 27 1:00 8:00 9 6:20 72 1:00 7:20 8:00 23 0:00 8:00 10 7:20 89 1:00 8:20 8:20 64 1:00 9:20

Example: Wayne International Airport Question How long will it take for the first 10 passengers to clear customs? Answer Passenger 10 clears customs after 9 minutes and 20 seconds.

Example: Wayne International Airport Question What is the average length of time a customer waits before having his bags inspected after he clears passport control? How is this estimate biased? Answer For each passenger calculate his waiting time: (Baggage Inspection Begins) - (Passport Control Ends) =0+0+0+40+0+20+20+40+40+0 = 160 seconds. 160/10 = 16 seconds per passenger. This is a biased estimate because we assume that the simulation began with the system empty. Thus, the results tend to underestimate the average waiting time.